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.

Friday, May 25, 2012

42 Years of (Mostly) Winning

I want to start by looking at one of the simplest measures of success of a basketball team, winning percentage, or the percent of games in which the Cats were victorious over the course of a season. I took these data from Wikipedia, although I only included the seasons since 1970. I have nothing against the team's earlier history, but for my purposes, the 1907-08 coachless team who won 1 of 3 games does not seem particularly germane.

It's also worth keeping in mind that there have been some important rule changes in college hoops that make it difficult to compare data from long ago with those of recent times. The most important of those are perhaps the use of the shot clock, initially 45 seconds when adopted in 1985 and changed to its modern 35 second version in 1993, and the addition of the three-point shot which was first used nationally in 1986. Also, since I've included NCAA tournament years below, it's worth noting that the first use of the 64 team format occurred in the 85-86 season, Lute Olson's third season as head coach. No doubt, some of Fred Snowden's teams that did not make the tournament at the time would have a good shot today.

The graph above (click on it to enlarge) shows the team's winning percentage from 1970 through 2012, or 42 seasons of NCAA basketball. Over this time, the team has had seven different coaches, although Lute Olson and Fred Snowden account for 81% of this time. In all the Cats have won a respectable 67.5% percent of their games (882-424), or just over two wins for every loss. In 42 years, the Cats have only had seven losing seasons (winning fewer than 50% of their games), the most recent being Lute Olson's first year as coach, the 83-84 season. This is why it has been good be an Arizona fan, at least over the last three decades. Like Olson, Sean Miller almost joined the list of losing coaches in his first year when the Cats went 16-15 just three seasons ago.

For obvious reasons, the major dips in winning percentage correlate with coaching changes, and the hiring of Snowden, Olson, and Miller all resulted in positive changes for the team. Sean Miller's bounce appears to be smaller, but it's important to keep in mind that by contrast, Snowden and Olson inherited the team in much worse shape than Miller, meaning that there was a lot more room for improvement. Lute Olson became the coach of a Ben Lindsey-coached team that had won only 4 of 28 games. Things could not have gotten much worse.

In the case of both Olson and Snowden, success came quickly after getting the job. Fred Snowden acquired a 6-20 team and in three seasons turned it into a 24-9 WAC powerhouse that took 1st place in the conference. Olson's winning percentage peaked in his fifth season in 87-88 when the Cats went 35-3, winning 92.1% of their games with the trio of Lofton, Kerr, and Elliot. Interestingly, the success of both coaches tailed off after their early years. For Snowden, the drop was precipitous. For Olson, it was present but almost imperceptible, and the "drop off" included a National Championship, National Runner-up, and nearly 20 more years of NCAA tournament berths.

The future of Miller's tenure is tough to predict, but the team has clearly improved under his direction, and with a highly touted recruiting class coming, expectations are high. In the following post, I'll look at these data a bit more to examine to what to what extent we can predict how next year's team will fare.

The Concept

It has been a few years since I first conceived of this project, but I have been waiting until I had the motivation to actually take a crack at it. Arizona basketball is one of my obsessions in life. I was fortunate to have entered graduate school at the University of Arizona in the Fall of 1995, about 18 months before the Cats won the National Championship game on March 13, 1997. That event forever attached me to this team. I never miss a game, although I rarely see them in person. It is a 1,000 mile drive from my home to the McKale Center, and I have made that drive a few times. Last season, I was in Boulder to watch them lose a heart breaker.

My intent is to write about the team but not from the usual perspective. I am not much of a basketball player or tactician. I am not much of a historian of the team, as my experience only goes back about 17 years when I, probably like many others, jumped on the Cats' bandwagon. What I hope to bring to anyone willing to read is a statistical perspective. Numbers are another of my loves in life, a passion I recognize that is not widely shared, although statistical analysis of all aspects of all things are increasingly in vogue. If you like college hoops and things quantitative, I think you'll probably find something of interest here, especially if you are an Arizona fan.

I spent a few years writing about the statistics of bowling, and most often, of my incredibly unskilled bowling team in Laramie, Wyoming. That was both an amusing and intellectually satisfying endeavor. Generally speaking, when one thinks of bowling, they do not think of quantitative analysis. I was inspired by people like Bill James, Nate Silver and Ken Pomeroy, the last of whom perhaps not surprisingly is a friend of mine from high school. We graduated from the same class and even played basketball against each other as kids. What I intend to write about will share many similarities with Ken's work, although the scale of my analysis will be different, as I intend to focus only one team.

My intent is simply to better understand the game and world of college basketball. The Arizona Wildcats will be my case study. In the Information Age, the amount of data available to anyone who is willing and able to ask questions of the world has grown substantially. That said, databases of basketball statistics that are widely available still do not have great temporal depth. So, as time goes on, I will be compiling whatever data I am able to glean from various sources, and as that database grows, so will the kinds of things I will be able to write about.

I will begin with a few posts that put the upcoming season (still six months away) into better perspective, and I will move on from there. No doubt, I will have something to say after every game, but I will not be able to write with the frequency of Bruce Pascoe or Greg Hansen. In addition to writing blogs in my underwear in my mom's basement, I do have other things to worry about, like a job.