Before the real games begin, I need to tie up a loose end from last year. Luck plays a role in all sports, but it seems more so in college hoops. It’s one of the reasons the sport is so unpredictable. Sure, talent and coaching are overwhelming factors in determining which teams succeed and which teams don’t. But wacky bounces and lucky breaks are what make things interesting. Along those lines, last year’s championship game, in which Syracuse beat Kansas 81-78, presented an opportunity to examine just how luck plays a role in a game between two nearly equal teams.
Kansas had one of the worst free throw shooting performances in championship history, making only 12 out of 30, which can be cited as one of the reasons they lost. Was their awful shooting simply bad luck? At first glance, one would think free throws are skill – and they are. But even the best shooting teams (and KU was not one of them in 2003) have an awful game or two from the line every season, and I don’t think they have any control over when they occur.
An interesting site to check out is Alan Reifman’s Hot Hand in Sports site, which is devoted to proving that a hot shooting (or other activity) streak can be explained by random chance. To put it another way, let’s say Joe Blow is a 70% free throw shooter. If he makes 8 in a row, he has no more (or less) than a 70% chance of making the ninth in a row. Streaks in individual performance are mostly – if not totally – random. This concept has been met with skepticism when presented to most sports fans, but there is a lot of compelling evidence presented or linked to on the site. So if you don’t believe it, I urge you check it out. To be fair the quality of the defense as well as shot selection also must play some role in streakiness, but I am focusing free throws here, so those factors won’t matter.
Alan mentions on the bottome of this page that based on random chance given Kansas’ season-long free throw percentage, their performance in the NCAA Championship game would only happen twice in 1,000 games. This is such an outrageous fact, that it leads me to the conclusion that there was something more that chance going on here. But this deserves a little more examination. Reifman uses Kansas’ team FT percentage in the calculation. To be more accurate, we should use the season FT percentage of the players who shot the free throws and give weight based on how many free throws each player shot. Doing this, using season FT percentages calculated before the game, yields an expected FT percentage for KU of 63.7 (Refiman used 67%). This makes the poor free throw shooting less rare, only expected to happen 7 times in a 1,000. Still, it seems to be out of the bounds of random chance. (One can use a binomial probability calculator to determine this. In this case n=30, k=12, p=63.7.)
The really really bad shooting can be isolated by half. In the first half KU shot 8-13 (61.5%), which is how many they would be expected to make given a season-long FT percentage for the shooters of 64.3. In the second half they went 4-17 (23.5%), with a FT percentage for the shooters of 63.3. Again, using the binomial calculator, the chances of this are less than one in 1,000. Assuming they shot 17 FT’s in a half for every game the next 15 years, one would only expect them to make 4 or fewer in one of those halves.
The second half debacle can be reduced to two players: Nick Collison (1-7) and Jeff Graves (2-7). Collison’s season FT% was .653, but he had been much worse beginning with the Arizona game on January 25th (58-106, .547). Using this value gives KU an expected 2nd half percentage of .589, although this still would mean the woeful performance would occur only once in 370 times.
The numbers are still so outrageous that this appears to be a case where random chance cannot totally explain streakiness. The temptation is to say Kansas “choked”, partly because it has been a term used to describe their post-season performance in the past. But that’s too simplistic. An additional explanation on the poor shooting is that Collison and Graves both played their most minutes of the year (Collison played 40, his season average was 32; Graves played 37 compared to an average of about 20). So fatigue probably played a role. But bad luck also played a role. Two mediocre free throw shooters both happened to have one of their worst FT shooting games ever in the most important game of their careers.
Addendum: Amazingly, Bucknell shot 1-17 (6%) from the line Friday night in a 64-52 loss to #3 Michigan St., a game in which they led with 5 minutes to go. Later in the year I’ll check out how unlikely that was. I am sure it will put the Kansas effort to shame.