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?
Showing posts with label data analysis. Show all posts
Showing posts with label data analysis. Show all posts
Friday, April 22, 2011
Tuesday, February 15, 2011
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.
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:
I then did the same with Standard Deviation of winning percentage:
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:
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.
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" |
[(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) |
 |
| Competitiveness (Y) against STDEV of Wpct (X) |
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.
Tuesday, February 8, 2011
NBA League Size and Competitiveness, Part Two: The Data
"Errors using inadequate data are much less than those using no data at all." - Charles Babbage
That is the spirit with which this post will proceed. The question we're trying to get at is whether or not a larger league in the NBA (or, really, in any sport) leads to a more "diluted" product. I've reinterpreted this question to be the following: is the league more or less competitive when there are more teams? As discussed in Part One, it's not easy to really tell where the overall talent level of a league is because all the statistics players compile - all the games they play, the championships team win, and so on - are contextual. The best player from the 1950s was still the best player from the 1950s, and looks great in retrospect, even if he wouldn't even make an NBA roster today.
Therefore, I transformed "diluted" into "competitive," because it seems to me that the one stands for the other. That is, when we think the league is diluted, what we're really saying is that the league is not competitive, that there are too many players who are not good enough to hang with the few good ones, and that the few good ones are causing a small set of teams to dominate. In a non-diluted league - in a competitive league - "everyone has a good team," to use Bill Simmons's language from my last post. The result, no one - or few people - have a team that just trounces everyone else.
So today we're going to make a first pass at the data. That first pass? Looking, simply, at the standard deviation of winning percentage for each year in NBA (and ABA) history. When was the league the most competitive (smallest standard deviation), when was it the least competitive (largest standard deviation), and is there any discernible trend as the league expands (does a larger league tend to be more or less competitive)? Without further ado, here's a graph of our results. X-axis is number of teams, Y-axis is standard deviation of winning percentage.
As you can see, there is a slight upwards trend here, but it's pretty small. The R value (R-squard is on the graph) is about 0.17, which is not really significant unless you're doing social sciences research. Nevertheless, a big reason why our correlation is so small is how spread out the standard deviations of winning percentage were when there were only eight to ten teams in the league. As you can see, the left-most data points are much, much more spread out than the rightmost, with values ranging from barely over 0.05 all the way to almost 0.20. What does this mean? It means that, in the league's most competitive season a mere 5% separated average teams from good teams, and almost everyone was within 10%. Put in sports-fan friendly terms, the best winning percentage in the league was about .600, while the worst was about .400. That's baseball territory. On the other hand, in the least competitive season, the separation led to a best team with an .800 winning percentage and a worst team with a .200 winning percentage. Now, that's not precise (we'll get into the exact numbers shortly), but that's roughly what standard deviation tells you.
So, back when there were only eight professional teams, there was a huge variety from year to year. Of course, with only eight teams we expect more variety in standard deviation, because, hey, fewer data points means each data point has more influence. Thus, if one team wins 90% of their games one season in an eight team league, that value is going to skew the overall standard deviation much more than if one team wins 90% of their games in a 30 team league. And, indeed, the 95-96 Chicago Bulls (who went 72-10) did not make 95-96 anywhere close to one of the least competitive seasons in NBA history. Had that happened in 1960, the story would have been different. For example, one of the "least competitive" - by standard deviation of winning percentage - seasons in NBA history was 1952, when a 12-57 Philadelphia team joined a 16-54 Baltimore team to drag the whole league down.
If we take only the seasons since the merger - that is, only seasons in which the league has more than 20 teams, we get the following instead:
Now we have an R value of .46, which is getting much closer to significant. Indeed, while random variation obviously plays a huge roll - as do hard-to-quantify things like player skill and pre-NBA training, as well as injury management and so on - there seems to be little doubt that larger leagues are at least somewhat less competitive, according to standard deviation of winning percentage. Consider that there have been only five seasons in which the SD of winning percentage was under 0.15 since the league went to 25 teams in 1988, whereas there were over 20 such seasons in the 40 years before then.
What this really shows, though, is not competitiveness or dilution, but talent distribution. That is, regardless of the level of talent in the league at any given time, the more spread out that talent is, the lower the standard deviation of winning percentage will be. The more concentrated, conversely, the higher the standard deviation of winning percentage will be. Whether this is a measure of dilution is up for debate. Also, while in a smaller league a larger standard deviation here might mean less competitiveness (one or maybe two dominant teams), in a 30 team league it might be exactly what we want (5 or 6 really good teams).
For example, this season the Miami Heat have Dwayne Wade, LeBron James, and Chris Bosh. The Los Angeles Lakers have Lamar Odom, Kobe Bryant, and Pau Gasol. The Boston Celtics have Kevin Garnett, Paul Pierce, Ray Allen, and Rajon Rondo. Now, any of those ten players would be the best or second best player on most other teams. Whether because of finances, smarts, collusion, or some combination of factors, we're currently watching a league where talent has conglomerated onto a small set of teams that routinely beat up on inferior opposition. While I didn't run the (still changing) numbers from this season's NBA, so far there's a team with an .840 winning percentage (San Antonio), three teams above .700 (Dallas, Miami, Boston), and six more teams above .600 (Chicago, Atlanta, Orlando, Oklahoma City, Los Angeles, New Orleans). On the other side of the coin, there's a .154 Cleveland team, plus five other teams below .300 (Sacramento, Minnesota, Washington, Toronto, and New Jersey).
Is this season's NBA competitive or not? There are, at this point, ten legitimately good teams, any of whom - given the right breaks - could win the NBA Finals. That sounds extremely competitive to me. On the other hand, there are also at least six teams that are flat out awful, meaning that a large portion of each day's games are over before they start. Is Cleveland really going to beat Miami? Does Minnesota stand a chance against Oklahoma City? Even though upsets happen, I doubt any circumstance would arise where a fan would feel like one of those inferior teams really deserved to beat one of the top ones. They would need lots of lucky breaks. And that, I think, is a mark of an uncompetitive league, when the bottom third of the league stands little to no chance against the top third.
But wait. Does that mean the league is uncompetitive, or does it just mean that talent is distributed unevenly? The latter is certainly true. The former is more a question of taste and perspective. We could say the same about the league being diluted. When it comes down to it, if you make the league smaller, players who seemed great in a 30 team league will look good, and players who seemed good will look average. Does that mean the league is better or worse? Or does it mean that our perspective changes?
Consider a historical example. When the ABA and the NBA merged for the 1976-1977 season, the NBA had one of its least competitive seasons ever, with a standard deviation of winning percentage under .100. Bill Simmons says, in The Book of Basketball, that this one time the league actually under-expanded, as the 18 teams from the NBA and the 8 remaining viable teams from the ABA became 22 instead of 26. That meant that a lot of ABA talent got redistributed to (mostly) bad NBA teams, meaning that talent was distributed about as evenly as ever in the history of the league. The 53-29 Lakers lead the NBA that season, with a 50-32 Denver and 50-32 Philadelphia on their heels. Those were the only three teams that won 60% of their games or more.
So where does 1976-77 sit in terms of dilution, competitiveness, and distribution of talent? Really, we can only answer the ladder. Talent was widely distributed. Was the league diluted? Was it competitive? That's a matter of opinion. Because talent was widely distributed, it was certainly competitive in a broad sense, but many fans would rather see great teams (and, by extension, terrible teams) than good ones (and merely bad ones). As far as dilution, that's a more complicated question still.
See, when the league goes from 8 teams to, say, 12 teams, we'll tend to think of it as diluted because players who weren't previously good enough now are. Similarly, contraction seems to eliminate dilution, because suddenly all of those marginal players are gone. But give it ten years after expansion and contraction, and we no longer feel that way, because it's a matter of perspective and perception. If the NBA cut 10 teams this offseason, the result would definitely be a short-term feeling of "raising the level" of the league, and probably increased competitiveness in the sense of a smaller standard deviation of winning percentages. However, after 10 seasons of the new, 20 team NBA, we'd get used to seeing guys who had previously been their team's #1 as role players on the "deeper" teams in the smaller league. New draft picks who once would have been franchise guys for bad teams would suddenly never be at the top of the league. These new would-be stars, however, would never be thought of as franchise players who turned into role players. We'd just consider them role players. Suddenly, over time, the league would start to look a lot like it does now, only with fewer teams.
The same goes in the other direction. A more diluted league is all well and good to talk about, but no one talks about how diluted NCAA Division I college basketball is, despite the fact that it adds new teams almost every year. Sure, talent distribution is pretty extreme in the NCAA, but even so there are usually a good 20 or so teams that have a legitimate chance to win the Tourney every season (if you think this is an exaggeration, consider Butler), given the right breaks, and a favorable series of match-ups in March Madness. Is the NCAA diluted? Maybe, in some sense, but in another sense it's almost a crazy question to ask.
I would argue the same is true in the NBA. Is the NBA diluted or not? That's not really a good question, because being diluted is relative, and the stats players compile are relative, and even wins and losses are relative. Bill Simmons believes the NBA is diluted because he grew up watching a league with a dozen teams in it. I don't, because I grew up watching a league with 27-30 teams in it. NCAA fans are used to the 400-something Division I teams, so there's never really a discussion.
What we do have, however, are some interesting measures of talent distribution and, in some sense, competitiveness. We've already seen the trend - as the league expands, there is both a tightening up of standard deviations of winning percentage (less variety from season to season), and a slight (very slight) upwards trend. Next time, we'll dive a little deeper into that data and look at some of the outlier seasons. Moreover, we haven't given up on the competitiveness question - when has the league been most competitive? With more teams or with fewer? - so we're going to tease out only the good teams and run the same analysis here on them (that is, how many good teams are there in a season, and how good are they). Stay tuned.
That is the spirit with which this post will proceed. The question we're trying to get at is whether or not a larger league in the NBA (or, really, in any sport) leads to a more "diluted" product. I've reinterpreted this question to be the following: is the league more or less competitive when there are more teams? As discussed in Part One, it's not easy to really tell where the overall talent level of a league is because all the statistics players compile - all the games they play, the championships team win, and so on - are contextual. The best player from the 1950s was still the best player from the 1950s, and looks great in retrospect, even if he wouldn't even make an NBA roster today.
Therefore, I transformed "diluted" into "competitive," because it seems to me that the one stands for the other. That is, when we think the league is diluted, what we're really saying is that the league is not competitive, that there are too many players who are not good enough to hang with the few good ones, and that the few good ones are causing a small set of teams to dominate. In a non-diluted league - in a competitive league - "everyone has a good team," to use Bill Simmons's language from my last post. The result, no one - or few people - have a team that just trounces everyone else.
So today we're going to make a first pass at the data. That first pass? Looking, simply, at the standard deviation of winning percentage for each year in NBA (and ABA) history. When was the league the most competitive (smallest standard deviation), when was it the least competitive (largest standard deviation), and is there any discernible trend as the league expands (does a larger league tend to be more or less competitive)? Without further ado, here's a graph of our results. X-axis is number of teams, Y-axis is standard deviation of winning percentage.
 |
| X is number of teams, Y is standard deviation of winning percentage |
As you can see, there is a slight upwards trend here, but it's pretty small. The R value (R-squard is on the graph) is about 0.17, which is not really significant unless you're doing social sciences research. Nevertheless, a big reason why our correlation is so small is how spread out the standard deviations of winning percentage were when there were only eight to ten teams in the league. As you can see, the left-most data points are much, much more spread out than the rightmost, with values ranging from barely over 0.05 all the way to almost 0.20. What does this mean? It means that, in the league's most competitive season a mere 5% separated average teams from good teams, and almost everyone was within 10%. Put in sports-fan friendly terms, the best winning percentage in the league was about .600, while the worst was about .400. That's baseball territory. On the other hand, in the least competitive season, the separation led to a best team with an .800 winning percentage and a worst team with a .200 winning percentage. Now, that's not precise (we'll get into the exact numbers shortly), but that's roughly what standard deviation tells you.
So, back when there were only eight professional teams, there was a huge variety from year to year. Of course, with only eight teams we expect more variety in standard deviation, because, hey, fewer data points means each data point has more influence. Thus, if one team wins 90% of their games one season in an eight team league, that value is going to skew the overall standard deviation much more than if one team wins 90% of their games in a 30 team league. And, indeed, the 95-96 Chicago Bulls (who went 72-10) did not make 95-96 anywhere close to one of the least competitive seasons in NBA history. Had that happened in 1960, the story would have been different. For example, one of the "least competitive" - by standard deviation of winning percentage - seasons in NBA history was 1952, when a 12-57 Philadelphia team joined a 16-54 Baltimore team to drag the whole league down.
If we take only the seasons since the merger - that is, only seasons in which the league has more than 20 teams, we get the following instead:
Now we have an R value of .46, which is getting much closer to significant. Indeed, while random variation obviously plays a huge roll - as do hard-to-quantify things like player skill and pre-NBA training, as well as injury management and so on - there seems to be little doubt that larger leagues are at least somewhat less competitive, according to standard deviation of winning percentage. Consider that there have been only five seasons in which the SD of winning percentage was under 0.15 since the league went to 25 teams in 1988, whereas there were over 20 such seasons in the 40 years before then.
What this really shows, though, is not competitiveness or dilution, but talent distribution. That is, regardless of the level of talent in the league at any given time, the more spread out that talent is, the lower the standard deviation of winning percentage will be. The more concentrated, conversely, the higher the standard deviation of winning percentage will be. Whether this is a measure of dilution is up for debate. Also, while in a smaller league a larger standard deviation here might mean less competitiveness (one or maybe two dominant teams), in a 30 team league it might be exactly what we want (5 or 6 really good teams).
For example, this season the Miami Heat have Dwayne Wade, LeBron James, and Chris Bosh. The Los Angeles Lakers have Lamar Odom, Kobe Bryant, and Pau Gasol. The Boston Celtics have Kevin Garnett, Paul Pierce, Ray Allen, and Rajon Rondo. Now, any of those ten players would be the best or second best player on most other teams. Whether because of finances, smarts, collusion, or some combination of factors, we're currently watching a league where talent has conglomerated onto a small set of teams that routinely beat up on inferior opposition. While I didn't run the (still changing) numbers from this season's NBA, so far there's a team with an .840 winning percentage (San Antonio), three teams above .700 (Dallas, Miami, Boston), and six more teams above .600 (Chicago, Atlanta, Orlando, Oklahoma City, Los Angeles, New Orleans). On the other side of the coin, there's a .154 Cleveland team, plus five other teams below .300 (Sacramento, Minnesota, Washington, Toronto, and New Jersey).
Is this season's NBA competitive or not? There are, at this point, ten legitimately good teams, any of whom - given the right breaks - could win the NBA Finals. That sounds extremely competitive to me. On the other hand, there are also at least six teams that are flat out awful, meaning that a large portion of each day's games are over before they start. Is Cleveland really going to beat Miami? Does Minnesota stand a chance against Oklahoma City? Even though upsets happen, I doubt any circumstance would arise where a fan would feel like one of those inferior teams really deserved to beat one of the top ones. They would need lots of lucky breaks. And that, I think, is a mark of an uncompetitive league, when the bottom third of the league stands little to no chance against the top third.
But wait. Does that mean the league is uncompetitive, or does it just mean that talent is distributed unevenly? The latter is certainly true. The former is more a question of taste and perspective. We could say the same about the league being diluted. When it comes down to it, if you make the league smaller, players who seemed great in a 30 team league will look good, and players who seemed good will look average. Does that mean the league is better or worse? Or does it mean that our perspective changes?
Consider a historical example. When the ABA and the NBA merged for the 1976-1977 season, the NBA had one of its least competitive seasons ever, with a standard deviation of winning percentage under .100. Bill Simmons says, in The Book of Basketball, that this one time the league actually under-expanded, as the 18 teams from the NBA and the 8 remaining viable teams from the ABA became 22 instead of 26. That meant that a lot of ABA talent got redistributed to (mostly) bad NBA teams, meaning that talent was distributed about as evenly as ever in the history of the league. The 53-29 Lakers lead the NBA that season, with a 50-32 Denver and 50-32 Philadelphia on their heels. Those were the only three teams that won 60% of their games or more.
So where does 1976-77 sit in terms of dilution, competitiveness, and distribution of talent? Really, we can only answer the ladder. Talent was widely distributed. Was the league diluted? Was it competitive? That's a matter of opinion. Because talent was widely distributed, it was certainly competitive in a broad sense, but many fans would rather see great teams (and, by extension, terrible teams) than good ones (and merely bad ones). As far as dilution, that's a more complicated question still.
See, when the league goes from 8 teams to, say, 12 teams, we'll tend to think of it as diluted because players who weren't previously good enough now are. Similarly, contraction seems to eliminate dilution, because suddenly all of those marginal players are gone. But give it ten years after expansion and contraction, and we no longer feel that way, because it's a matter of perspective and perception. If the NBA cut 10 teams this offseason, the result would definitely be a short-term feeling of "raising the level" of the league, and probably increased competitiveness in the sense of a smaller standard deviation of winning percentages. However, after 10 seasons of the new, 20 team NBA, we'd get used to seeing guys who had previously been their team's #1 as role players on the "deeper" teams in the smaller league. New draft picks who once would have been franchise guys for bad teams would suddenly never be at the top of the league. These new would-be stars, however, would never be thought of as franchise players who turned into role players. We'd just consider them role players. Suddenly, over time, the league would start to look a lot like it does now, only with fewer teams.
The same goes in the other direction. A more diluted league is all well and good to talk about, but no one talks about how diluted NCAA Division I college basketball is, despite the fact that it adds new teams almost every year. Sure, talent distribution is pretty extreme in the NCAA, but even so there are usually a good 20 or so teams that have a legitimate chance to win the Tourney every season (if you think this is an exaggeration, consider Butler), given the right breaks, and a favorable series of match-ups in March Madness. Is the NCAA diluted? Maybe, in some sense, but in another sense it's almost a crazy question to ask.
I would argue the same is true in the NBA. Is the NBA diluted or not? That's not really a good question, because being diluted is relative, and the stats players compile are relative, and even wins and losses are relative. Bill Simmons believes the NBA is diluted because he grew up watching a league with a dozen teams in it. I don't, because I grew up watching a league with 27-30 teams in it. NCAA fans are used to the 400-something Division I teams, so there's never really a discussion.
What we do have, however, are some interesting measures of talent distribution and, in some sense, competitiveness. We've already seen the trend - as the league expands, there is both a tightening up of standard deviations of winning percentage (less variety from season to season), and a slight (very slight) upwards trend. Next time, we'll dive a little deeper into that data and look at some of the outlier seasons. Moreover, we haven't given up on the competitiveness question - when has the league been most competitive? With more teams or with fewer? - so we're going to tease out only the good teams and run the same analysis here on them (that is, how many good teams are there in a season, and how good are they). Stay tuned.
Friday, October 29, 2010
On Science Education
I am not a science teacher by trade, but I have found myself teaching science more than any other subject area. Perhaps this is in part a result of my upbringing - my mother is a science teacher - and perhaps a result of pure chance. Regardless of why science has found me and I have found science, my background as a graduate of St. John's has followed close at hand, with the result that I think about science a little differently than many people do, a fact that has helped me to understand science myself, but has not always been to my advantage.
What do I mean by that? Well, one of the most fundamental but unarticulated problems in science education is a failure among the important people in the process to agree on what science really is. That's not to say they should agree, or that agreement is even possible, but rather to say that the lack of a clear definition of science has led to a hodge-podge of curricular methodologies and pedagogies that are non-complementary, and which do more to alienate and confuse students than to empower or interest them.
Scientists, ironically, are probably the most to blame for this situation. There is great lamentation in scientific world about how poorly students do in science. The solution, it seems to these people, is to make science more "real" for students. That is, to align science classes closer to their own experiences as scientists. The problem is, they perceive science to be, generally, a fairly static thing. The average scientists definition of science (and I don't have research to back this up, just my own experiences) seems to be something like this: Science is a set of well-established theories and facts about the natural world arrived by employing a fixed methodology to places where our knowledge is lacking, in order to expand our understanding.
Now there's nothing particularly wrong with this, except it's extremely boring and a waste of student's time. The idea that science is, at its heart, about theories and facts, and an easy-to-use scientific method, to me trivializes the real efforts of science. No, science is not just collecting data and analyzing ad infinitum, the real power of science to affect people's lives lies in something more fundamental to it. To me, science is about a process that is dynamic and contextual. Scientific knowledge is conditional and flexible. Being a scientist is about creativity, critical thinking, and learning.
How much more interesting is this perspective to students? Frankly, they probably don't care how we define science. More important is the result of this perspective on curriculum, on pedagogy, on what happens in the classroom. In the former, the scientist's classroom, students sit and listen to lectures, they engage in laboratory sessions with known answers, they are asked multiple choice questions, they fill in worksheets with word banks. Basically, they're miserable. Even a field trip, in the traditional science classroom, generally leads to little more than the dissemination of information, the collection of useless and meaningless data, or the acquisition of some boring science "skill" that is irrelevant to a student's life.
On the other hand, the latter classroom is organized around the concept of science as inquiry, meaning students are encouraged to develop a more sophisticated understanding of how science really works. That is, by giving students enough structure to keep them on task, but enough freedom to let them develop their own observations, questions, hypotheses, and even experiments and conclusions, students get to learn the real pitfalls of scientific work. What's more, they still learn the content. Perhaps not as much as if they were just lectured at for an hour straight, but what they do learn, they learn better. More importantly, memorizing facts, equations, theories, and methods is a waste of time in our modern world; better to learn how to synthesize, how to analyze, and how to ask good questions.
To illustrate: How many of you readers out there remember anything about how to calculate the effect of friction on a moving body from your high school physics class? For those of you who don't remember, how long do you think it would take you to look it up? I'll give you hint, type in "friction" in Google, and click on the Wikipedia page. There's your equation, plus explanations of how to use it. Good thing your science teachers wanted you to memorize all that.
Beyond acquiring facts, which is manifestly a waste of time, the other biggest problem with traditional science education is that it is built around collecting data. I certainly acknowledge that good data collection is important, but I will also say that data in itself is worthless unless there's some kind of analysis on the other end, not to mention some kind of purpose for collecting it on the front end. It's easy, in pre-made experiments, to point to the supposed "purpose" of certain data, but the whole point of good science education, to my mind, is to get students to make those decisions themselves. What data should they collect? Why? How will they use it?
Now an experienced educator will respond by saying that they need to see that process in action before they can do it themselves, and so we should provide them with situations where they are not designing experiments, where they are working with fake data, where they are performing analysis without doing the legwork to get there. That's fair, but only if we call attention to why we're doing that. Many teachers emphasize the importance of data analysis for its own sake, not as a part of a broader scientific process, and certainly not as a pathway towards meaning.
Ah, there's an interesting word. I suppose, if I had to summarize the two approaches to science education I've discussed here, I would say that the first is about information and the second is about meaning. The problem is, looking for meaning in science is not encouraged by scientists for reasons that are difficult to fathom (though the Freudian in me wants to suggest mean things about scientists being afraid of meaning because of the spiritual, emotional, and social emptiness of their own pursuit of information). The cries that students do poorly in science, to me, reverses the reality: science does poorly for students. Make science real, make it authentic, make is about ideas and not facts, make it about processes and not methods, make it about discussions and not dictation, and then you'll see students do well.
Science is a liberal art, in the root sense of the term. The study of science can help free you from other people's conclusions, from propaganda, from drug commercials that say "studies show..." Science, however, can also bind you and blind you. Unfortunately, the classroom (and, more importantly, the legislator's table and the teacher training program) is, in this discipline as in many others, a battlefield. A battlefield where the "fluffy," holistic, more authentic side is losing, not because it is actually worse, but because it's harder to do well, harder to assess, harder to standardize. Those are fair criticisms, but it might be that part of what's wrong in education, broadly, is that we shy away from what's better but harder too often.
What do I mean by that? Well, one of the most fundamental but unarticulated problems in science education is a failure among the important people in the process to agree on what science really is. That's not to say they should agree, or that agreement is even possible, but rather to say that the lack of a clear definition of science has led to a hodge-podge of curricular methodologies and pedagogies that are non-complementary, and which do more to alienate and confuse students than to empower or interest them.
Scientists, ironically, are probably the most to blame for this situation. There is great lamentation in scientific world about how poorly students do in science. The solution, it seems to these people, is to make science more "real" for students. That is, to align science classes closer to their own experiences as scientists. The problem is, they perceive science to be, generally, a fairly static thing. The average scientists definition of science (and I don't have research to back this up, just my own experiences) seems to be something like this: Science is a set of well-established theories and facts about the natural world arrived by employing a fixed methodology to places where our knowledge is lacking, in order to expand our understanding.
Now there's nothing particularly wrong with this, except it's extremely boring and a waste of student's time. The idea that science is, at its heart, about theories and facts, and an easy-to-use scientific method, to me trivializes the real efforts of science. No, science is not just collecting data and analyzing ad infinitum, the real power of science to affect people's lives lies in something more fundamental to it. To me, science is about a process that is dynamic and contextual. Scientific knowledge is conditional and flexible. Being a scientist is about creativity, critical thinking, and learning.
How much more interesting is this perspective to students? Frankly, they probably don't care how we define science. More important is the result of this perspective on curriculum, on pedagogy, on what happens in the classroom. In the former, the scientist's classroom, students sit and listen to lectures, they engage in laboratory sessions with known answers, they are asked multiple choice questions, they fill in worksheets with word banks. Basically, they're miserable. Even a field trip, in the traditional science classroom, generally leads to little more than the dissemination of information, the collection of useless and meaningless data, or the acquisition of some boring science "skill" that is irrelevant to a student's life.
On the other hand, the latter classroom is organized around the concept of science as inquiry, meaning students are encouraged to develop a more sophisticated understanding of how science really works. That is, by giving students enough structure to keep them on task, but enough freedom to let them develop their own observations, questions, hypotheses, and even experiments and conclusions, students get to learn the real pitfalls of scientific work. What's more, they still learn the content. Perhaps not as much as if they were just lectured at for an hour straight, but what they do learn, they learn better. More importantly, memorizing facts, equations, theories, and methods is a waste of time in our modern world; better to learn how to synthesize, how to analyze, and how to ask good questions.
To illustrate: How many of you readers out there remember anything about how to calculate the effect of friction on a moving body from your high school physics class? For those of you who don't remember, how long do you think it would take you to look it up? I'll give you hint, type in "friction" in Google, and click on the Wikipedia page. There's your equation, plus explanations of how to use it. Good thing your science teachers wanted you to memorize all that.
Beyond acquiring facts, which is manifestly a waste of time, the other biggest problem with traditional science education is that it is built around collecting data. I certainly acknowledge that good data collection is important, but I will also say that data in itself is worthless unless there's some kind of analysis on the other end, not to mention some kind of purpose for collecting it on the front end. It's easy, in pre-made experiments, to point to the supposed "purpose" of certain data, but the whole point of good science education, to my mind, is to get students to make those decisions themselves. What data should they collect? Why? How will they use it?
Now an experienced educator will respond by saying that they need to see that process in action before they can do it themselves, and so we should provide them with situations where they are not designing experiments, where they are working with fake data, where they are performing analysis without doing the legwork to get there. That's fair, but only if we call attention to why we're doing that. Many teachers emphasize the importance of data analysis for its own sake, not as a part of a broader scientific process, and certainly not as a pathway towards meaning.
Ah, there's an interesting word. I suppose, if I had to summarize the two approaches to science education I've discussed here, I would say that the first is about information and the second is about meaning. The problem is, looking for meaning in science is not encouraged by scientists for reasons that are difficult to fathom (though the Freudian in me wants to suggest mean things about scientists being afraid of meaning because of the spiritual, emotional, and social emptiness of their own pursuit of information). The cries that students do poorly in science, to me, reverses the reality: science does poorly for students. Make science real, make it authentic, make is about ideas and not facts, make it about processes and not methods, make it about discussions and not dictation, and then you'll see students do well.
Science is a liberal art, in the root sense of the term. The study of science can help free you from other people's conclusions, from propaganda, from drug commercials that say "studies show..." Science, however, can also bind you and blind you. Unfortunately, the classroom (and, more importantly, the legislator's table and the teacher training program) is, in this discipline as in many others, a battlefield. A battlefield where the "fluffy," holistic, more authentic side is losing, not because it is actually worse, but because it's harder to do well, harder to assess, harder to standardize. Those are fair criticisms, but it might be that part of what's wrong in education, broadly, is that we shy away from what's better but harder too often.
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