Monday, November 19, 2012

Fun with sports math

Sticking with our sports theme for the day—and adding in some statistical analysis because that's what we do around here—I thought I'd share a couple of recent articles about the baseball postseason that I found interesting. First up, from the Freakonomics blog (emphasis mine):
When the playoff in baseball began, 10 teams – and their fans – were very happy.  But the playoffs being what they are, we knew that only one team – and its fans – would actually be happy when the whole thing was over... 
So what did the Tigers and all the other “losers” (and yes, that includes the Yankees) learn from the playoffs? 
For an answer, let me quote the following from The Drunkard’s Walk: How Randomness Rules Our Lives (a wonderful book by Leonard Mlodinow): 
if one team is good enough to warrant beating another in 55% of its games, the weaker team will nevertheless win a 7-game series about 4 times out of 10.  And if the superior team could beat its opponent, on average, 2 out of 3 times they meet, the inferior team will still win a 7-game series about once every 5 match-ups.  There is really no way for a sports league to change this.  In the lopsided 2/3-probability case, for example, you’d have to play a series consisting of at minimum the best of 23 games to determine the winner with what is called statistical significance, meaning the weaker team would be crowned champion 5 percent or less of the time.  And in the case of one team’s having only a 55-45 edge, the shortest significant “world series” would be the best of 269 games, a tedious endeavor indeed! So sports playoff series can be fun and exciting, but being crowned “world champion” is not a reliable indication that a team is actually the best one. (p. 70-71)
So, no, the "best" team doesn't always win the title, because there's just way too much randomness involved, even in a multiple-game sample as opposed to football's one-game sample. That's why it's entertaining. That's also why the Giants beat the Patriots twice, but I digress.

So if the "best" team doesn't always win the title, maybe the "hottest" team does? Let's ask our friends at the Harvard College Sports Analysis Collective.
Every so often, a playoff series in the NHL, MLB, or NBA will be fought between a team that has just come off of a sweep and a team that has barely survived a competitive 7-game series.  While the latter team is still battling and exerting itself in games, the former will be resting, recovering from the 4-game series, and preparing for the next round... 
Each time a series like this occurs, we are given two contrasting arguments by media figures.  On the one hand, the team that swept has had ample time to recuperate from injuries, rest their bodies and arms, and watch video on both potential teams it could face.  On the other hand, in the large gap of time between games, the team could have “lost momentum,” somehow dissolving the focus and chemistry that had led to the team’s initial success... 
Across the NHL, MLB, and NBA, and looking only at matchups where the previous round was also a best-of-7 series, this scenario has only occurred 29 times throughout history.  The team that has swept has won 20 out of these 29 occasions, and has needed, on average, 5.3 games to defeat its next opponent.  This is not too distant from what one would expect; the teams that swept, in general, have better regular season records, so they tend to be stronger than the opponent who has struggled to emerge from a previous series.  The results, however, are more interesting when broken down by sport. 
Out of the 14 times this matchup has occurred in the NBA playoffs, only twice has the team that went to 7 games in the previous series won the next series...  Much more frequently, the team that has swept in the previous series has gone on to win.  Whether the reason for its winning is that it generally has had better records, or because they were well-prepared and well-rested, is impossible to say for sure. 
The NHL had a similar pattern to the NBA, until 1993; since then, 5 out of 6 teams that went to seven games won the next series against the team that had swept... 
In the MLB, this type of matchup has only occurred four times, mainly because the LCS is the only 7-game series that occurs before another series, and the LCS has not always been a 7-game series.  In all four of these matchups... the team which went to 7 games in the LCS won the World Series...
Although the few data points we have suggest such, concluding that rest is more important in the NBA, whereas momentum is more important in the MLB and NHL is impossible.  In truth, both of these components probably impact the outcome of a playoff series, but probably even more important is how good at winning the team is. Out of these 29 series, 21 of them were won by the team with the better winning percentage (or, points for NHL).  Being well-rested is helpful — but being good is even more helpful.
Alright, then. So, over time, the best team does win more often than not, regardless of how "hot" they are. But in any given playoff series, whether the team is "hot" or "good" seems to take a serious back seat to "luck". Good talk. All of this really bring us right back around to the greatest sports cartoon of all time, from XKCD (in case you were wondering, yes, this entire post was just an excuse to run this cartoon again... I love it):

So, enjoy your sports, by all means. But don't get too carried away with building glowing and complex narratives based on the results of the games. More often than not, it's just a lot of random noise.


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