Tonight, the bracket for the NCAA Division I Women's Basketball Tournament was revealed; unsurprisingly, the undefeated NCAA basketball 107-win-streak-holding UConn team was the number 1 overall seed. 107 wins dwarfs the previous record, the UCLA Men's 88 wins under (my fellow Boilermaker) John Wooden between January of 1971 and January of 1974 (1).
The probability of a team to have 107 straight wins, given a naive assumption of a 50% chance of winning, is 6.1630E-31% (2). Ignoring the rounding resulting from using 64 bit floating point arithmetic, that is roughly a 1-in-162,259,276,829,213,000,000,000,000,000,000 chance. For comparison, the diameter of the Universe is "only" 5.5E23 miles (3), and the odds of winning the Powerball Jackpot is 1-in-292,201,338 (or 0.0000003422% probability) (4). One would have to win the Powerball 3.8 times to equal the probability of a NCAA basketball team having a streak like UConn has.
Of course, UConn is no average team who would have a 50-50 chance of winning a game. Widely considered one of the most dominant teams ever, during the streak they have only won three games with a margin of fewer than 10 points (5). So to evaluate the probability of UConn setting this streak, I'm going to use, yet again, the Pythagorean expectation (6) to estimate the expected winning percentage for UConn during the seasons of their streak (7). From there I will calculate the probability of UConn's streak using the same method as I did with naive odds. The exponent used will be the 11.5 used by Ken Pomeroy for men's basketball (8). While Ken Pomeroy's ratings include adjustments to points for strength of schedule and pace, I'm not going to do so for this calculation. Since UConn's performance is partially based upon their schedule, adjusting for strength of schedule would mean that would have to be re-accounted for later in the calculation, leading to extraneous work. Pace is not going to be considered for similar reasons; since I'm looking to measure UConn's performance as how well they played but not necessarily how good they are. Adjusting for pace would not improve showing how well they played their previous games. For all basketball scoring statistics, the source is the NCAA's website.
UConn's performance is ridiculous. And they are somehow getting less dominant over the span of their streak, with their Pythagorean expectation reducing year to year. In fact, this past year they were "only" 3rd in scoring offense and 6th in scoring defense. That still made them the only team to be in the top ten in both scoring offense and defense. What is even more absurd is their Pythagorean expectation, which averages over 99.8%. This means that the probability of the 107-game streak is nearly 81%. For reference, I calculated Alabama football this year to have a Pythagorean expectation of 98.61%; they would have had an 81.0614% probability of going 15-0. Of course, their unlikely loss did happen. UConn, if they keep up their performance (which is likely, given this is a year coming off the loss of a number of senior starters) are favored (i.e. a probability of over 50%) to have a streak of 351 games.
So how does UConn's performance compare to UCLA's?
Wooden's UCLA teams during the streak were dominant, but they weren't UConn dominant. They would have only been favored to have a (still respectable) 15 game streak. They would have a 1.8764% chance of their 88 game streak. While still orders of magnitude higher than the naive odds, it doesn't hold a candle to what UConn has done. UCLA would have had a 0.7953% probability of achieving UConn's streak.
UConn's play has been so dominant that they took an accomplishment with literally astronomical odds and made themselves the heavy favorites to do just that. The nearest accomplishment in men's basketball is an astronomically unlikely event that was changed to 'unlikely but plausible' under what is considered historically dominant play. While the fact that women's college basketball has much less parity than the men's game has helped UConn be in a position to make this run, the level of (continuing) dominance of their opponents is an incredible accomplishment. It should not reduce the accomplishments of players and coaches who have worked hard to achieve this either, and can not control the state of the game in general.
What I'm saying is I'm very happy the Boilers are on the other side of the bracket from the Huskies.
References and Footnotes
(1) https://en.wikipedia.org/wiki/Basketball_winning_streaks
(2) 0.5^107=6.1630E-33
(3) https://en.wikipedia.org/wiki/Observable_universe
(4) http://www.lotteryusa.com/powerball/
(5) Against Florida State, Maryland, and Tulane, all during the 2016-2017 season
(6) https://en.wikipedia.org/wiki/Pythagorean_expectation
(7) 2014-2015, 2015-2016, and this season, 2016-2017
(8) http://kenpom.com/blog/ratings-glossary/
The probability of a team to have 107 straight wins, given a naive assumption of a 50% chance of winning, is 6.1630E-31% (2). Ignoring the rounding resulting from using 64 bit floating point arithmetic, that is roughly a 1-in-162,259,276,829,213,000,000,000,000,000,000 chance. For comparison, the diameter of the Universe is "only" 5.5E23 miles (3), and the odds of winning the Powerball Jackpot is 1-in-292,201,338 (or 0.0000003422% probability) (4). One would have to win the Powerball 3.8 times to equal the probability of a NCAA basketball team having a streak like UConn has.
Of course, UConn is no average team who would have a 50-50 chance of winning a game. Widely considered one of the most dominant teams ever, during the streak they have only won three games with a margin of fewer than 10 points (5). So to evaluate the probability of UConn setting this streak, I'm going to use, yet again, the Pythagorean expectation (6) to estimate the expected winning percentage for UConn during the seasons of their streak (7). From there I will calculate the probability of UConn's streak using the same method as I did with naive odds. The exponent used will be the 11.5 used by Ken Pomeroy for men's basketball (8). While Ken Pomeroy's ratings include adjustments to points for strength of schedule and pace, I'm not going to do so for this calculation. Since UConn's performance is partially based upon their schedule, adjusting for strength of schedule would mean that would have to be re-accounted for later in the calculation, leading to extraneous work. Pace is not going to be considered for similar reasons; since I'm looking to measure UConn's performance as how well they played but not necessarily how good they are. Adjusting for pace would not improve showing how well they played their previous games. For all basketball scoring statistics, the source is the NCAA's website.
So how does UConn's performance compare to UCLA's?
Wooden's UCLA teams during the streak were dominant, but they weren't UConn dominant. They would have only been favored to have a (still respectable) 15 game streak. They would have a 1.8764% chance of their 88 game streak. While still orders of magnitude higher than the naive odds, it doesn't hold a candle to what UConn has done. UCLA would have had a 0.7953% probability of achieving UConn's streak.
UConn's play has been so dominant that they took an accomplishment with literally astronomical odds and made themselves the heavy favorites to do just that. The nearest accomplishment in men's basketball is an astronomically unlikely event that was changed to 'unlikely but plausible' under what is considered historically dominant play. While the fact that women's college basketball has much less parity than the men's game has helped UConn be in a position to make this run, the level of (continuing) dominance of their opponents is an incredible accomplishment. It should not reduce the accomplishments of players and coaches who have worked hard to achieve this either, and can not control the state of the game in general.
What I'm saying is I'm very happy the Boilers are on the other side of the bracket from the Huskies.
References and Footnotes
(1) https://en.wikipedia.org/wiki/Basketball_winning_streaks
(2) 0.5^107=6.1630E-33
(3) https://en.wikipedia.org/wiki/Observable_universe
(4) http://www.lotteryusa.com/powerball/
(5) Against Florida State, Maryland, and Tulane, all during the 2016-2017 season
(6) https://en.wikipedia.org/wiki/Pythagorean_expectation
(7) 2014-2015, 2015-2016, and this season, 2016-2017
(8) http://kenpom.com/blog/ratings-glossary/
Comments
Post a Comment