Tuesday, September 6, 2011

Tuesday Trivia: The State of Parity

Welcome to the first regular Tuesday Trivia feature, in which we examine the state of parity in college football. A quick Google search for "college football parity" yields a range of articles, from mainstream sports journalists to hand-wringing partisans to bloggers all discussing the effect of reduced scholarships and other rules changes on parity. There are a few high-profile upsets and recurring underdogs that make waves, but are these a sign of real change or just flashes in the pan as many naysayers claim (there's even a whole Facebook group devoted to the notion that Boise State is overrated).

Before we can really discuss whether parity is changing, though, we first need to define it. Is it the number of different teams at the top? Is it the odds that a lesser team could defeat a top-tier team? Is it a snapshot across all of Division I Football Bowl Series (FBS) teams? Let's look at a few sets of standings and try to establish a definition of parity.

League 1: Top Dog and Small Pack

Rank Team WinPct
1 Adams 0.800
2 Boston 0.500
3 Chicago 0.400
3 Denver 0.400
3 Frank 0.400

Here we have one clear front-runner (Adams) one middling team (Boston) and three mediocre teams that are all tied. Adams is clearly going to win the majority of titles, but at the same time even the lowest teams have a not-reasonable shot at winning; log5 says any of the bottom 3 have roughly a 1-in-6 shot of winning.

League 2: Top Dogs and Whipping Boys

Rank Team WinPct
1 Adams 0.750
1 Boston 0.750
1 Chicago 0.750
4 Denver 0.125
4 Frank 0.125

In this scenario we have a trio of powerhouses and a pair of whipping boys. Any of the 3 teams at the top could win, but the bottom-feeders have an unrealistic 1-in-22 shot of winning; as a point of reference, the infamous Stanford-over-USC upset that topped a previous Tuesday Trivia edition was a 1-in-22 upset.

League 3: Center-heavy

Rank Team WinPct
1 Adams 0.750
2 Boston 0.500
2 Chicago 0.500
2 Denver 0.500
5 Frank 0.250

In this league we have three exceedingly average teams, one good team, and one bad team. The top team has a 3-in-4 shot of winning against the middle of the pack, but a 9-in-10 shot against the bottom feeder.

Which one of these leagues has the most parity and which has the least? League 1 has a large blob of mid-level talent that will make for some interesting games, and even the top team won't have any easy games. League 2 has a very clear delineation between the haves and the have-nots. League 3 has a clear front-runner, but it also has a whipping boy that gives teams a game off. My personal gut reaction would be to say that league 1 represents the most league with the most parity, followed very closely by league 3, and league 2 with the least equitable distribution of talent.

That's my gut, but how to quantify that? The measure of parity I'm proposing here actually a measure of disparity; we use the standard deviation of the winning percentages, where a lower value of disparity represents a greater amount parity in the sport. Here's how it looks with our sample leagues:

League Disparity
1 0.086
3 0.088
2 0.171

These values confirm the gut feeling of leagues 1 and 3 having a lower levels of disparity, whereas league 2 has a clear division of talent.  But what does it look like when we apply this formula to all of FBS at large over the last nine seasons?

Even given our small sample size we can see a small yet decreasing disparity in overall talent in the league. The downward trend is slow, but explains nearly 40% of the variance in the distribution of winning percentages. In layman's terms this means that there is certainly an observable and significant decrease in the overall unequal distribution of talent in the league, but it isn't quite as drastic as some observers would have us believe.

We'll continue to see occasional upsets of top talent by underdogs, but we should be careful to not read too much into these individual events. With over 700 games between FBS teams per year, even a one-in-a-hundred event is bound to happen a few times over the course of a single season, and one-in-a-thousand upsets will occur nearly every year. As to which upsets are fluke occurrences as opposed to a sign of something more fundamental is left as an exercise to the reader.