Sunday, May 27, 2012

The Memory of a Basketball Team

Basketball teams should have institutional memory. From one season to the next, some players graduate, others transfer, and a few head to the pros. Although new recruits come in, the players and coaches that remain carry on certain tendencies of the team from the year before, so we should not expect the outcomes in terms of wins and losses or various aspects of offense and defense to be independent from year to year. In other words, the 2012-2013 basketball season should be similar in some ways to that of last year. Sean Miller has added a nice incoming class which includes Brandon Ashley, Grant Jerrett, Mike Korchek, Mark Lyons, Kaleb Tarczewski, and Gabe York. But a number of impactful players remain, like Solomon Hill, Kevin Parrom, Angelo Chol, Jordin Mayes, and Nick Johnson.

In this post, I want to take a closer look at Arizona’s winning percentages from 1970 to 2012 to see to what extent the outcome of a basketball season can be predicted by the outcome of the prior season. This is not a difficult thing to do, and for my fellow nerds out there, the method used for doing so is called serial correlation.

The graph above compares the winning percentages for adjacent years of Arizona basketball from 1970 through 2012. If basketball teams had no institutional memory, there should be no relationship between what happened during prior and subsequent years, but from that graph, that is clearly not the case. In general, the seasons in which the Cats did well were followed by good seasons, and poor years were followed by more losing. The relationship is hardly perfect, but it is real. Notice that there are no examples of very good seasons (win% > .800) followed by atrocious seasons (win% < .500). Nor are there cases of really bad years followed by great ones. It takes time to turn a bad team into a good one, or a good team into one that loses. So, what does this mean for next year’s prospects?

I am going to look at this problem two ways. A simple approach is to just look at the graph above and examine similar cases to last season. In the 11-12 season, the Cats went 23-12, winning 65.7% of their games. How did similar Cats teams from the past fare? One rather depressing case is Lute Olson’s 06-07 team which won 64.5% of their games, a season that was followed by Kevin O’Neill’s team that won only 55.9% of their games, finishing with a 19-15 record. On a more positive note, going from 03-04 to 04-05, the team improved from .667 to .811. Just eyeballing the scatter associated with a winning percentage of .657, one could predict that next year’s team would finish with a winning percentage somewhere in the neighborhood of .400 to .950, a fairly broad range of possible outcomes and one that is not particularly satisfying. On the positive side, a losing season would be unlikely.

The graph above shows the frequency distribution of change in winning percentage season over season from 1970 to 2012. I know that’s a mouthful but bear with me. It just counts how often the Cats’ winning percentage changed by certain amounts. The tallest bar near the center of the graph corresponds to a change in winning percentage ranging from -.05 to +.05, meaning very little change. Again, a bad team one year is most likely to be a bad team the next year. The same is true for a good team or one that falls in between.

There are, however, cases of serious improvement or decline, but they are not common. The greatest improvement the Cats have shown over this time period came in Fred Snowden’s first season as coach beginning in 1972. Snowden turned a losing team (6-20 the year before) to a winning one (16-10), or a change in a winning percentage of +.385. The worst decline the Cats have shown belongs to Lute Olson from the 02-03 to the 03-04 seasons. The team went from a stellar 28-4 record to a still respectable 20-10 finish, or a change of -.208. Although anything is possible from one year to the next, all things are not equally likely.

Using the distribution shown in the second graph, it is statistically a fairly simple matter to predict next year’s winning percentage with better accuracy, although the result is very similar. In brief, there is a 50% chance that the Cats will finish next year with a winning percentage between .557 and .757. There is a 75% chance that will finish between .487 and .827, and there is a 95% chance that they will finish between 0.367 and 0.947, very similar estimate to the one derived before.

In sum, it is clear that one can predict to some extent the performance of a basketball in a season that has not yet happened based on the results of the prior season. Of course, this is one basis used to rank teams before the season even begins, as in the ESPN and AP polls. It should be noted, however, that there is a lot of slop in this system, at least as I have examined it. It would be fascinating to try to narrow these predictions further. For example, do extreme swings up or down in winning percentage correlate with years of major turnover in a program? That’s another problem for another day.

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