Predicting a Final Score

Being able to predict final scores, aside from potentially impressing your sports geek friends, is not an incredibly useful skill. However, that little fact will not stop me from presenting my method for doing so on this weblog. I figure if you usually take the time to read this, you might find it interesting.

The score in a basketball game is really a function of three things: the pace of the game, and each team’s efficiency in scoring points. There are a number of ways that a team can get to 60 points, for example. They can run their offense at a breakneck pace of 90 possessions per game at an efficiency rating of 66.6. Or, they could slow things down to a crawl at 50 possessions per game with and efficiency rating of 120. Either way, you multiply the efficiency rating (as a percentage) by the pace to get the number of points.

Another example, in table form:

Pace	Poss/gm	Eff	Pts
Very fast	90	77.8	70
Fast	80	87.5	70
Average	70	100.0	70
Slow	60	116.7	70
Very slow	50	140.0	70

Thus, it makes sense, when you’re trying to predict the final score of a game, to really predict three things. In order to be as accurate as possible, you have to predict the pace at which the game will be played, along with the efficiency ratings for the visitor and the home team. Let’s start with the easiest part, the pace. We’ll use Harding’s upcoming game against Delta State as an example for predicting the score.

The concept of pace is relatively simple. It represents the number of possessions a team receives per game, and it is a function of how quickly a team gets the ball and either takes a shot or turns the ball over. The GSC average pace, through yesterday’s games, is 69.0.

There is one other important concept with regard to pace. For a single game, pace is a function of both teams’ attempts to play the game at their preferred pace. Ideally, I would use the average opponents’ team pace to figure out the pace at which a team really tries to play, but without those numbers, I will compare each team’s pace to the GSC average like so. Harding, which plays the most up-tempo style in the GSC, has a pace rating of 76.0. Presumably, since the GSC average is 69, other teams are slowing Harding down from the pace they would really like to play by 7 possessions per game (76 – 69 = 7). This is not actually the case, since Harding has yet to play a GSC (West) team, but it is a necessary assumption. As a result, I would say that Harding’s preferred pace is actually 83 (76 + 7 = 83).

Like I said, a single game’s pace is a factor of both teams’ preferred paces, so we also have to figure out the preferred pace of Delta State. DSU plays the second-most up-tempo style in the division, averaging 75.6 possessions per game. Using the same method as before, we get 82.2 as their preferred pace (75.6 – 69 = 6.6, 6.6 + 75.6 = 82.2). Averaging the two paces together, we get 82.6 as the predicted pace for the Harding-DSU game, which is about as quick as it gets in the GSC.

Next is the more involved part, predicting efficiency for each side:

A team’s single game offensive efficiency is a function of both that team’s previous offensive efficiency and their opponent’s previous defensive efficiency ratings. However, I can’t just average those ratings right away, because teams have played vastly different strengths of schedule, which would have a profound impact on their efficiency ratings.

Adjusting for strength of schedule is difficult for these numbers, although not quite as difficult as it was with PER. For these purposes, I will assume two things. First, the average GSC West team is about a 43.0 on my team rating scale. This is an educated guess based both on a subjective look at current performance and an objective look at current efficiency ratings. GSC West teams, on average, are about 8 points of efficiency better than their opponents this year, with an average schedule strength of 39.2. 43.0 just seems about right for a division average.

My second assumption is that GSC teams have a range of possible efficiency ratings. The average offensive and defensive efficiency is about 105, and roughly 15 points either way represents a good range of possible values (90 to 120). Ratings outside that range are somewhat rare and would practically never happen for an entire season. Thus, my assumption is that in adjusting for schedule strength, whatever adjustment I make shouldn’t cross those boundaries.

Now, on to the adjustments. Harding’s current schedule strength is 37.6, as you can see from the table below. In other words, their average opponent has been 87.4% as good as the average GSC West team. Thus, you would expect a 12.6% decline in their performance, within the boundaries I suggested previously (efficiency of 90 to 120). You can also see the numbers for Delta State here.

Team	Sched. Strength	Avg. GSC Tm.	% of avg.	difference
Harding	37.6	43.0	87.4%	-12.6%
Delta State	36.4	43.0	84.7%	-15.3%

Scientifically, this isn’t a great model, but I think it works for these purposes. Given Harding’s current offensive efficiency of 110.9, you would expect a decline of 3.9 points based on schedule strength (-12.6%) and the range of decline (110.9 – 90 = 20.9, 20.9 x -12.6% = -2.6). After the adjustment, Harding’s new adjusted offensive efficiency would be 108.3. Below are the figures for Delta State, as well as the same calculations for defensive efficiency (for which lower is better).

Team	O-Eff	% change	change	New O-Eff
Harding	110.9	-12.6%	-2.6	108.3
Delta State	117.1	-15.3%	-4.1	113.0

Team	D-Eff	% change	change	New D-Eff
Harding	100.7	12.6%	2.4	103.1
Delta State	94.8	15.3%	3.8	98.6

Now, I have a couple of other subjective adjustments to make before I put everything together and predict a final score. The first of these is home-court advantage. This is probably larger for a typical game at the Rhodes Field House than anywhere else in the GSC, but since most people won’t be back for the Delta State game (sadly, since they’re the best team in the conference), I will only make a one-point adjustment each way.

Next, there are two other subjective issues to tackle. Some games feature such a large disparity in talent levels that one team jumps out to a huge lead and then plays backups for the rest of the game, lessening the impact of that team’s advantage. I imagine that if Harding played Duke, we wouldn’t see a whole lot of J.J. Redick and Shelden Williams after the first few minutes. Also, there is the issue of a team playing scared, or in shock, because of an unexpected talent difference or weakness. Such a game was played between #1 Duke and #2 Texas last month, when Duke took a commanding lead and blew out the #2 team in the country, despite their seemingly similar ability levels. There’s not really a way to account for the latter, but the former can be accounted for by subjectively lowering the margin of victory in a potential blowout.

Now, on to the prediction for Harding against Delta State. First, we will want to average Harding’s offensive efficiency (108.3) with Delta State’s defensive efficiency (98.6), in order to find Harding’s predicted efficiency level for the game, which turns out to be 103.5 ([108.3 + 98.6] / 2 = 103.5). Using the same calculation, we get DSU’s efficiency as being 108.1, which means that DSU will be the predicted winner. Now, I’ll give Harding a one-point edge each way as a home-court advantage, making the new ratings 104.5 and 107.1, but that doesn’t change the predicted outcome.

Team	O-Eff	Opponent	D-Eff	New Eff	Home Court Adjusted
Harding	108.3	Delta State	98.6	103.5	104.5
Delta State	113.0	Harding	103.1	108.1	107.1

Now, to predict the actual score, we multiply the efficiency ratings (as percentages) to the predicted pace of the game (82.6, from way back at the beginning), and we have a final score prediction: Delta State 88, Harding 86.

Team	Eff	Pace	Points
Delta State	107.1%	82.6	88
Harding	104.5%	82.6	86

This prediction is subject to change, since DSU does have a game against Henderson State on Thursday, but I don’t expect anything drastic.

Now, if you haven’t already had enough, I’ll discuss my method for evaluating predicted scores.

I use two things to evaluate a final score prediction: average team point difference and margin of victory difference, adding the two together for something I’ll call Prediction Quality (PQ). Let’s say that Harding beats DSU 92-85. In this case, I was off on Harding’s score by six and DSU’s score by three, for an average of 4.5. Since I said that DSU would win by 2, but Harding actually won by 7, that’s a margin of victory difference of 9. Add the two together and we get 13.5.

Now, if DSU wins 87-84, I’ve done a pretty good job. The average team point difference is 1.5 (88 – 87 = 1, 86 – 84 = 2, [1 + 2] / 2 = 1.5), and the margin of victory difference is 1 ([+3 for DSU] – [+2 for DSU] = 1), for a total of 2.5. Just for the fun of it, I’ll try to track my predictions and errors using this system throughout the conference season. If anyone out there has a better idea, let me know, and I’ll track it, too.