A Different Way of Looking at Basketball Team Strength

At last, our long national nightmare is over! Lobo Hoops is back! With tonight being the Lobo Howl, I thought that it would be fun to show some analyses that I’ve been playing around with that provide a slightly different way of measuring team strength and using that to look back at the last couple of Mountain West Conference seasons.

Setting up the Problem

The main idea behind this sort of analysis is a pretty simple one: teams play differently at home and on the road. From that idea, I thought about how we could separate that difference and come up with a way to determine relative powers of all the teams in college basketball. What I came up with was this equation:

$y_n = \theta_i - \theta_j + \eta_i$ ,

where $y_n$ is the point differential in game $n$ (so there is one of these for each game played in the season), $\theta_i$ and $\theta_j$ are the relative powers of the two teams involved in game , and $\eta_i$ is the boost that team gets for playing at home (this parameter doesn’t show up if the game is at a neutral site). Using this equation, I set up a Bayesian hierarchical model to estimate the relative powers and home boosts for all of the teams in D-1 college basketball for both 2014 and 2015.

I won’t get into the math too much here, but it turns out that this idea has been around for a little bit so there are some other references that go into more depth. A good example of this is Glickman and Stern’s 1998 paper in JASA, “A State Space Model for National Football League Scores.” Although they are using NFL data, the ideas behind their model are mostly the same. A big difference is that they’re accounting for the teams changing as time goes along. The way they handle it seems relatively straightforward for the NFL, but it seems more complicated for college basketball, if for no other reason than there are 10 times as many teams in college basketball than the NFL and the games aren’t as consistently spaced. Also, fitting a model with that many parameters would make my laptop melt. So, for now, these results don’t account for any time dependency, although I have played around with some other ways of doing that.

From using Markov chain Monte Carlo (MCMC) methods to fit the model, we don’t just end up with estimates for the relative power and home boosts for each team, we end up with estimated posterior distributions for each team’s relative power and home boost. From that, we can also come up with an estimate of the probability that one team will defeat another team by using these posterior distributions. Basically, we want to see how likely it is for a value drawn from one team’s relative power posterior distribution to be greater than a value drawn from another team’s. We could also add in the home boost if we are interested in seeing that probability that a home team will beat an away team, but we’ll be focusing on neutral site games in this post.

2014-2015 Results

First, because it is most fresh in our minds, we’ll look back to last season’s results. In the table below, we see the relative powers for each MW team at home and at a neutral site, all sorted by neutral power. We also have the difference between those two values (the home boost) and each team’s conference record. It’s worth keeping in mind that the powers could be thought of as being in terms of points, so we can estimate the scoring margin of a game by looking at the difference between the two teams’ values. Also, the average team in college basketball will have a neutral power of about 0 and a home boost of about 3.

Mountain West Team Power 2015

Team	MW Wins	MW Losses	Neutral Power	Home Power	Home Boost
San Diego St	14	4	10.55	13.96	3.41
Boise St	14	4	7.93	16.10	8.17
Colorado St	13	5	7.17	12.77	5.60
UNLV	8	10	3.78	9.00	5.22
Utah St	11	7	3.64	5.63	1.99
New Mexico	7	11	3.54	5.16	1.62
Wyoming	11	7	1.93	8.53	6.60
Air Force	6	12	-1.35	1.69	3.03
Fresno St	10	8	-3.78	4.48	8.26
Nevada	5	13	-8.01	0.38	8.38
San Jose St	0	18	-15.66	-12.78	2.88

We see some interesting things in this table. First, over the course of the entire basketball season, the Lobos were about the sixth best team from the conference in terms of neutral power, neck and neck with UNLV and Utah State. Now, because this isn’t time dependent, they probably weren’t even this good at the end of the season when all of the injuries were taken into account, so the loss to Air Force in the MW tourney, while disappointing, wasn’t a massive upset. We also see that the Lobos had the worst home boost of all the teams in the conference last season. There are a couple of ways of interpreting that. If we’re feeling pessimistic, that means that the Pit isn’t as imposing of a venue as we might like to think. If we’re feeling optimistic, that means that the team wasn’t as affected by going on the road as some other teams. Either way, there wasn’t a huge difference between the powers of the team whether they were playing in Albuquerque or elsewhere.

For some non-Lobos related thoughts, Boise State was a good team last year but they were amazing at home. Their play at home is clearly the reason that they ended up as regular season co-champions with San Diego State, who were the best team in the conference in terms of neutral power by a decent margin. SDSU was estimated to have a higher neutral power than most team’s home power, which again explains why they did so well last season, including in the NCAA tournament.

In the following plot, we can see a heat map of the probabilities that Team A (the rows) defeats Team B (the columns). The shade of the box determines the probability, ranging from low probability (dark) to high probability (light). For example, on a neutral court UNM was estimated to have an 86% chance of defeating Air Force, so that box is shaded light gray. On the other hand, San Jose State was unlikely to beat anyone, so their entire row is shaded dark gray.

MWC Probs 2015

Again, we see that the Lobos were sort of in the middle of the pack, with some teams that they were estimated to be unlikely to beat, some that they were likely to beat, and some games as toss-ups. We also see that SDSU had a good chance of beating anyone on a neutral court, as we would expect from their neutral power.

2013-2014 Results

We also decided to look back at the 2013-14 season to see how well these results hold up in other years. In the table below, the results for the power and home boost estimates can be found.

Mountain West Team Power 2014

Team	MW Wins	MW Losses	Neutral Power	Home Power	Home Boost
San Diego St	16	2	14.32	15.72	1.39
New Mexico	15	3	11.98	14.76	2.78
UNLV	10	8	10.89	7.40	-3.48
Boise St	9	9	8.63	9.81	1.18
Fresno St	9	9	3.01	6.03	3.03
Wyoming	9	9	2.80	8.08	5.27
Nevada	10	8	2.79	2.39	-0.39
Utah St	7	11	1.23	8.64	7.41
Colorado St	7	11	-0.14	7.20	7.34
Air Force	6	12	-0.64	-5.25	-4.60
San Jose St	1	17	-7.42	-4.96	2.45

One of the first things that sticks out to me is that the league as a whole was better in 13-14 than in 14-15. Three teams had higher neutral power ratings that season than any team from last year and some teams that were “improved” last season might have actually been a little worse relative to the national average (i.e., Boise State and Wyoming), but they were better in comparison to the rest of the conference. Another thing to notice, is that teams with large home boosts one year didn’t necessarily have large home boosts the other. This was actually the case across all of the teams. In fact, it seems as though there is almost no correlation between the home boost of one season and the next. One theory for that is that because the teams are so different year to year, in terms of what players are on the team and what their experience levels are, that the teams will just play differently at home and on the road each year. For example, I would guess that a veteran team would likely see a smaller difference in their play than a young team (this might be worth looking into at some point).

In the following plot, we have the same sort of heat map as before, just this time it’s for the 2013-14 season. Again, each box represents the probability that Team A (the rows) defeats Team B (the columns).

We see that SDSU, UNM, and UNLV were clearly the upper tier of the league with Boise just behind. There was a pretty large gap after that, so those teams were heavily favored to beat all of the other teams on a neutral court. This actually goes really well with the results of the tournament, where these were the final four teams, even though Boise was the 6 seed going into the tourney.

Conclusion

This method seems to do a good job of determining the relative power of each team, giving us an idea of how similarly the teams have been performing. This analysis made the (admittedly faulty) assumption that each team’s power remained constant throughout the season, but simply watching the Lobos last year would tell you that isn’t the case. In the future, I’ll be looking at different ways to take that change into account to provide a better idea of what a team’s current power is. We also see that there isn’t a big correlation between the home boosts from one year to the next, so although the Lobos weren’t much better at home than on the road last year, that’s no indication that won’t be the case this year. We also don’t know if having a large home boost is necessarily a good thing! Regardless, we’re excited about this upcoming season and once conference play starts, we’ll probably revisit this analysis to see where things stand at that point.