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Intro to a geeky stat
By rbk | November 28, 2007
The regular season is now 20% over (6 games vs. D-I played, 24 to go). I figured that this was as good a time as any to round up the relevant stats and take a peek at how we’re doing, as well as how we stack up against our competition and the the nation.
Adjusted for schedule, the Vols rank 19th in the nation offensively (117.5 PP100) and 23rd defensively (83.6 PP100) . Not bad. Now I will introduce another fun (and geeky) stat: Pythagorean expected win percentage.
Pythagorean expected win percentage (or “Pythag” as I describe it verbally) has its origins in the statistical analysis of baseball teams. Essentially, it was designed to calculate how many games a team should have won, based on how many runs it scored and how many runs it allowed. Obviously, most teams aren’t going to match this expectation exactly– they may win one game 15-2 and then lose the next 8-7. Then they have scored a bunch more runs than they allowed, but are still just 0.500. Get the picture? Anyway, the basic formula is
E(W%) = runs scored^2 / (runs scored^2+runs allowed^2)
For this particular team, E(W%) = 11.5^2 / (11.5^2+4.5^2) = 0.867. You can see that they are perhaps playing better than their record would indicate. If it weren’t just 2 data points (games) we might like to use this information to predict that they will win more games than they will lose, and to date have just been “unlucky” to achieve only a 0.500 record.
A similar formula can be used for basketball, using points scored and points allowed– but we have a problem. The scales between these two sports (total scores per game) are very different, so we can’t expect one formula to work for both. In fact, the formula used for basketball can be modified to more closely match outcomes. The end result is that instead of squaring all terms, a higher degree is used for the exponent– anywhere between 11 and 17, typically. Ken Pomeroy has found that 11.5 is the best exponent to use for NCAA basketball, making the formula
Pythag = points scored^11.5 / (points scored^11.5+points allowed^11.5)
Problem #2– as we’ve already discussed before, tempo matters in basketball. In baseball, there’s no such thing– everyone gets 9 innings, 3 outs per inning. But in basketball, possessions vary by tempo. So we will use our handy dandy tempo-free measures, offensive efficiency and defensive efficiency, in points-per-100-possessions.
If we plug-and-chug, as a math professor used to say, we get a Pythag rating for Tennessee of 0.980. That means Tennessee has played well enough, according to the formula, to expect to win 98% of its games. That’s good enough for #13 in the country, and for what it’s worth, West Virginia and Texas are 1-2 in that stat. Now, the Pythag is a bit inflated at this point in the season. 98%, by the end of the year, will only have been achieved by the top 3 or 4 teams in the nation, and #13 will be more in the 94-96% range.
And of course, we must qualify this by saying most teams have only played 5-7 games or so. These ratings will fluctuate considerably in the next month, and late in the season they will be much closer to being fixed (and accurate).
Now, the way I use this stat is primarily to rank and compare teams– the actual number, as an estimate for win %, is not terribly meaningful to me. But it does represent, in my mind, the most accurate portrayal of how well a team is actually playing. Note that wins and losses play no part in the calculation, so this is strictly quality of play, not outcome. Some teams will play very well and not have a record that reflects it (Kentucky was #14 in Pythag last year but lost 12 games), and other teams will win more games than their Pythag would suggest (Tennessee was #31 last year). What Pythag allows you to do is to look before last year’s UK-UT game and say that both teams play good basketball, and that Kentucky had a good chance of winning (and did in fact win 1 of 2). Poll rankings and RPI do not give you a very reliable way to make this assessment.
This will be a stat I mention frequently, so I thought it was important to give you at least a working knowledge of what it means. Tennessee is off to a good start in Pythag this year, and hopefully it will remain high as we plow into the meat of our schedule.
Topic: Uncategorized | Tags: geek stats, Ken Pomeroy, Pythag
November 28th, 2007 at 4:54 pm
Man that was geeky and biased. Gol Vols!
December 11th, 2007 at 10:13 am
[...] slipping statistically 11 December 2007 — rbk On November 28th, when I introduced the pythag statistic, Tennessee was rated 0.980, good for #13 in the country. In the two weeks since, our pythag rating [...]
January 7th, 2009 at 4:15 pm
[...] when it comes to overall team strength is Pythag (Pythagorean Expected Winning Percentage—see here and here for more on the stat). The number in itself is not that meaningful to me but when used to [...]