More Humidor!

My last post ended up being oddly prophetic, as Tim Lincecum 'caught' the evil Rockies cheating just this last home series.  Apparently he - or the Rockies - didn't read the post, which concluded that cheating by mixing in non-humidor balls would be, basically, a colossal waste of the Rockies' time and energy.  Anyway, if the Rockies were cheating, it didn't do a lot of good, as the team lost 2 of 3 and are now all-but-eliminated from the NL West race.  Maybe next year they'll start cheating earlier in the season, instead of just in September.

In all seriousness, I want to further explore this humidor-cheating theme.  The charge against my favorite team is, frankly, extremely severe, and if there is any warrant for it, I'd like to know.  If, on the other hand, this is a witch-hunt that has more to do with irrational fears and the human propensity for finding patterns where there aren't any, well, I'd like to know that too.

Whereas last time we looked at theory - and theory flatly rejected the notion that the Rockies would gain from cheating by mixing non-humidor balls in with humidor balls - today we're going to look at data.  Now, because the theory says that the Rockies would get little to no benefit from cheating as described, what we have to look at instead is whether or not the Rockies have been unduly lucky.  Do they, in short, win more late comebacks than other teams?

Lets start with the most basic stats - and this includes both home and road games.  The Rockies have come back to win 29 games this season.  They have, on the other hand, blown 39 leads.  They have won 10 walk-off games, and have watched the other team walk off 9 times.*  Neither of those numbers looks particularly suspicious - indeed, it's the 39 (!) blown leads that are surprisingly high, apparently the Rockies are forgetting to take the non-humidor balls out when they go back to the mound - but let's dig deeper anyway.

* For comparison's sake, let's also look at the San Francisco Giants, the Rockies division rival who seems most convinced that the Rockies cheat with the humidor.  The Giants have won 35 games by comeback, and have lost 22 games in which they had a lead.  They have 6 walk-off wins and 5 walk-off losses.

Another informative statistic here is the 2010 Rockies record when they are behind at the start of the Xth inning.  Consider:

Behind to start the 2nd: 10-19, .345
3rd: 10-29, .256
4th: 11-39, .220
5th: 11-43, .204
6th: 12-48, .200
7th: 15-51, .227
8th: 10-54, .156
9th: 3-56, .051

The same table for the 2010 Giants.
2nd:  11-21, .344
3rd: 14-28, .333
4th: 14-37, .275
5th: 15-47, .242
6th: 12-55, .179
7th: 13-55, .191
8th: 8-57, .123
9th: 6-61, .090

This table in isolation, and even with a Giants version for comparison, isn't all that meaningful, so let's look at the MLB league-wide numbers as well.

2nd: 330-783, .296
3rd: 408-1115, .268
4th: 413-1325, .238
5th: 367-1518, .195
6th: 317-1640, .162
7th: 263-1757, .130
8th: 170-1892, .082
9th: 96-1999, .046

To summarize, the Giants have been better than the Rockies at coming back starting behind in the 3rd, 4th, 5th, and 9th innings.  The Rockies have been better coming from behind in the 2nd, 6th, 7th, and 8th.  Both teams have generally out-performed the rest of the league, which at least in part owes to the fact that both teams are above-average teams.  The Yankees, for example, are basically as good or better than both the Rockies and Giants coming from behind in every inning.  The Pirates are worse.  Makes sense.

I want to call out some particular numbers from the last chart.  The Rockies are 3-56 when trailing going into the 9th inning.  Three wins, 56 losses.  Sure, a lot of that has been on the road, but that 3-56 is way worse than the Giants 6-61, for example.  This more or less reinforces what we looked at last post: changing out humidor balls for non-humidor balls in the bottom of the ninth ain't gonna win many games.

In case you're not convinced, here are some numbers from previous seasons. In 2009 the Rockies went 2-63 (for an awesome .031 winning percentage) in games they trailed going into the ninth inning, and 4-58 in games they trailed going into the 8th.  In 2008 those numbers were 3-79 and 8-74 respectively.  Even in the magical 2007 the Rockies went 6-62 in games they trailed going into the 9th, almost identical to this year's Giants.

I don't want to spend forever parsing these numbers, because we'll just get the same thing over and over.  If baseball-reference made it easier, I'd pull these apart and separate home and road, but what we'd find is that the Rockies come from behind and blow leads more often at home, simply because Coors Field is such a good hitters park.  Remember that the Rockies have blown 39 leads this year? That's not because of a bad bullpen, indeed, far from it. The Colorado bullpen has been worth, according to fangraphs, 50 runs above replacement this year (or 5 wins), good for 5th in all of Major League Baseball.  I think that 39 blown leads has a lot to do with where the Rockies play, humidor balls or no.

"OK Mr. Smarty-pants," you're probably saying, "You've given me all kinds of mediocre data that doesn't show that the Rockies aren't cheating, and you've yet to supply an alternative hypothesis." On the first point, you're right.  I can't prove the Rockies aren't cheating because, as my last post said, there's no real reason to believe that the kind of cheating in question would actually benefit the team.  Instead, I'm trying to show, in this post, that there's not really a compelling reason to even suspect that the Rockies are cheating in the first place.  They don't win an inordinate number of comeback victories and they don't score an inordinate number of late runs (once you account for Coors Field, that is; I didn't show this data, but I did look, and if you ask nicely and really care, I will).  In short, they're not better than anyone else at winning games that they don't lead.

Now, as to your second point, I do have a hypothesis for why the Rockies have such extreme home/road splits.  I don't think the humidor has anything to do with it, rather, I think there are a couple things at work.  One is familiarity.  Every team in the Majors plays better at home than on the road, for any number of reasons that no one is quite sure about.  Sleeping in your own bed, a batter's eye you're used to, a mound that feels more comfortable... Whatever.  It just happens.  So it's no surprise that Rockies pitchers do better than those from other teams at Coors, and likewise it's no surprise that Rockies hitters benefit more from Coors than visiting hitters.  They know the park better, they're used to the way the ball breaks (or doesn't) out of the pitcher's hand, and they got a better night's sleep.

Beyond even that, though, I think the Rockies front office has figured out what kind of players play best at Coors Field.  Especially on the pitching end, the Rockies have a particular skill set they seem to target, and they seek a lot of castaways from other teams (Jorge De La Rosa, Jason Hammel, Huston Street, Manny Delcarmen, etc) and try to turn them into Coors Field specialists.  What is that skill set?  Hard to say, but I can point you to some numbers that I find interesting.

There are a lot of numbers we can look at, here, but I think the most informative ones are strikeouts and walks.  As two of the "three true outcomes," strikeouts and walks are the numbers that should be least susceptible to the altitude and cavernous alleys of Coors Field.  That's not to say Coors should have no effect on strikeouts and walks, but rather that the effect shouldn't be as big as it is on batting average or home runs.

So what do we see?  Rockies hitters have, as of today, 3016 Plate Appearances at Coors and 2959 on the road.  In those, Rockies hitters have struck out 555 times at home and 655 on the road.  In rates, the Rockies lineup strikes out 18.4% of the time at home, and 22.1% of the time on the road.  That's a pretty substantial difference.

What about walks?  The Rockies have drawn 288 walks at home and 274 on the road.  In rates, again, that's 9.5% at home and 9.3% on the road.  This is not, it seems to me, a substantial difference.  The strikeouts are telling, however, especially if you consider this amazing piece from Athletics Nation about Carlos Gonzalez.  It seems to me that the Rockies are probably taking more or less the same approach on the road as they do at home, but they're getting fooled by a lot more pitches - and especially fastballs, if you read the Cargo article - away from Coors.

More interesting, however, is the Rockies pitching staff.  At Coors, Rockies pitchers have faced 2988 hitters, while facing 2847 on the road.  At Coors, Rockies pitchers have struck out 596 hitters, while they've k-ed 577 on the road.  That's 19.9% of plate appearances turning into strikeouts at home, and 20.3% out on the road.  Not a substantial difference, which might owe to the kinds of pitches that Rockies pitchers throw.  Namely, they rely on the kinds of pitches that are least effected by the altitude and dry air at Coors.

Here's the really interesting thing, though.  Rockies pitchers have walked 217, or 7.3% of hitters at home, while walking 279, or 9.8% of hitters on the road.  That is definitely a significant difference, and while I think it's impossible - or at least beyond the scope of this post - to figure out why exactly that's happening, I strongly suspect it has something to do with the way that balls break differently when the Rockies aren't at altitude.  If, as the Cargo piece suggests, it's fastballs that are most effected, it stands to reason that more of those 3-2 and 3-1 (fastball) counts are turning into walks on the road than at home.

That's just speculation, but the point is not to prove anything, as I've said.  The point is to show that there's a perfectly reasonable - and much less conspiratorial - explanation for the Rockies huge home-road splits than "LOLCOORZ" and "OMGHUMIDORZ."  Given that the Rockies have been merely average - if not worse - at coming from behind in the last few years, and given that cheating with humidor balls is theoretically close to useless, and given that the Rockies front office is probably trying to build a team that capitalizes on the advantages of Coors Field...  Given all of those things, it takes a particularly hysterical and extremely cynical kind of person to believe that the Rockies are getting away with some awful sin against the sanctity of baseball.*

*O.K.  That's the end of the post unless you're a Rockies fan.  If you are, then feel free to read on to the part where I shed any semblance of objectivity and rant for a few sentences.  Enjoy.

So, yes, Tim Lincecum, you and your namby-pamby cry-baby Giants (and your awful, bourgeois Silicon Valley fans, and your too-good-for-everyone-else ballpark*) have officially made it to the top of my baseball hate list.  Higher than the Dodgers, higher than the Yankees.  Even higher than the Red Sox.  Congratulations.

* The cheapest seat at AT&T is $16!  And what kind of baseball stadium sells sushi and has wireless Internet access?  And I thought baseball was supposed to be for everyone.  Give me a $4 Rockpile seat any day.

Humidor!

It's even on ESPN! Rob Neyer, in his blog, is the latest high-profile baseball writer to pick up on the Rockies-might-be-cheaters idea (alternatively, depending on source, "might" could show up as "must").  A whisper and a rumor that began with Giants announcer Jon Miller has now expanded to such proportions that the great gods of Confirmation Bias, Hearsay, and Circumstantial Evidence have taken over.  While most rational people - like Neyer - do not believe the Rockies are cheating, the rampant cynicism of Internet goers everywhere, combined with their love of their own teams, has ignited a firestorm of anti-Rockies hate.

Circumstantial evidence leads the way, of course.  Fans point to Troy Tulowitzki's recent hot-streak, the magical Septembers of 2007, 2009, and, hopefully, 2010, and a handful of impressive comebacks the Rockies have engineered, as if those things are proof of improper humidor usage.  In the process, of course, we're ignoring Miguel Olivo's collapse to below mediocrity, Carlos Gonzalez's recent slump, the whole of the 2008 season, the terrible starts the Rockies have had in other seasons (including this one), and the impressive comebacks other teams sometimes engineer against the Rockies.

My point here, however, is not to argue against circumstantial evidence with circumstantial evidence in the opposite direction.  My point is to ask a very specific question to which I hope to find a very specific answer.  The question is this: if the Rockies were cheating by using non-humidor balls during their own at bats and humidor balls during their opponents at bats, what would we expect the result to be?  As far as I know, for all of the vehemence about this issue, no one has bothered to turn a statistical eye on the situation, and it seems to me that we should probably do so before we start slinging accusations around.

The first thing I want to pull out are historical Park Factors for Coors Field (from baseball-reference.com):

1995 - 128
1996 - 129
1997 - 113
1998 - 125
1999 - 125
2000 - 129
2001 - 121
2002 - 117
2003 - 110
2004 - 119
2005 - 110
2006 - 107
2007 - 109
2008 - 105
2009 - 113
2010 - 120

There's a lot of variability in there, of course, but there's a noticeable difference between what's going on before 2002 (when the humidor was put in) and after.  How big a difference?  Well, let's run some (very basic) statistics.

1995 - 2001 Average: 124.3
1995 - 2001 Standard Deviation: 5.7

2002-2010 Average:  112.2
2002-2010 Standard Deviation: 5.4

The SDs here are not totally valid, because we have too few values to really have a normal distribution of data.  Nevertheless, it is not the case that every year is equal.  If we looked across the league, the same would be true; park effects are subject to variation just as a player's BABIP, or home run totals are.  A full season may be a lot of data, but it's not enough to establish an answer for what the real park effect of a stadium is.  In the case of Coors, it seems as though there's a 10-15 percent range, for example, which is fairly substantial.

Regardless, there's a difference here.  From 1995-2001, Coors inflated scoring by an average of 24 percent.  From 2002-2010, that number has fallen to 12 percent.  In real terms, that means that 5 runs elsewhere, in the pre-humidor era, was equal to about 6 runs at Coors, while 5 runs in the humidor era is worth 5.5 at Coors now.

Now if we look at Tom Tango's wonderful Run Expectancy Spreadsheet, we figure out how much of a difference we can expect a half-inning of non-humidor balls might make.  The leftmost column in Tango's sheet is for "run environment," meaning we can calculate the expected runs per inning depending on the number of runs per game the environment in question yields.  The National League this season is very nearly a 4.40 run environment (as in, 4.4 runs per team per game), which means that the Run Expectancy each inning is 0.489.

Coors Field with humidor is probably close to a 4.95 environment, yielding a .55 Run Expectancy per inning.  Coors without humidor jumps up to a 5.45 run environment, which means a .606 RE.

The short-form, here, is that, if the Rockies are cheating late in games (which seems to be the conspiracy theory; I haven't heard it suggested that the Rockies are doing this all game), we'd expect them to see a jump from .55 runs per inning to .606 runs per inning once they switch out the balls.  Undoubtedly the sample size here is going to be too small to make conclusions if we go straight to the data right now, so let's look at a little more theory.

The assumption in our Rockies Cheat theory is that Colorado switches out the balls when they're behind late in games.  Let's start by looking at a single inning - the ninth.  If the Rockies are down by 1 run in the bottom of the ninth, how much does switching out humidor balls for non-humidor balls help?  Well, the likelihood of scoring at least one run - and thus tying or winning the game - with humidor balls is about 29%.  The likelihood of the same with non-humidor balls is about 32%.  The likelihood of scoring two or more - and thus winning outright - with humidor balls is 14%, while the same with non-humidor balls is about 16%.

Let's think about this.  If the Rockies are down by a run in the ninth inning, the switch from humidor balls to non-humidor balls will get them a tie only 3% more often, and a win only 2% more often.  Over the course of the season, that comes out, roughly, to somewhere between zero and one games.  If the Rockies are switching humidor balls for non-humidor balls in the ninth inning, they're not getting that much benefit from it.

Of course, you could argue that they start switching in the seventh inning.  Suddenly that 3% difference between 29 and 32 turns into... a 4% difference (between roughly a 65% and 69% chance of scoring at least one run in one of the three innings respectively).  Considering that, humidor balls or not, the other team continues to hit as well, the odds of winning a game down by a run in the seventh inning are not hugely different for the Rockies in either of those situations.

Upping the deficit here will do what you might expect, decrease the likelihood of a comeback and, in the process, decrease the difference between humidor and non-humidor balls.  You might argue that homers become more likely with non-humidor balls, but that's covered already in the change in the park factor.  And, what's more, the exact point here is that the increased odds of hitting a homer with non-humidor balls compared to humidor ones is probably so small in a given at bat that it's negligible.

I know that this brief theoretical look at the humidor proves nothing, but I hope it does show that, in order for the Rockies to really benefit from putting different balls in play, they'd have to do it systematically and at almost all times over the course of the season.  Considering the likelihood that they'd get caught doing that would skyrocket (compared to just doing it close and late in games), I don't see any reason for them to risk it.

I guess the point here is, if the Rockies are cheating by mixing in non-humidor balls in late innings, they should really stop.  Not only is MLB likely to find out in the long run (or the short run), they're not even benefiting that much from doing it.  Sure, those one or, let's be generous, two extra wins might mean the difference between the watching the playoffs from the dugout or from the living room couch, but that effect is far more subtle than what the hysterical cries of the masses (and Jon Miller) suggest.  The implication is and has been that the Rockies win so much at home principally because they're cheating in the late innings, and that's just patently absurd.  Even if they are cheating, they're getting so little from it that it would take 50 to 100 games to see even a one game difference.