Win Probability and Tennis

As a huge baseball statistics nerd, I love Fangraphs.com.  Well, I don't really read many of their articles, nor do I engage in their often contentious comment threads.  Rather, I love the thing that made it famous: win probability graphs.  If you haven't seen one, they look like this.

Hey look, the Royals lost a game they should have won!

The premise is simple.  Given any game situation, you can calculate - based on the number of expected runs scored for both the remainder of the inning and the remainder of the game - how likely each team is to win.  Certain events, like home runs, tend to increase your odds significantly, while others, like strikeouts with the bases loaded and two outs, tend to hurt them.  Of course, context becomes extremely important, and the graph will fluctuate more in closer games like the Royals versus Tigers game above.

Now the cool part is not even the graph itself, but the "Leverage Index" beneath it.  Basically, the amount of change that is possible/likely in any given situation is mapped beneath the graph.  This leads to a clear, quantitative mapping of high and low leverage situations.  This in turn, leads to cool calculations of things like "clutch," which fangraphs calculates by comparing a player's performance in low leverage situations to his performance in high leverage ones (instead of the standard, and unsatisfying "close and late").

All of this is old hat to baseball fans, and my point isn't to recap what you already know or could find on fangraphs.  Rather, I want to put out a call to coders, web developers, and tennis fans to do this for tennis.  I've seen a man named Jeff Sackmann produce a "Tennis Win Expectancy Graph" for a particular match, but as far as I know, there is no widely available tool to let tennis fans calculate win probability on their own, much less a live scoreboard like on fangraphs.

If anything, win probability for tennis should be simpler than for baseball.  Rather than having to calculate run expectancies, your set of variables are much, much smaller.  If you use the tour wide statistic, as Sackmann does, that the server will win 64% of points, you can, theoretically, easily produce a win probability algorithm.  Turning that into a graph is obviously not too difficult, given Sackmann's own work.

So let's make it happen! Tennis needs would benefit from win probability graphs as much as baseball.  Questions that win probability (and leverage index) could help answer include:
1) Do great players "raise their level" on key points, or are they just always better?
2) How much of a difference in point-by-point leverage is there between a three and five set match?
3) What is the "most important" point in a given match?
There are countless others, so I won't list them all.  But even these should whet the appetite of the statistically-minded tennis fan.

Now you're probably thinking: "great, so do it yourself."  If only I could.  I have spent most of the day watching the U.S. Open and playing around with Excel.  But while the mathematics are not beyond me (though they are harrier than you might think), the coding is.  Perhaps someone else wants to take the baton?  If so, I'd be a happy contributor, cheerleader, partner in the process, to whatever degree I can.

Hey, fangraphs isn't just graphs, it's also writers.  If someone starts "tennisgraphs," I'll be happy to write for it.

Fuzzy Fundraising Math

This New York Times article is a wonderful example of the old adage about lies, damn lies, and statistics.  Apparently relying upon widespread lack of understanding of mathematics and an inability or unwillingness to think critically about information, Jim Messina - President Obama's campaign manager - presents some shady numbers, and then points to them as evidence of “more grassroots support at this point in the process than any campaign in political history.”  He's not lying, just statistic-ing.

 The numbers are as follows:
- $86 million raised for the DNC and Obama's reelection campaign in the second quarter.
- 552,462 separate donors.
- Average contribution of $69.
- 98% of contributions under $250.

Well let's break out our calculators, shall we?  552,462 donors times an average donation of $69 equals... $38.1 million.  But wait, Obama has raised $86 million!  Huh?  Where did the other $47.9 million come from?

Reading more closely tells you that the average contribution may be $69, but there's no indication as to how many donors have written multiple smaller checks, instead of one big one.  In order for the math to work out, that $86 million required about 1.25 million separate donations, even if there were 552.462 separate donors.  The actual average contribution per donor, meanwhile, is over $150.

That's starting to sound a little less "grassroots," no?  Don't get me wrong, the sheer number of contributors here is impressive, and a great many of those - maybe as many as 98% - are average Joes and Johns contributing $20.  But that's not where the bulk of Obama's funding comes from.

Unfortunately, given the numbers we have to work with here, we can't draw any certain conclusions about the percentage or amount of Obama's current campaign money that comes from corporate sources.  For that matter, the Citizen's United vs. FEC ruling makes it nigh impossible to track that corporate money anyway.  What we can do, however, is hypothesize.  Let's assume that those 98% of donors giving $250 or less per donation are only donating once.  After all, we're still over a year from the election, and I'm guessing Mr. Middle Class Obama Supporter isn't cutting multiple $50 checks to reelect the President right now.

If we assume that 98% of donors, then, are contributing an average of $69 overall (instead of per donation), we get the following:

- 98% of 552,462 donors is 541,412.  An undeniably impressive number of grassroots donors, but far from the full story.
- Those donors have provided, following this hypothesis, about $37.4 million.
- That means the remaining 11,050 donors have contributed, across multiple donations each, $48.6 million.
- The average, then, amount of money donated by each of those 11,050 donors is roughly $4,400 dollars.

Remember that we're still well over a year away from the election.  That's a lot of money from a small number of people for just one fiscal quarter's worth of fundraising.  It's not unreasonable to assume that a small subset of those 10,000 donors - whether they be individuals, oil companies, financial firms, or health insurance providers - will be contributing as much as $50,000 each by the end of the election cycle.  Perhaps the President should be careful whilst pushing for closing loopholes and levying higher taxes on the wealthiest wage earners, lest they lose the ability to contribute so much to his campaign.

For all of the talk about "grassroots" and "yes we can," it's worth remembering that those grassroots contributions, no matter how you slice it, are not the bulk of Obama's campaign money.  And when executive push comes to legislative shove, the golden rule wins out: he who has the gold, makes the rules.

Defining a Season: 2007-2010

Part the last of a Rockies mini-series of posts.
Part three is here.  Part two is here.  Part one is here.  The introduction is here.

2007 Colorado Rockies: 90-73, 2nd place, 0.5 GB, Wild Card, Lost World Series

The Rockies 2007 season is best remembered for the absurd late-season run of 14 wins in 15 games to close the regular season.  By sweeping the first two rounds of the playoffs, the Rockies ultimately won 21 of 22 before being swept by the Boston Red Sox in the World Series.  Because of that flukey run, however, it's easy to forget that this Rockies team was actually solid top-to-bottom all season.  Indeed, the Rockies underperformed for much of the year, and that they needed such a winning streak just to make the playoffs was not indicative of their quality season-long.  There truly was no weakness on the 2007 Rockies roster: the rotation, bullpen, and lineup were all solid, if not spectacular.  Nevertheless, the transition from under-performance to playoff darling was fueled by two out-of-nowhere players.

Defining Players: SPs - Ubaldo Jimenez and Franklin Morales

These two pitchers' careers went in opposite directions after the miraculous 2007 runs, but that only masks how fundamentally similar their mutual arrival on the scene was during the Rockies World Series season.  If anything, Morales was the better of the two in 2007, starting 8 games and putting up a 3.43 ERA (compared to Ubaldo's 15 starts with a 4.28 ERA).  Regardless, both players were a surprise to people outside of the Rockies organization, young guns who came from nowhere to lead - or at least serve as 2/5ths of a dominant rotation - the Rockies into the playoffs.  In a sense, their careers since 2007 are also perfectly indicative of the Rockies: Morales's failure to harness his awesome stuff speaks to the 2008 and 2010 additions of the team, while Ubaldo's better command and work-horse mentality indicative of the 2009 campaign.

2008 Colorado Rockies: 74-88, 3rd place, 10.0 GB

The 2008 season was extremely disappointing for the Rockies, both because they had just made the World Series the year before, and because the NL West was as weak as it had ever been (the Dodgers won it with a 84-78 record).  It's hard to say exactly what went wrong in '08.  A number of offensive players took small steps backwards and the rotation was just a touch worse.  Above all, the late run that saved '07 from the same fate failed to materialize, with the team all but collapsing down the stretch.

Defining Player: SS - Troy Tulowitzki

After nearly winning both the Rookie of the Year award and the Gold Glove (but losing out on both) in his 2007 campaign, Tulo suffered as bad a sophomore slump as a great player can.  His batting average fell from .291 to .263, his OBP from .359 to .332, and his SLG from .479 to .401.  In all, his value to the team was so much less in '07 that a not-insignificant portion of the Rockies failings can be pinned on him.  Add to that an injury that cost Tulowitzki much of the '08 season, and it's not hard to see how 90 wins became 74 for a team that was never quite great in the first place.

2009 Colorado Rockies: 92-70, 2nd place, 3.0 GB, Wild Card

The '09 Rockies were eerily similar to the '07 version.  After a slow start, a solid rotation and reasonably deep lineup woke up under new manager Jim Tracey - after Clint Hurdle, who had been at the helm since 2002, was fired - and eventually rode a late-season charge into the playoffs.  The trade of Matt Holliday the previous off-season proved a stroke of genius, netting both the young and improving Carlos Gonzalez and excellent closer Huston Street in exchange for a player who was destined to leave Colorado after '09 anyway.  While Gonzalez would share time in the outfield with Brad Hawpe, Seth Smith, Dexter Fowler, and Ryan Spilborghs, Street was the anchor of another excellent Rockies bullpen.  Beyond the solid performance from the pitching staff and the Holliday-less outfield, bounce-back seasons from two key Rockies both lead the way, and were symbolic of the season as a whole.

Defining Players: SS - Troy Tulowitzki and 1B - Todd Helton

Both Tulowitzki and Helton has miserably disappointing seasons in 2008, but both bounced back to produce well-above league-average campaigns in '09.  While the rest of the lineup and pitching staff improved incrementally from their under-performances in 2008, it was Tulo and Helton's giant leaps forward that propelled the team back into the playoffs.  Helton's .325/.416/.489 slash line harkened back to the good old days of his early career, while Tulo's .297/.377/.552 showed that Tulo might end up being more than just a great fielder with a decent bat.  Indeed, Tulo eclipsed 30 homers for the first time in 2009, becoming not just the leader on the field for the Rockies (a role he shared, by default, with the veteran Helton), but securely becoming the leader in the lineup as well.

2010 Colorado Rockies: 83-79, 3rd place, 9.0 GB

It's easy to forget how much better a season 2010 was than 2008 for the Rockies, because the narrative that has been constructed is that they were parallels.  The narrative goes like this: coming off of an improbable last season charge to make the playoffs, the Rockies followed it up in the next season by promptly collapsing and failing to compete.  But the '10 Rockies did compete, only falling apart late in the season, echoing 2007 in the reverse by losing 13 of their last 14.  Before that collapse, the team had been a very respectable (and competitive) 82-66, well within reach of the 91 wins that would have won them the wild card.  The problem was, beyond the continued excellence of Tulowitzki and the emergence of Carlos Gonzalez, the offense lacked a single other player who put up a 100 or better OPS+.  The offense wasn't bad, per se, but it just wasn't good enough, even with an excellent pitching staff and a near Cy Young season from Ubaldo Jimenez.

Defining Player: C - Miguel Olivo

Like the team he played for, Olivo actually started well in 2010, making a strong case for an all-star berth.  Like the team he played for, however, Olivo ended up not having enough offense.  By the end of the season his OBP - his longtime nemesis - rested at .315.  That was a career high for Olivo, but not good enough for an every-day Major League player, even a catcher.  His 27 walks were also a career high, but it bears remembering that he drew the vast majority of those in the first half of the season.  Perhaps the most damning moment for Olivo in 2011, however, has nothing to do with him, but with the front office.  After extending Chris Iannetta in the offseason, Olivo's hot April, combined with some early-season struggles from Iannetta, resulted in 'netta's demotion to AAA and Olvio's promotion to full-time starter.  That itself was not the cause of the Rockies shortcomings in 2010, but it certainly did not help.

Conclusion

Trying to determine a defining player for a single season is, ultimately, an exercise in futility.  But it doesn't look like it.

The reason it doesn't look like it is simple enough: we love to construct narratives.  It's how we understand what goes on around us, how we make sense of a complex and often confusing world.  It's a lot easier to remember, in short, a season as a failure or a success, a disappointment or a surprise, than to remember the exact won-loss record, the number of games back, the statistics of each and every player.

In trying to find a player whose individual narrative either matched up with or underscored the narrative for the entire Rockies team, I did exactly that: I looked through the won-loss record, the number of games back, and the statistics of each and every player.  But then I turned it into a narrative, and that's where the futility comes in.  Ultimately, how can I do justice to Miguel Olivo's 2010, or Todd Helton's 2006, or Andres Galarraga's 1994?  Sometimes I listed statistics, but only to illustrate a point: the players I selected were, in some sense, a microcosm of a team's successes and failures.  But in other ways they were no such thing: they were merely grown men playing a game for a lot of money, men who undoubtedly care about winning, but whose narratives are far less intense than those of a fan.

In the end, though, it's impossible to escape narratives, and undesirable to boot.  Ironically, even the most sabermetrically-minded baseball fan is doing little more than building narratives.  Are his narratives more quantitative?  Sure.  Are they more objective?  Probably.  But they are narratives just the same, built of words and sounds and ideas and stories, even if those stories are contained in season-long numbers and fancy statistical acronyms instead of anecdotes and clutch homers.

Of course, I've been more stat-head than story-head in this series, but that's exactly the point.  The stats tell a story, too, and an interesting one.  Silly though it may be to pin a whole season - for better or worse - on a single player, doing so might just give us a certain insight, or help us better enjoy a sport we already love.

Defining a Season: 2002-2006

Part three of a series of Rockies-centric posts.
Introduction here.
Part one here.
Part two here.
Part four here. 

2002 Colorado Rockies: 73-89, 4th place, 25.0 GB

It was during 2002 that a new era of Rockies baseball began with the hiring of Clint Hurdle as manager.  Following a slow start, the Rockies let go of Buddy Bell and replaced him with the former hitting coach, a move that I would not go so far as to say defined the Rockies for the next five seasons, but definitely set a certain tone.  Clint Hurdle's hiring was an indication that the team was changing, trying to get younger and trying to build from within.  While witnessed the disastrous collapses of Neagle and Hampton, Rockies fans in 2002 also watched the first wave of young up-and-comers from the Rockies growing minor league system in Jason Jennings, Juan Uribe, and Juan Pierre.

Defining Player: CF - Juan Pierre

Pierre was an exciting young player in 2002, but despite his impressive speed, he wasn't a particularly good player.  He didn't get on base enough, was not quite a good enough fielder, and was completely without power.  His slash line (.287/.332/.343) left much to be desired, especially playing at Coors Field, and despite his youth it was hard to see him as a centerpiece on a future contender.  Nevertheless, on a team now stuck with aging, mediocre, and largely overpaid players around the diamond, Pierre was a symbol of a different approach, a glimpse of a future of home grown talent.  Beyond being a symbol for a future approach, however, Pierre was also an important part of the post-2002 trade that sent Mike Hampton to the Florida Marlins, meaning he also played a key, if ironic, role in the transition to the home-grown approach.

2003 Colorado Rockies: 74-88, 4th place, 26.5 GB

There was little compelling about baseball in Colorado during the dark-ages of the mid-2000s.  Todd Helton and Larry Walker would quietly put up All-Star numbers year after year, but no one else was particularly compelling.  Sure, the offense hit plenty of homers (the 2003 team had 7 players with 10 or more HR), and the bullpen was usually solid, and the rotation usually at least a little better than it looked, but there were simply too few players good enough to push the team to .500, let alone to contention.

Defining Player: 3B - Chris Stynes

Unless you're a die-hard Rockies fan, you probably have never heard of Stynes.  Even if you're a die-hard, you probably had forgotten about him.  But he was the Rockies starting third baseman for the whole of the 2003 season, punching up a miserable slash line of .255/.335/.413.  Of all the players from the dark ages of Rockies baseball, Stynes is the most mediocre, the most forgettable.  If someone were to ask: why couldn't this team manage to win more than 74 games, you could do worse than answering "Chris Stynes," not because of who he was, but because of what he represented for an organization treading water.

2004 Colorado Rockies: 68-94, 4th place, 25.0 GB

After the 2002 and 2003 seasons, things got worse before they got better.  The 94 losses the Rockies suffered in 2004 was the worst in franchise history since the inaugural season in 1993.  Nevertheless, at the bottom of the proverbial barrel (so far, anyway), there was a scrap of hope.  The new organizational focus on building from within didn't quite start to payoff in 2004, but it did bear its first fruit.

Defining Player: LF - Matt Holliday

Perhaps its not fair to say that Matt Holliday was the defining player of one of the worst seasons in Rockies history, but I still think he fits precisely because it was him - and his generation of minor league teammates - that the organization had changed its philosophy.  As the Rockies floundered throughout the 2004 season, Holliday put up a solid .290/.349/.488 line.  Excellent?  Hardly, but at only 24 Holliday showed promise that none of the other young players the Rockies had developed ever had (since Helton, that is).  Here was a power hitter, an anchor for the lineup to replace the now departed Larry Walker.  Here was, in short, the future.

2005 Colorado Rockies: 67-95, 5th place, 15.0 GB

Things began to come together for the Rockies in 2005.  That's strange to say, given that they finished in last place in the worst division in baseball (as the mere 15 games back indicates, the Padres won the division with an 82-80 record).  However, this was the rookie season for Clint Barmes, Garrett Atkins, and Brad Hawpe.  While none of those players would ever approach Holliday in talent or production, they would all become important pieces to the 2007 World Series team.  And, more importantly, each of them was drafted and developed by the Rockies.  There were growing pains, to be sure, as the 67-95 record indicates, but the future was looking bright.

Defining Player: SP - Jeff Francis

The future was bright not because of the offensive players listed above, important though they would be in 2007.  No, the most important rookie in the '05 season was Francis, the first of so many first-round pitchers the Rockies had drafted to actually make it to the big leagues.  Francis, like the Rockies, was far from impressive in 2005.  His 5.68 ERA was well-deserved, given a SO/BB rate under 2, a fairly high 1.3 HR/9 rate, and a pitch-to-contact approach that is always dangerous in Colorado.  Nevertheless, there were glimpses from Francis (and his young rotation-mate, back from a near-fatal blood clot suffered in 2004, Aaron Cook) that he could tame the Coors Field beast, along with the help of the now operating humdior.

2006 Colorado Rockies: 76-86, tied for 4th place, 12.0 GB

In a still-weak division, the Rockies in 2006 were a team on the brink.  That's easy to say after-the-fact, but the signs were there even at the time.  The core of Helton, Atkins, Holliday, and Hawpe provided enough offense that little else was needed to fill out a contender's lineup.  Meanwhile the top of the rotation, featuring Cook, Francis, and Jason Jennings, was well above-average.  The bullpen remained solid as well, though mostly a collection of cast-offs from other teams (a trend for the Rockies front office).  Though the team finished 10 games under .500, they were really just another year of development from their young players, plus the arrival of a certain shortstop and certain pitcher, away from ending nearly a decade of futility.

Defining Player: 1B - Todd Helton

Though the team as a whole was young, unproven, but about to explode, the 2006 team's shortcomings were defined best by the Helton.  This season looked like the beginning of the end for Todd, the first season in which he would fail to hit 20 home runs, and easily his worst season by batting average, OBP, and slugging percentage in his career.  However, his place here is not merely because he underperformed his talent as the team struggled to a 76-86 season, but because the beginning of his decline underscored the urgency of the next few seasons, and because Helton would, like the rest of the team, have an excellent season in 2007.  On a team of young up-and-comers, a team transitioning from age to youth, from hitting to pitching, Helton was not merely harkening back to old days, but also a reminder that he too was once a young star, an up-and-comer, and that chances to win are sometimes few and far between.  Not for his shortcomings, but because he was for so long the only shining light on a miserable team, does Helton deserve to be remembered as an iconic player not just for the 2006 Rockies, but throughout the early 2000s.

Defining a Season: 1998-2001

Part two of a series of Rockies-centric posts.
Introduction here.
Part one here.
Part three here. 
Part four here. 

1998 Colorado Rockies: 77-85, 4th place, 21.0 GB

If the '96 and '97 seasons were the beginning of the decline of the Blake Street Bombers, the '98 season was the end.  Ellis Burks was traded for a just-as-old, but not-nearly-as-good Darryl Hamilton, Vinny Castilla turned 31, and Dante Bichette's power contined to fade.  Even the outstanding rookie campaign of Todd Helton couldn't lift what proved to be a fatally flawed roster in what ended up being manager Don Baylor's final season.  The '98 season was disappointing, perhaps, because expectations were still high after three straight seasons in which the Rockies were at least good, if not great.  But it was impossible to ignore that a team already in decline had taken a fateful step towards sub-.500 baseball.

Defining Player: SP - John Thomson

I know what you're thinking.  Who is John Thomson?  In 1998, Thomson was the Rockies best pitcher, the only member of the rotation with an ERA under 5.00 (his was 4.81).  While Coors Field didn't do any favors to Darryl Kile and Pedro Astacio, they didn't do any favors to themselves, either.  Despite the still potent - if decreasingly so - lineup, the Rockies rotation in 1998 was inadequate, and Colorado found itself on the losing end of a few too many blowouts.  That the bullpen was, once again, excellent was some consolation, but hardly enough for a team who's best pitcher was, in the end, John Thomson.

1999 Colorado Rockies: 72-90, 5th place, 28.0 GB

As if it wasn't bad enough that the Rockies finished in last place for the first time in 1999, the second-year Arizona Diamondbacks broke their record for fastest expansion team to make the postseason, winning 100 games and the division in only their second season.  Meanwhile the Rockies were a mess.  The once vaunted bullpen began to crack, the remaining Bombers - except for Helton and Larry Walker (who spent a significant part of the season on the disabled list) - lost their clout, and the rotation was, if not terrible, at best mediocre.  Coors Field, meanwhile, continued to inflate offensive numbers to an absurd degree, which excused the horrid offense and deflected blame to a not-as-bad-as-it-looks pitching staff.

Defining Player: SS - Neifi Perez

In many ways, Neifi is the defining player for a whole era of Rockies baseball.  He manned shortstop almost every game between 1998 and his trade in 2001, and at no time was he even a remotely passable offensive player.  In 1999 he had one of his worst seasons, hitting a good-on-the-surface .280, but with only a .307 OBP and .403 slugging percentage.  Neifi's 12 home runs in 1999 would end up being a career high, but even so, his OPS+ was 62.  For that reason, he is the defining player of the 1999 season because he looked like an acceptable player, but wasn't.  He was a sinkhole, an out waiting to happen, an incapable hitter even at Coors Field (where his OBP was a measly .326) whose road numbers were simply awful (.251/.287/.356).  Neifi's empty batting average, his mirage power, and the perception that he was actually good typify the Rockies organization during a season in which the team lost 90 games despite looking like they weren't that bad.

2000 Colorado Rockies: 82-80, 4th place, 15.0 GB

Despite a strong NL West and an offseason during which the team made few significant changes, the Rockies bounced back from their 1999 season with a surprising above-.500 campaign in 2000, giving hope for a post-Bombers future.  This was a fateful season, however, because the rotation was better than mediocre, and the offense worse, and yet the offseason that followed would see the acquisition of Denny Neagle and Mike Hampton.  In reality, the offense needed far more help than the rotation did, but Coors Field made it seem the other way.

Defining Player: SP - Pedro Astacio

Pedro Astacio had a 5.27 ERA in 2000, and his was the second lowest in the Rockies rotation.  His 12-9 record was nice enough, but he surrendered 32 home runs, and gave up almost 10 hits per 9 innings.  What gets lost in those sub-par numbers, however, is his 193 strikeouts against only 77 walks, and the adjusted ERA+ of 110, meaning Pedro was actually 10% better than league average.  Throughout his career with the Rockies, Astacio was a victim of misperception: he always seemed a worse pitcher than he was.  Sabermetrics hadn't yet taken hold in the baseball world at large, and so the Rockies saw what was actually a strength as a weakness.

2001 Colorado Rockies:  73-89, 5th place, 19.0 GB

In many ways, this was the worst season in Rockies history.  After a lot of preseason hype - including some bold proclamations that the Rockies were the team to beat in the NL - and a hot start, the Rockies fell apart.  The chief reason was an offense that sported only two better-than-league-average hitters, Larry Walker and Todd Helton.  Moreover, the expensive contracts for Hampton and Neagle did not pay dividens, as John Thomson lead the pitching staff in ERA and ERA+, and Pedro Astacio was, in many ways, better than both free agents.

Defining Player: SP - Mike Hampton

 Could there be a more perfect symbol for a team with high expectations that didn't work out?  Could there be a better symbol for a team that looked like it could hit, that pitched better than it seemed to do, but was not quite good enough at either?  Hampton was all of those things, with a price tag of over $100 million.  What doomed Hampton, more than anything, is that he couldn't strike anyone out (5.4 SO/9).  At Coors Field, in a part where batted balls turn into hits more than almost anywhere else in baseball, this was a cardinal sin.  That said, Hampton wasn't horrible.  His ERA+ in 2001 was 99, placing him firmly as league average.  But for a supposed ace, the highest paid pitcher in history (at the time), that wasn't good enough.

Defining a Season: 1993-1997

Part one of a series of Rockies-centric posts.  See the introduction here, part two here, part three here, and part four here.

1993 Colorado Rockies: 67-95, 6th place, 37 Games Back (GB)

The Rockies inaugural season was impressive despite the abysmal .414 winning percentage.  Colorado led the league in attendance with almost 4.5 million fans, thanks to Mile High Stadium, and boasted their first batting champion in Andres Galarraga.  In all, the 1993 was a season of unbridled optimism, an unspectacular but promising first step in a career.

Defining Player: SP - David Neid

Neid was the Rockies first pick in the inaugural draft, a former Braves prospect and a promising young talent.  Though injuries would stop him from ever becoming the pitcher he had the potential to be, in 1993 Neid showed glimpses of his quality, including a complete game 5-3 win against the Mets in April.  Indeed, Neid - the Rockies' opening day starter and presumptive ace - started the season 3-1 with a 3.10 ERA.  Beyond all that, though, Neid was a symbol of all things new in Colorado: a rookie pitcher on a rookie team, an early promise that the Rockies would have an anchor in their rotation for years to come, and an early fan favorite.  That things didn't work out that way only further reinforces his place as the defining player of the '93 season, for reasons that will become clear.

1994 Colorado Rockies: 53-64, 3rd place, 6.5 GB at time of strike

The strike season was disappointing for fans across baseball, but it was especially hard on the Rockies* because of their rabid new fanbase.  By the time the season was called off, the Rockies attendance had already surpassed 3 million, and while their 53-64 record was far from great, it was a vast improvement over the '93 campaign.  The mere possibility of losing the 1995 season was frustrating to fans who had approved a new ballpark to be opened that year.  After the expectation and excitement of 1993, 1994 should have been another step forward - and it was, to a point - but it turned out a kind of limbo.

* It was hardest on the Montreal Expos, who comfortably lead their division by 6 games - at 74-40 - when the rest of the season was called.  After the strike fan interest waned and, before long, the team was moved to Washington, D.C.

Defining Player: 1B - Andres Galarraga

The Big Cat gets the nod here because he was good in 1994, but not nearly as good as he was in '93.  He followed up his league-leading .370 batting average with a .319 effort, and while he crushed a crowd-pleasing 31 homers in only 103 games, he also struck out 93 times, and the lack of adequate support in the lineup left him with only 85 RBI to go with his power.  What's more, the strike put him in limbo as much as anyone.  The promise of stardom - after a solid, but far-from-special career before the Rockies - had started to shine on Andres, but the strike robbed him of a full year of productive baseball at a time when he could least afford it.  Like Neid in '93, he was destined never to be at the heart of the Rockies again after 1994, as Larry Walker and then Todd Helton would steal the spotlight.

1995 Colorado Rockies: 77-67, 2nd place, 1.0 GB, Wild Card

Never before had a team made the MLB playoffs as early as the third year of their existence, but thanks to the shortened season, the addition of the wild card, and some shrewd moves by the front office and career years by the players, the Rockies managed to play their way into the postseason in 1995.  They were promptly crushed by their nemesis, the Atlanta Braves (who had, incidentally, beaten them in every matchup they had in 1993).  Even so, the Rockies were historically good for a 3rd year team, and their new ballpark and hitter's heaven named Coors Field was packed every night.

Defining Player: RP - Curtis Leskanic

The '95 Rockies performed better than expected thanks largely to their bullpen, and that bullpen was great thanks largely to Leskanic.  He worked in over half of the teams games, leading the league with 76.  He struck out 107 in 98 innings.  Despite Coors Field, he boasted a 3.40 ERA, and surrendered only 7 home runs all season.  Above all, though, Leskanic represents the '95 Rockies because, while he had always had decent stuff, this was by far the best season of his career, and it was totally unexpected.  He was still relatively young, like the team he pitched for, and he came out of nowhere to outperform all expectations quietly, but consistently.

1996 Colorado Rockies: 83-79, 3rd place, 8.0 GB

The '96 Rockies were the victims of an excellent division.  Both the San Diego Padres and the Los Angeles Dodgers won at least 90 games, leaving a solid Rockies team in the dust.  Despite a solid record and another season of leading the league in attendance, 1994 was a disappointment coming off of the playoff berth in 1995.  Despite being in only their 4th season, this Rockies team is the second oldest (by average age of the players) in Rockies history, behind only the 2004 edition.  Though young in a grander sense, this was a team with a rapidly closing window.

Defining Player: SP - Kevin Ritz

Not only was his own window rapidly closing, Kevin Ritz was the perfect mix of good and bad in 1996, capturing the essence of the team's season.  His 17-11 record was good, but his 5.28 ERA (and 99 ERA+,  meaning that even adjusted for Coors Field he was merely league average) is none-too-pretty.  He was a horse, starting 35 games and working 213 innings, but he walked exactly as many hitters as he struck out (105).  At 31 years old, this was a strange season for Ritz: good, but not as good as his 1995.  Nevertheless, he was rewarded with a raise from $740,000 to $2.5 million going into 1997, expectations high after his moderately successful '95 and '96 seasons, but set up for disappointment.

1997 Colorado Rockies: 83-79, 3rd place, 7.0 GB

Expectations were high coming into 1997, and in many ways this was the Rockies most disappointing season.  They were contenders for most of the season, and were once again done in by a solid division and a lack of depth in both the rotation and the lineup.  The Blake Street Bombers were in their heyday, but four of the team's regular starters had an OPS+ under 100 (league average).  Similarly, the Rockies used six different starting pitchers regularly in '97, but only two managed to be above league average.  Even another excellent campaign from the bullpen wasn't quite enough.

Defining Player:  LF - Dante Bichette

No player was not-quite-enough enough than Dante Bichette.  As Larry Walker bashed his way to a deserved MVP award in 1997, putting up incredible numbers (Coors aided or not), Bichette was the poster-child for the overrated Blake Street Bomber.  He hit 26 homers, with a .308 average and .343 OBP, but those numbers are less impressive thanks to Coors, and his defense was bad enough that he actually was worth exactly 0.0 Wins Above Replacement for the season.  Dante was coming off of a number of good - or at least better - seasons, but like the Rockies he was getting too old too fast, and it was too hard to admit that this iconic figure for a young organization wasn't good enough to play for a contender.

A New Mini-Project: Constructing Narratives with the Colorado Rockies

I want to try an experiment.  For a while I've had this idea of going through the Rockies history and picking the player from each season that most exemplified the team that year.  I don't mean the best player, or the most famous, or the most highly paid, or anything like that.  I mean the player who's individual narrative most mirrors that of the team as a whole.

There are a few ways to do this, I think, but the method I'm going to use is this: I'm going to write a sentence (or maybe a haiku?) to describe each season, and then I'm going to look through the roster from that season and see which players best reflect the sentence I've written for the team.  While the result, hopefully, will be an interesting - to a Rockies fan anyway - trip down memory lane, I also expect to do some meta-analysis, to ask questions like the broad "How do we construct narratives?" and the more specific "What is the relationship between statistics - like W-L record or home runs - and the words that make up our stories?"

To save both you and me from an incredibly long post, I'm going to break this up and post a bit of it each day or two.  After that, and barring any significant event that demands a Nicht Diesian commentary, I promise I'll get the next Beethoven post up soon.

Part one, covering 1993-1997, is here.
Part two, convering 1998-2001, is here.
Part three, covering 2002-2006, is here.
Part four, covering 2007-2010, is here.

10 Playoff Teams? No Thank You

Bud Selig has made it abundantly clear that, starting in 2012, Major League Baseball will expand its playoff structure to include ten teams.  At present, the MLB playoffs feature eight teams, four from each league.  Each division champion, along with a single wild card - the owner of the best non-division champion record in the league - advance to the playoffs.  In the first round, the best division champ plays the wild card while the other two division champs square off in best of five game series.  The second round features the winners of those series in a best of seven, and then the World Series, also best of seven, pits the champions of each league against each other.

I describe the system in detail because it's a good one.  It works.  The playoffs are compelling and entertaining, and, given how short they are relative to the season, completely non-indicative of who has the best team.  Adding another team to each league's playoff pool will do nothing to change that and, indeed, will only exacerbate the problem.

Of course, this move is all about money.  Bud is certain that more playoff games equals more cash for himself, his owners, and the league in general.  So the whole thing is a no-brainer, even though most baseball fans seem to despise the idea.  What few apologists there are, however, like to point out that deserving teams are often left out of the playoffs as they are currently constructed.  For example, in the National League in 2008, the Los Angeles Dodgers made the playoffs with a 84-78 record, while the Houston Astros (86-75), the St. Louis Cardinals (86-76), and the New York Mets (89-73) were all better.  Of course, Bud's solution to this problem isn't actually a solution, because Los Angeles won their division that season, and would have made the playoffs regardless.

Here's how the new system will work.  Before the best of five first round, the now two wild cards will play each other in a best of three (read, complete toss-up) series.  This punishes the wild card team for not winning its division, of course, but also rewards a team that previously wouldn't have made the playoffs with a non-trivial chance of winning the World Series.  In 2008, for example, the Dodgers still make the playoffs, but wild card Milwaukee would have to play New York in a first round three-gamer while all of the other teams sat and watched.

Rather than levying philosophical objections against this new system, I want to show what it would actually do.  So let's look at the MLB since the wild card first entered the league in 1995, and see how things would be different in this new system.  I'm not going to list division winners, just what that first round matchup would have been.  Listed first is the actual wild card from the season in question, with the new entry second.  I've also bolded the particularly egregious situations where the second wild card is more than five games behind the actual wild card, and thus, in my opinion, is a farce.

1995
American League - New York Yankees (79-65) vs. California Angels (78-67) 
National League - Colorado Rockies (77-67) vs. Houston Astros (76-68)

1996
AL - Baltimore Orioles (88-74) vs. Seattle Marines (85-76)
NL - Los Angeles Dodgers (90-72) vs. Montreal Expos (88-74)

1997
AL - New York Yankees (96-66) vs. Anaheim Angels (84-78)
NL - Florida Marlins (92-70) vs. New York Mets or Los Angeles Dodgers (88-74)

1998
AL - Boston Red Sox (92-70) vs. Toronto Blue Jays (88-74)
NL - Chicago Cubs (89-73) vs. San Francisco Giants (89-73)

1999
AL -  Boston Red Sox (94-68) vs. Oakland Athletics (87-75)
NL -  New York Mets (97-66) vs. Cincinnati Reds (96-67)

2000
AL - Seattle Mariners (91-71) vs. Cleveland Indians (90-72)
NL - New York Mets (94-68) vs. Los Angeles Dodgers (86-76)

2001
AL - Oakland Athletics (102-60) vs. Minnesota Twins (85-77) 
NL - St. Louis Cardinals (93-69) vs. San Francisco Giants (90-72)

2002
AL - Anaheim Angels (99-63) vs. Seattle Mariners or Boston Red Sox (93-69)
NL - San Francisco Giants (95-66) vs. Los Angeles Dodgers (92-70)

2003
AL - Boston Red Sox (95-67) vs. Seattle Mariners (93-69)
NL - Florida Marlins (91-71) vs. Houston Astros (87-75)

2004
AL - Boston Red Sox (98-64) vs. Oakland Athletics (91-71)
NL - Houston Astros (92-70) vs. San Francisco Giants (91-71)

2005
AL - Boston Red Sox (95-67) vs. Cleveland Indians (93-69)
NL - Houston Astros (89-73) vs. Philadelphia Phillies (88-74)

2006
AL - Detroit Tigers (95-67) vs. Chicago White Sox (90-72)
NL - Los Angeles Dodgers (88-74) vs. Philadelphia Phillies (85-77)

2007
AL - New York Yankees (94-68) vs. Detroit Tigers or Seattle Mariners (88-74)
NL - Colorado Rockies (89-73) vs. San Diego Padres (89-73)

2008
AL - Boston Red Sox (95-67) vs. New York Yankees (89-73)
NL - Milwaukee Brewers (90-72) vs. New York Mets (89-73)

2009
AL - Boston Red Sox (95-67) vs. Texas Rangers (87-75)
NL - Colorado Rockies (92-70) vs. San Francisco Giants (88-74)

2010
AL - New York Yankees (95-67) vs. Boston Red Sox (89-73)
NL - Atlanta Braves (91-71) vs. San Diego Padres (90-72)

For those of you keeping score, that's ten times since 1995 that one of the wild cards would have a record over five games better than their first round opponent.  There are also a number of division-rival matchups here, which I'm sure MLB would love, but which complete defeats the point of finishing better than your division rivals during the season.  For example, just last year the Yankees finished 6 games better than the Red Sox, and yet Mr. Selig wants them to play each other in a three game playoff in the first round?

Crunching the numbers, here's what we're looking at (leaving out the strike-shortened 1995):

Average W-L of Wild Card: 93.2 - 68.8
Average W-L of Wilder Card:  88.9 - 71.1

So the second wild card would have been, on average, four games worse than the first wild card.  Whereas wild card have averaged 93 wins, the second wild card would have averaged under 90.

Two things to wrap this up, since I'm more interested in showing the data here than grinding my axe overmuch (too late!).  First, baseball isn't basketball or football.  The better team doesn't win every time.  Letting the 2001 Oakland A's (102 wins) play the Twins (85 wins) in a three game series would be a travesty, because there's every possibility that the Twins win that series.  Upsets may be fun and all, but we like to feel like they're at least somewhat deserved, right?

Second, why would baseball ruin all the goodwill it has accumulated in the last few years?  While the NFL just went and shot itself in the foot with a lockout, and the NBA is about to do the same, MLB has ironically become the most dependable American sports league (behind, maybe, the MLS; but despite its growth MLS remains a second-tier league).  Baseball is in a good place right now, why mess with it by adding an inferior (very inferior) second wild card to each league in the playoffs?

Losing the WAR: Rockies Pitchers

Last time we looked at the worst single-season offensive performances by Rockies players, putting together 13 man team that would give the modern day Pittsburgh Pirates a run for their money.  Today we'll fill out the roster with the 12 worst pitchers in Rockies history, beginning with the worst of the worst.

Starting Pitcher - Mike Hampton, 2002, -1.5 WAR
Other Stats: 7-15, 6.15 ERA, 78 ERA+, 74 Ks, 91 BBs, Silver Slugger Award (best hitting pitcher), $9.5 million salary

Yeah, he walked more hitters than he struck out.  Actually, Hampton was worth -0.6 WAR total if you count his positive 0.9 WAR offensive performance in 2002, but even with that boost Hampton would still crack this list.  I don't know what's more damning for Hampton, that he was a significantly more valuable offensive player than pitcher for the Rockies in 2002, or that he was, at the time, playing with the richest contract ever given to a pitcher.  The Rockies may have only paid $9.5 million for Hampton's considerable talents in 2002, but they continued to play $10+ million a year to Hampton until 2008.  That's a lot of money for a guy who put up a negative WAR in his Rockies career.

Really, there's no question that Hampton deserves to be the "ace" of this team.  No player had a more disappointing career with the Rockies.  After Hampton was signed in 2001 - coming off of a career season for the Astros in 1999 and another solid season in 2000 with the New York Mets - expectations were extremely high for the Rockies.  There was talk of contending for a playoff spot or even a World Series title.  There was talk about the Rockies finally being able to attract high-quality free agents to Denver.  There was talk of the Monforts opening up the checkbook.  And then Hampton struggled through 2001 and collapsed in 2002, and the Rockies traded him in 2003, setting the franchise back five years.

Starting Pitcher - Pedro Astacio, 1998, -0.7 WAR
Other Stats: 13-14, 6.23 ERA, 83 ERA+, 39 HR surrendered (league leader), 17 HBP (league leader)

Pedro Astacio was the best pitcher on the Rockies from 1997 until he was traded in 2001, but the 1998 season was an exception.  Astacio was still figuring out pitching at Coors - evidenced by the 39 homers he surrendered in '98 (and the 38 in '99) - and the Rockies had not hatched the humidor idea.  Add to that some bad luck - Astacio's FIP was 5.24, still bad, but much better than his 6.23 ERA - and Astacio's season looks much worse than it really was.

Despite a rough '98, it's tough to criticize Astacio overmuch because all of those things that went wrong for him in '98 went right in '99 (except the home runs).  He finished 17-11 with a 5.04 ERA, (actually a 115 ERA+) recorded 210 strikeouts, and put up a 4.56 FIP at the height of the Coors Field bandbox era.  In all, Astacio amassed 5.3 WAR in '99, easily compensating for his '98 debacle.  Which really goes to show, it was - and is - far too easy to misinterpret pitching performances by Rockies pitchers.

Starting Pitcher - Jamey Wright, 2005, -0.6 WAR
Other Stats: 8-16, 5.46 ERA, 88 ERA+, 171.1 IP, 201 H, 101 K, 81 BB

Jamey Wright owns the dubious distinction of being one of only 15 pitchers in all of major league history with a career ERA of 5.00 or higher whilst pitching at least 1000 innings.  A part of that comes from pitching for the Rockies for 6 seasons, but Wright has spent 9 seasons on other teams, so it's not all Coors's fault.  Jamey's 2005 was, needless to say, pretty bad, but not spectacularly so.  Really, the Rockies couldn't have expected much more from Wright than what he gave them: over 150 innings of below average pitching, good enough to not be completely embarrassing, but not good enough to actually contribute to a winning team.  At the time the Rockies were still a couple years away from competing, so there was little harm in turning the ball over to Wright every fifth day, especially given his under $1 million salary.

Starting Pitcher - Byung-Hyun Kim, 2006, -0.1 WAR
Other Stats: 8-12, 5.57 ERA, 88 ERA+, 1.55 WHIP, 57 priceless at bats

If Jamey Wright somehow had an unembarrassing -0.6 WAR season in 2005, Kim had an extremely embarrassing -0.1 WAR season in 2006.  His pitching was pretty much in line with Wright's in 2005.  He was, in short, an inning-eater (though, because he came up a closer and because he had a propensity for not throwing a lot of strikes, Kim didn't tend to make it very deep in games), a stop-gap while the Rockies waited for Ubaldo Jimenez and company to vault into the Majors in 2007.  What made Kim embarrassing was his hitting.  Of course, you can't dock a pitcher for being a bad hitter, but I have never seen someone look more lost at the plate than Byung-Hyun Kim did.  He tried to hit like Ichiro, and ended up looking like a 5-year-old using a bat about 12 ounces too heavy.*  Miraculously, Kim hit .160 in 2006, in the best offensive season of his career (his career line: .124/.156/.144).  As a fan who watched many of those 8 hits he collected in 2006, I can safely say that he was lucky.

*This is also a reasonable description of how he looked when he pitched.

Starting Pitcher - Josh Fogg, 2006, -0.4 WAR
Other Stats: 11-9, 5.49 ERA, 89 ERA+, 1.55 WHIP, 1 absurd shutout, 93 K, 60 BB, 206 H, 172 IP

Josh Fogg was a thoroughly unremarkable pitcher throughout his Rockies career.  He became a fan favorite in 2007 thanks to a smattering of lucky performances against big name pitchers, earning himself the nickname "Dragon Slayer."  In reality, he was a player who never seemed to be trying all that hard, and who never, in his entire career, managed an ERA+ better than 97 (his 2007 number).  Even so, his pitch-to-contact style - as evidenced by his combined 153 walks and strikeouts in 172 innings in 2006 - led to an improbable shutout.  Against the Seattle Mariners, Fogg pitched a two-hitter, walking one and thus facing the minimum 27 opponent batters thanks to three Mariners double plays.  Needless to say, his game score of 83 was by far his best in an otherwise uninspiring season.


Mop-up / Spot Starter - Jose Acevedo, 2005, -0.9 WAR
Other Stats: 2-4, 6.47 ERA, 1.59 WHIP, 74 ERA+

The Rockies have become somewhat famous for their reclamation projects.  Fogg, Kim, and Jorge De La Rosa (especially De La Rosa) have earned Bob Apodaca a reputation as something of a miracle worker.  The thing is, the Rockies take a flier on about 5 pitchers a year who they hope they can transform from mediocre to passable, or passable to good.*  The reality is, for every De La Rosa or Jason Hammel that Apodaca does manage to set right, there are a dozen Jose Acevedos who never make it.  Which is fine, because they don't really cost anything.  The problem with Acevedo in particular, however, was that he stuck around long enough to put up miserable numbers in 2005.  Not surprisingly, '05 was Acevedo's last season as a Major Leaguer.

* This year's project is John Maine, a former Met who was excellent in 2006 and 2007, good in 2008, and then completely fell off of a cliff.  Keep your eye on him, though, because he's got as much raw talent as anyone 'Dac has had to work with in a long time.

Relief Pitcher - Mike DeJean, 1999, -1.0 WAR
Other Stats: 2-4, 8.41 ERA, 56 G, 61.0 IP, 83 H, 13 HR, 32 BB, 31 K, 1.89 WHIP

No, that's not a typo.  Mike DeJean pitched his way to a 8.41 ERA over 61 innings in 1999.  He really did surrender 13 home runs while facing 288 batters.  DeJean is a case study for evaluating relief pitchers, because while his 1999 is unfathomably bad - and, really, it's tough for relievers to pick up even this much in the way of positive or negative WAR because they pitch so relatively few innings - DeJean was actually a good pitcher for the Rockies in 1997, 1998, and 2000.  What's more, he pitched well for a few other teams before returning to Colorado for some solid performances in 2005.  The moral of the story?  Even one transcendently bad season for a relief pitcher does not mean that pitcher is bad.

Relief Pitcher - Gabe White, 2001, -0.4 WAR
Other Stats: 1-7, 6.25 ERA, 67.2 IP, 18 HR

White was unlucky enough to surrender 18 homers in 2001 against only 290 batters faced.  I say "unlucky," because throughout most of his career White did much better than that.  Indeed, like DeJean White had more good seasons than bad, though because many of his teams used him as a lefty specialist, he rarely accumulated much more than 0.5 WAR in either direction.

White - like Astacio - is the rare player on this list who would make the "best Rockies ever" team, too.  In 2000, the year before his homer-happy debacle that earned him this spot, White put up a career-high 3.3 WAR, finishing 11-2 (out of the bullpen!) with a 2.17 ERA.  That's pretty good, and goes to show how misleading the small sample sizes of relief pitchers can be.  In 2000, for example, White surrendered 5 homers in 83.0 innings, struck out 82 and walked only 14.  In 2001, he gave up 18 (as listed above), struck out 47 and walked 26.  So, three times more homers, about half as many strikeouts, and nearly twice as many walks.  Did he change that much?  Was he burnt out after a busy 2000?  Was he just unlucky in 2001?  Was he exceptionally lucky in 2000?  It's hard to say; probably the answer is some combination of the four, but we don't have enough data to reach a conclusion.

Relief Pitcher - Matt Herges, 2008, -0.4 WAR
Other Stats: 3-4, 5.04 ERA, 93 ERA+, 46 K, 24 BB, 1.60 WHIP, 64.1 IP

Herges, or as a friend calls him, "Hergie Pie," is the definition of a journeyman, barely-above-replacement pitcher.  Taking away his exceptional (for him) first and second full seasons with the Dodgers, he was worth 0.4 WAR over his career, bouncing around so much that he actually ended up playing for every single team in the National League West, as well as the Marlins, the Indians, and the Expos.  While there is little worth mentioning about Herges, it is significant that he did not start his Major League career until he was 29 years old, but managed to last until he was 39.  Unfortunately, the Rockies have him his biggest payday of his career after a solid campaign in the miracle 2007 season, floating him $2 Million for his services in 2008.  Like just about everyone else with the team, he couldn't replicate his 2007 success, and the Rockies were stuck with a (relatively) expensive below-replacement-level, 38-year-old pitcher with the dubious distinction of being mentioned in the Mitchel Report.  Fun.

Lefty Specialist - Mike Munoz, 1995, -0.7 WAR
Other Stats: 2-4, 7.42 ERA, 73 ERA+, 37 K, 27 BB, 9 HR, 43.2 IP, 64 G

Munoz wins the "most unexpected member of this team" award, at least for me.  Perhaps because I was still an optimistic young fan in 1995, far too young to really know much of anything about baseball except that I loved the Rockies and that they were making the playoffs in their third year of existence, I didn't ever consider that maybe some of the players might not be all that good.

Munoz had a better year with Colorado in 2004, but throughout his career he was always a LOOGY (Lefty One Out GuY).  Anyone who appears in over 450 games, but pitches 364 innings is probably facing one or two batters at a time most nights.  And that was Munoz.  The result is that, sometimes a LOOGY has a bad season because of a few bad outings, or because he just happens to miss the strike zone on a few key pitches.  Despite the small sample size and pitching in the inagural season of Coors Field, however, it would be impossible to leave Munoz's '95 off of this team.  For a LOOGY to accumulate -0.7 WAR - in a shortened season no less - is impressive.  In a bad way.

Setup Man - Todd Jones, 2003, -1.4 WAR 
Other Stats: 1-4, 8.24 ERA, 61 ERA+, 39.1 IP, 61 H, 8 HR, 2.01 WHIP

-1.4 WAR in less than forty innings!  I had an unofficial rule that pitchers had to reach 50 innings to be considered for one of these spots (to weed out some of the -0.2 WAR in 10 innings kind of guys), but Jones easily earned this spot despite his midseason release and subsequent signing with Boston.  Jones was a "veteran presence" guy gone wrong for Colorado.  Once upon a time he was a good closer for the Detroit Tigers, but by his mid-30s he was - or looked - done as a Major League pitcher.  Coors Field proved too much for him, and he, to top it off, something of an ass, known for his homophobia, his bigotry, and his general closed-mindedness.  On a team built - for better or worse - around character, Jones did not fit in.  For some reason the Sporting News gave him a column late in his career,* and the writing was (or is, it seems he may still have this gig), well...  It was subpar.

*Indeed, his column began as he was on the Rockies, and while it was called "the closer," he never played that role in Colorado.  Somehow he miraculously became a passable closer again from 2005-2008.

Closer - Shawn Chacon, 2004, -1.7 WAR
Other Stats: 1-9, 7.11 ERA, 70 ERA+, 35 Saves in 44 Chances, 1.94 WHIP

And at least we reach the end.  Assuming this team somehow ever had a lead going into the ninth inning, it would be almost certain to squander it, thanks to Shawn Chacon.  The Greely native was the Rockies golden-child, becoming the first Colorado pitcher to make an All-Star game in 2003.  Thanks to injuries, and in an effort to preserve his arm, the Rockies moved Chacon to the pen in 2004, slotting him in as their closer.  The results were disasterous, and Chacon was gone from the Rockies by mid 2005, traded to the Yankees for Ramon Ramirez.  Of course, Ramirez was later flipped to the Kansas City Royals for Jorge De La Rosa, so it's not all bad.

Anyway, despite his solid 2003, Chacon never really demonstrated that he had the talent to pitch at the Major League level.  Rockies fans and ownership was overly-optimistic about him from day one, and while he may have stuck - had he not faced injury trouble - as a four or five starter, he was overmatched as an ace.  He was also overmatched - or at least misplaced - as a closer, struggling to handle the role, especially in a ballpark as unforgiving as Coors Field.

Wrap-Up

Ironically, the Rockies probably have a much better "worst ever" team than most franchises thanks to their relatively recent entry to the league (the same reason they have a much worse "best ever" team).  Even so, the team we've assembled in these last two posts would be absolutely dreadful.  There are a couple good hitters who can't field and a couple good fielders that can't hit, but mostly it's players who can't hit, field, pitch, or do much of anything else on a baseball field.  Or, at least, players who couldn't do much of anything for a particular season.

Baseball-Reference WAR (as opposed to Fangraphs WAR; we used BR in these posts) is calculated to a standard of 52 wins.  That is, a replacement level team should win roughly 52 games (and lose 110).  This Rockies team, as a whole, is a -21.5 WAR team, meaning they would go about 30-122, a .246 winning percentage.  I also played around with a lineup tool that estimated the offense would produce roughly 750 runs.  Given that total, we can estimate - in order to finish 30-122, that this team would surrender roughly 1300 runs.  Or, in other words, the average score of a Worst Rockies Ever game would be 8 to 4.5.  Eight!  If that seems high, take a look at the pitching staff again, and remember that it has a pretty much terrible defense - especially in the outfield - to back it up.  Eight runs a game might even seem low.

Fortunately, the real Rockies are much, much better than this.  And, even more fortunately, the season is about to start.

Losing the WAR: Colorado Rockies Hitters

A popular mini-project that baseball fans like to play around with is building fictional rosters of the best players in team history, or the best players in the league today, or the best players all-time.  The thing is, these lists are usually focused upon just that: the best.  What if we looked at the question from the other side?  Who were the worst players in a team's history?  How bad would an all-time worst Rockies (since, you know, we're all Rockies fans in Nicht Diese Tone land) roster be?

I went through baseball-reference.com's Rockies pages to dig up the worst single-season performances in Rockies history, by position.  For simplicity's sake I used WAR as my metric of choice, but in a few cases of ties I went with a combination of other statistics and personal opinion.  The roster, along with comments, is as follows:

Catcher - Joe Girardi, 1995, -0.6 WAR
Other Stats: .262/.308/.359, 58 OPS+, 76 Ks to 29 BBs.

Girardi was never a great player, and this was one of his worst seasons.  To his credit, the Rockies did make the playoffs in '95, but not so much due to Joe's contributions.  His .308 OBP was especially uninspiring, and while he did manage to hit 8 homers, that "power" was almost certainly the result of the inaugural season at Coors Field (6 of the 8 came at home).  Indeed, Girardi was a test-case for Coors Field, hitting .291 at Coors and .228 on the road.  Remarkably, Girardi - who was 30 years old in '95 - went on to have a number of decent, if unspectacular seasons, with the Yankees and Cubs in the late '90s.

First Base - Todd Helton, 2010, 0.4 WAR
Other Stats: .256/.362/.367, 87 OPS+, 8 HR, 37 RBI, 118 G, 90 Ks to 67 BBs.

Let's get this one over with...  Helton is, as you know, probably the best player in Rockies history.  Well, that's not totally clear, because there's a good case to be made for Larry Walker.  But Helton has spent his entire career in purple pinstripes, and figures to retire with Colorado in the next few seasons.  Indeed, it was practically inevitable that he would hold this "worst ever season by a Rockies first baseman" spot if only because the Rockies have only had two starting first basemen in their entire history.  Think about that for a minute.  The Rockies have been around since 1993, and the only contenders for this spot are Helton and Andres Galarraga.  The Big Cat actually did have a season of 0.2 WAR in 1994, but both he and Helton's contributions were entirely from defense, and Andres still slugged over .500 in the strike-shortened '94 campaign (it's just that the park adjustment is so big that his offense looks bad).

Anyway, it's about time Helton start moving towards retirement.  2010 was the first season in Helton's career in which he struck out more than he walked (first since his call-up in '97, anyway, when he struck out 11 times and walked 8 in 35 games), and his 8 home runs is, frankly, sad for a first baseman playing in Colorado.

Second Base - Mike Lansing, 1998, -0.2 WAR
Other Stats: .276/.325/.411, 78 OPS+, 18 GDP, 12 HR (after hitting 20 the year before in Montreal)

Lansing is the rare player who actually got worse after coming to Coors Field.  In 1997, playing for the Expos, he hit .281/.338/.472, mashed 20 homers, and accumulated 2.5 WAR.  Not a bad season.  Hardly what you build a roster around, but exactly the kind of player you want to have to fill out a team.  Lansing fell off the proverbial cliff in '98, though, and while he was still a solid defender, his inability to hit made him worse than replacement level for a team in dire need of an identity up the middle and at the top of the lineup.

Third Base - Ian Stewart, 2009, 0.2 WAR
Other Stats: .228/.322/.464, 95 OPS+, -0.8 defensive WAR

The Rockies have never been a great team at third base, but have usually been solid.  Charlie Hayes, Jeff Cirillo, Garrett Atkins.  No one's idea of world-beaters, but good enough to play on a contender.  Stewart, of course, was supposed to be the guy who went out and beat worlds.  A top draft pick, a highly touted prospect (so good that the Rockies didn't pick Evan Longoria when they had the chance), and now a frequent "potential breakout" player every season, Stewart just hasn't put it together, and time is running out.

One of Stewie's biggest problems (besides his work ethic, which many experts have called into question) is his reliance on the long ball.  Stewart is very much a "three true outcomes" player (meaning a large percentage of his at bats end in either walks, homers, or strikeouts) who works the count and waits for his pitch.  The problem is, he's often too patient, taking drive-able pitches, and thus doesn't draw nearly enough walks.

That said, in 2009 Stewart's value was hindered significantly because the Rockies trotted him out to second base in 21 games and the outfield for 9, enough to ruin his fielding WAR for the whole season.  Stewie is actually a decent, if unspectacular, fielder at third - certainly better than his predecessor, Atkins.  What's more, while Stewart ultimately had an unimpressive 2009, Atkins gets honorable mention (and a bench spot) for being even worse than Stewart in this playoff year.  He doesn't edge out Ian for the starting spot only because the Rockies benched him midway through the season, and he didn't really come close to the theoretical 500 PA requirement I made to be a starter on this team.

Short Stop - Neifi Perez, 1998, -1.2 WAR
Other Stats: 162 G, 712 PA, .274/.313/.382, 68 OPS+, -0.9 defensive WAR, 22 Sac Bunts


Better known to Cubs fans as "Ne!f!," Perez was, for a time, possibly the worst player in baseball.  It's truly remarkable that he lasted in the majors from 1996 to 2007, posting a career WAR of exactly 0.1.  He was, in short, replacement level for his career, just as good or bad as any number of minor leaguers.  What makes his longevity even more surprising - or maybe explains it - is his dubious distinction of being one of the few players to face three separate suspensions for testing positive for amphetamines.  Yeah, Neifi is just that kind of player.

Anyway, Perez's 1998 was one of his worst seasons, and yet he played every single game, led the team in plate appearances, and often hit near the top of the lineup (and was asked to give up outs by sacrifice bunting a lot).  What's more, in addition to spotty-at-best offensive ability, WAR believes that Perez was a vastly overrated defender.  His 1998 numbers bear that out.  Even using traditional metrics, its hard to see him as a great shortstop: he committed 20 errors for a fielding percentage of .975.  Not terrible, but far from what you expect out of a guy with a .313 OBP playing at Coors Field.

Left Field - Dante Bichette, 1999, -2.8 WAR
Other Stats: .298/.354/.541, 102 OPS+, 6 SB and 6 CS, 34 HR, 133 RBI

By WAR, this was the worst season of any player in Rockies history.  Not even Mike Hampton's 2002 (we'll get there) could touch Bichette in '99.  At 35 Dante was done - certainly done in the field - his legs gone and his bat slipping.  Still, Dante was a decent hitter late in his career (his 102 OPS+ means he was just above league average), and by traditional numbers like HR and RBI he still looked pretty good.  The biggest issue here was defense.  13 errors in left field is no one's idea of acceptable, leading to an abysmal .952 fielding percentage.  Add to that an utter lack of range (his Range Factor of 1.78 was well below the league average of 1.98) and you've got a recipe for disaster.  Obviously Bichette can still be the cleanup hitter for this all-time worst Rockies team, but he's going to give up just as much as he provides on offense by being a butcher in the field.

Center Field - Cory Sullivan, 2005, -1.1 WAR
Other Stats: .294/.343/.386, 83 OPS+, 83 Ks to 28 BBs, 23 EBH (meaning 88 singles), 64 R

Ugh.  In a long line of no-hit, kind-of-fast, ok defensive center fielders,* Sullivan has the dubious distinction of being the worst.  And that's saying something; not everyone can be worse than Curtis Goodwin.  Sullivan, however, was remarkable because unlike the other "kind-of-fast" players, he wasn't really fast at all.  For his career - which is now almost 500 games long - he has only 32 stolen bases, and he has been caught 10 times.  Not exactly a speed demon (Sullivan's replacement Willy Taveras once stole 68 in a single season).

*To wit: Juan Pierre, Curtis Goodwin, Tom Goodwin, Darryl Hamilton, Willy Taveras, and now Dexter Fowler.**  The Rockies LOVE this type of player, for some reason.

**No, Dexter Fowler can't hit.  He can't.  This is an argument you won't win.  In over 1000 PAs in his career, Fowler's slash line is .259/.351/.401.  At Coors Field half the time (his road slashes: .220/.308/.334; translation: yikes!).  That's not cutting it.  Look, I get that he has an awesome name, and that he's super fast, and he's probably the coolest player on the Rockies (except maybe Ubaldo), but that doesn't change the fact that he's basically another iteration*** of the Rockies center-field prototype.

***OK, I'll concede that he has a chance to be better because he's 24.  These things aren't predictive, but his top comp at age 24, according to baseball reference, is Lou Brock.  Then again, some of his other top comps include Felix Pie and Jermaine Allensworth.  So, yeah.  There's that.

I bring up the speed issue because that's really Sullivan's biggest problem.  He fits the mold of a certain type of player, but doesn't actually do the things those players do.  So, for example, he hits a lot of singles, but he doesn't steal bases or stretch extra base hits enough to really make up for his lack of power.  He doesn't score many runs, in part because he often hits at the bottom of the lineup, but also because he can only ever get himself to first base.  He also strikes out a ton, and rarely walks.  His biggest strength, in many ways, is his skill as a bunter.  Plus, he's an overrated defensive player (career -1.8 WAR in the outfield).  Sullivan, for his career, is below replacement level (-1.2 WAR total).  How do players like him stick in the Majors?  We'll never know.

Right Field - Brad Hawpe, 2008, -1.7 WAR
Other Stats: .283/.381/.498, 121 OPS+, 134 Ks to 76 BB, -4.1 defensive WAR

Dante and Brad are on this list for the exact same reason.  Only, Dante was, early in his career, a passable defensive outfielder.  This was never true of Hawpe, who has always been a first baseman playing right field.  2008 was his worst defensive season (at a stunning -4.1 WAR, or over 40 runs!) by far, and his defense alone earned him his spot among the worst Rockies of all time.

Let's not let Hawpe off the hook offensively, however.  In 2007 Brad was a monster at the bat, setting career highs in home runs, RBI, runs scored, BB, OBP, SLG, and OPS+.  In 2008 he regressed hard, his offensive WAR dropping from 3.2 to 2.4.  That's not a ton, but it's still nearly a full win.  Throw in a truly horrid defensive season, and you have a recipe for disaster.  Also, I still blame Hawpe for blocking Seth Smith - an infinitely more talented player - throughout his early career, and starting in 2008.  Hawpe's illusory value as a hitter is at least partially responsible for stunting Smith's development to the point that he may never realize his potential.  That and Jim Tracy being a terrible* manager.

*By all accounts Tracy is great in the clubhouse, well-liked, and good at getting the best effort out of his guys, for what that's worth.  But tactically...  Ew.  And he does seem to have an irrational dislike of certain players (Chris Ianetta, Seth Smith) and an irrational love for others (Spilly, Jason Giambi).  Plus, he's going to pitch Ubaldo Jimenez's arm off within the next two seasons.  Mark my words, Ubaldo will be done as an effective pitcher by 2013.  And that really upsets me.

Given Hawpe's age in 2007 (28 years old), you might think the Rockies could have seen some drop-off coming.  Traditionally players peak around 27 or 28, and even younger defensively.  But the Rockies held onto Hawpe, who promptly fell off of a cliff in 2010.  Add him with Garrett Atkins to the "players the Rockies maybe should have gotten rid of sooner" trio.  The final member of the trio?

Bench, Outfield - Ryan Spilborghs, 2009, -0.7 WAR
Other Stats: 393 PA, .241/.310/.395, 1 amazing walkoff grandslam, 77 OPS+

OK, yes, Ryan Spilborghs hit a walkoff grand slam against the Giants in a key moment in the playoff race in an extra inning game that - to top it off - I attended (which is remarkable because I don't live in Colorado anymore, and didn't at the time; that was I think the only home game I made it to in 2009).  So that goes in his favor.  On the other hand, he was a miserable defender, and put up an OBP of .310.  .310!  As a Rockie!

Spilly has been a passable fourth outfielder throughout his career, but in 2009 and 2010 (now that he's over 30) he has suddenly found himself playing 130+ games a season.  Problem is, if you take away his 2.1 WAR 2007 (in his age 27 season, also known as his prime), he's a career below replacement level player.  He also has, as any Rockies fan with a sense of aesthetics can tell you, below replacement level facial hair.

Bench, Outfield - Darryl Hamilton, 1999, -1.0 WAR
Other Stats: .303/.374/.389, 76 OPS+, -0.8 defensive WAR, 4 SB and 5 CS, 91 G, traded mid season

Look who it is!  Another no-hit, kind-of-fast, ok-at-defense center fielder!  Hamilton was perhaps the worst of the bunch, lasting only one season (that his, half of '98 and half of '99) before getting traded.  The best part?  The Rockies got Hamilton for... Wait for it... Wait for it... Ellis Burks!  As in, the best center fielder in Rockies history (at least before Cargo, who will likely settle in RF anyway).

Now Burks was 32 at the time, but he went on to have productive seasons in 1999, 2000, 2001 and 2002.  And, what's more, Hamilton was also 32, so it's not like the Rockies were getting younger.  Hamilton, meanwhile, was flipped in '99 for Rigo Beltran (who pitched 12 innings for the Rockies and gave up 15 runs) and Brian McRae (another no-hit, kind-of-fast center fielder who played for the team for about a week).  So, yeah, Darryl Hamilton was a go-between in the classic "trade Ellis Burks for nothing" move.

Anyway, Hamilton was Cory Sullivan before Cory Sullivan was Cory Sullivan.  At least, to his credit, he did have a few good seasons early in his career.  As a Rockie, however, he was less that replacement level, and he especially stands out because the Rockies gave up one of their best players for him.

Bench, Infield - Walt Weiss, 1994, -0.7 WAR
Other Stats: .251/.336/.303. Wait, look at that again.  A .303 SLG.  In Colorado.  That's all you need to know.

Walt Weiss once hit a ball out of the infield in the air, but the wind was blowing out at 30 MPH that day.

Weiss owns the dubious distinction of "leading" the NL with his bafflingly low .303 SLG in 1994.  That Weiss couldn't hit for power, at least, was made up for by his inability to hit for average, his mediocre defense, and his complete lack of speed.  He did, at least, have a pretty good eye, and rarely struck out.  So there's that.  But everything else about him - throughout his career - screamed "bench player."  And yet, he was a starter for no less than nine teams, once made the All-Star game, and won the Rookie of the Year in 1988.  Weiss did have good seasons - and even played decently well for the Rockies from 1995-1997, but '94 was one of his worst seasons.

Bench, Infield - Garrett Atkins, 2009, -0.2 WAR
Other Stats: .226/.308/.342, 64 OPS+, 9 HR in 399 PA, $7.0 Million salary.

Ironically, Garrett's worst season was also his highest-paid one.  Despite only really playing half a full-load - thanks to a mid-season benching - Atkins accumulated -0.7 WAR offensively and was, in fact, one of the inspirations for this series.  In all, I couldn't elevate him over Stewart because he didn't play enough, but his 2009 remains one of the worst performances in Rockies history from a player who everyone expected much better from.  Atkins was only 29 in 2009, and was coming off of a challenging 2008.  But in '08 he still hit 21 homers and posted an SLG of .452, ending up with a 1.0 WAR.  His complete and total collapse was surprising to say the least.  Hell, it's worth taking a look at his career arc, by WAR:

2003 and 2004: -0.7 WAR (September callups)
2005: 1.5 WAR
2006: 6.4 WAR
2007: 2.9 WAR
2008: 1.0 WAR
2009: -0.2 WAR
2010: -1.0 WAR (with Baltimore)

Atkins went from MVP votes in 2006 to not-good-enough-to-start-for-the-Orioles in 2010.  Wow.

Bench, Catcher - Kirt Manwaring, 1997, -2.1 WAR
Other Stats: .226/.291/.276!!!!!!! 375 PA, 1 HR, 10 GDP, 38 OPS+, -0.2 defensive WAR

Actually, those stats don't even capture the worst part of Kirt Manwaring's 1997.  Let me run another set of numbers by you, so you can compare them with Manwaring's.

.297/.386/.535, 120 OPS+, 17 HR in 298 PA, +0.2 defensive WAR, 1.8 total WAR.

That was Manwaring's "backup," Jeff Reed.  Reed had the single best season of his career in 1997, outperforming Manwaring in every conceivable way.  And yet the two split time close to evenly all season.  Indeed, Manwaring had 77 more plate appearances than Reed, despite an OBP and SLG below .300!

To top it off, the Rockies actually contended in 1997, finishing 83-79, only 7 games back of the Giants.  Larry Walker won the MVP with his best season, and the team was really only a couple pieces and parts away from a playoff appearance.  One of those pieces was Jeff Reed, who languished on the bench while Kirt Manwaring put up what has to be the single worst offensive season in Rockies history.

I know what you're thinking: if Manwaring was that bad overall, what did his splits look like?  I'm glad you asked.  Away from Coors, Kirt's line was a shocking .198/.279/.222.  That, my friends, is pitcher territory.  In theory, Manwaring was a terrific defensive catcher, and while WAR doesn't like him in 1997, evaluating catcher defense is notoriously impossible.  Even if, however, we give Manwaring the benefit of the doubt...  Even if we throw a full win at him on defense, he'd still have one of the worst seasons in Rockies history.

The only thing keeping Manwaring out of the "starting lineup" for this team is his lack of playing time.  If you are so inclined, though, you can slot him in instead of Girardi.

That wraps up our look at the worst position players in Rockies history.  Next up, the pitching staff.  You'll never guess who the "ace" is. (Hint: he's a better hitter than Kirt Manwaring).

NBA League Size and Competitiveness, Part the Last: Calculating Competition

Today we embark on a journey through the perilous land of inventing your own statistics.  As a wrap-up for this series on NBA competitiveness and league size, I wanted to create a kind of competitiveness index based upon the regular season results in any given season.  That has proved to be a more difficult task then I originally anticipated, for reasons which will become clear.

First off, though, why would I want to do something like this?  Well, as I discussed in Part One, I'm reading The Book of Basketball, by Bill Simmons, and was struck by how definitive his assessment of which NBA seasons were competitive and which weren't is.  In particular, some of the early seasons in the NBA sparked comments like, "Everyone had a good team back then."  I wanted to try to figure out if he was right because, as sabermetrics has taught us, often people who are passionate and well-informed fans of a sport still don't really understand what's going on.

For example, in baseball it was long believed that carrying a .300 batting average alone was sufficient to make you a good hitter.  "A .300 hitter" was - still is - an honorable appellate, as well as a since qua non of baseball success.  What about a player like Juan Pierre, though, whose career .298 average puts him close enough to be called a .300 hitter? Is he really any good?  Old-time baseball wisdom would say yes.  He's fast, he hits for a high average, and he's the kind of guy that people assume is a good fielder, whether he is or not.  But even offensively, you can dive deeper into his batting lines and see that he's a deeply, deeply flawed player.

You see, Juan Pierre does not really draw walks.  Nor does he hit for power.  So despite a career .300 average, he sports a .347 OBP - not bad, but not good enough for someone who aspires to be an integral part of a team's success.  Moreover, his .366 career slugging percentage means that he's a singles hitter.  Those many hits he does generate aren't in the gaps or over the fence (as evidenced by his 14 career homers in almost 1600 games).  Now, the traditional baseball viewpoint would be that all of Pierre's singles are made up for by his stolen bases...  Which is fair, except he has lead the league in getting caught stealing 6 times, and stolen bases only 3 times.

 Which is all to say that being a .300 hitter alone used to look great, and still looks great.  But looks can be deceiving.  No one should confuse Juan Pierre with a great hitter.  Similarly, sometimes a league might look competitive without actually being competitive.  And so I embarked on this little blog-project to prove Simmons right and/or wrong.

In Part Two I found and discussed that, while defining competition - let alone assessing it - might be very difficult, we can at least see that, as the league gets larger, so too does the standard deviation of winning percentage.  From one perspective that means that the league is getting less competitive - in the sense that teams are less jumbled together - but from another it means the league is getting more competitive - in the sense that there are more elite teams in any given season.  And that's exactly what my work for today's post shows.

What I did was develop a formula for "competitiveness," using the number of above-.500 teams, the mean of their winning percentages, and the standard deviation of their winning percentages.  My reasoning was this: if a higher percentage of teams are above .500 in a given season, the league is more competitive.  Similarly, the higher the average winning percentage of those teams, the more competitive the league is.  Lastly, the more condensed those winning percentages are (the lower the standard deviation), the more competitive the league is.  The advantage of this approach, of course, is that we can completely ignore any team that finished .500 or worse.  Those teams, I reasoned, don't really count (even if many of them do make the playoffs, thanks to the NBA's "everybody makes it" attitude towards the postseason).  The disadvantage, as the statistically acute among you will see, is that the components I have selected here are all closely related to standard deviation of winning percentage league wide.

What does that mean?  Well, let me show you.

X - Number of teams, Y - "Competitiveness"

My formula for competitiveness is messy, but worth sharing.  Brackets indicate the separate components, which I tried to normalize so that 1 was more or less "average":

[(0.5 + Percentage of teams above .500)] x [10 x (mean above .500 - .5)] x [(stdev above .500 - mean above .500) / (stdev above .500 + mean above .500)] x 50

I multiplied the whole thing by 50 just to pull it up into a more readable and intuitive range.  Basically, 50 is normal (as you can see, the trendline above is close to, though not quite at, 50), while anything above 50 is a particularly competitive season, and anything below 40 is uncompetitive.

Now this graph alone doesn't show you anything problematic.  Like our graph from Part Two, it has a weak, but present trend going upwards, and...  Wait.  It looks very similar to that graph.

So I graphed "competitiveness" by year, and made the following line graph:

"Competitiveness" (Y) by season (X)

 I then did the same with Standard Deviation of winning percentage:

STDEV of Wpct (Y) by season (X)

Now you may notice that these two graphs look almost exactly the same.  With a sinking feeling - starting to realize the folly of my ways - I graphed the two against each other:

Competitiveness (Y) against STDEV of Wpct (X)

 The result is unambiguous.  My "Competitiveness" ranking basically tells me that when the standard deviation of the winning percentages league wide are high, the competitiveness is also high.  Which, of course, is the opposite of what I was suggesting in Part Three.  Yeah.

The result is hardly surprising, as I said, because of the components in my formula.  While the percentage of better-than-.500 teams may not have much bearing on standard deviation of winning percentage, obviously when the mean of the winning percentage of teams above .500 is higher, so too will be the standard deviation of winning percentage of all teams.  Meanwhile, the final component of my formula - accounting for standard deviation of above-.500 winning percentages - will be inversely related to standard deviation of winning percentages league wide, but not enough, obviously, to disrupt the high correlation between "competitiveness" and SD of winning percentage league wide.

But really, this only goes to show that "competitiveness" is a highly ambiguous term.  Where one fan might think the most competitive season is the one where all of the teams are bunched together, another might prefer the one with five great teams and five terrible ones.  It's really a matter of perspective.

Where Simmons makes his determination, then, is probably the best place: skill of players in the league.  While you do have to be careful here - because all evaluation of player skill is heavily influenced by the relative skills of his contemporaries, and things like changing league sizes mess with our understanding of what is good and what is great - probably the best way to assess the competitiveness of the league at any point is to assess the overall skill of the players in the league at a given time.  That's a much more challenging project, but I can imagine going through players and seeing where great careers overlap, and figuring out when talent has been at its apex and nadir.  Of course, Simmons does that kind of thing for a living - though without relying too much on numerical analysis and going more with his perception, a more-than-fair, if perilous, approach.  John Hollinger also does that for his living, relying absolutely on numbers.  So between the two of them, you can probably get a good sense of what's going on.

Finally, if you want to see the nuts and bolts of my work - messy as it is - I've posted my workbook to GoogleDocs.  Do with it what you will.