A method for making strength-of-schedule adjustments

So let's say that we have the basic end products of a season of some sport: quizbowl, baseball, football, whatever: first, a win-loss record (and a record of each team's schedule to whom those wins and losses took place) and a few cumulative stats (perhaps points for and against, yards for and against, runs for and against, strikeouts for and against, whatever).

When determining which of two teams is stronger, pundits often attempt to appear effete by moving past the low-hanging fruit of win-loss record, and they instead latch on to net statistics like net points. Generally, a team that outscores its opponents by an average of twenty points per game is better than one that outscores its opponents by an average of five. But is that any better or worse than saying that the former team is better because it went 14-2, not 10-6?

I say not really. I say not really in large part because strength of schedule is unaccounted for. One team playing a much weaker schedule can inflate net points even more than it might inflate record, and vice-versa. So we need to construct a baseline.

Suppose there are six teams in two divisions. Each team plays its two division opponents twice each and the teams in the other division once each, for a seven game season. We have teams A, B, C and teams D, E, F. I propose we construct

rat_A = net_stat_A +(1/7)(2*rat_B + 2*rat_C + rat_D + rat_E + rat_F)
rat_B = net_stat_B +(1/7)(2*rat_A + 2*rat_C + rat_D + rat_E + rat_F)
rat_C = net_stat_C +(1/7)(2*rat_B + 2*rat_A + rat_D + rat_E + rat_F)
rat_D = net_stat_D +(1/7)(2*rat_E + 2*rat_F + rat_A + rat_B + rat_C)
rat_E = net_stat_E +(1/7)(2*rat_F + 2*rat_D + rat_A + rat_B + rat_C)
rat_F = net_stat_F +(1/7)(2*rat_D + 2*rat_E + rat_A + rat_B + rat_C)

What does this mean? This will produce team ratings where zero is a perfectly average team (having played an average schedule and put up a total of zero net points up against it, or having played a schedule of teams a total of seven points above average and put up negative seven net points against it, et cetera). Moreover, these ratings can be solved pretty quickly with a little linear algebra, or with an iterative method: let's suppose that we initialize all the ratings to the net statistics. Let's say A is +40 on the year, B is +5, C is -20, D is +30, E is -10, F is -45. So we write

new_rat_A = 40 +(1/7)(10 - 40 + 30 - 10 - 45) = 40 - 55/7 = 32.14
new_rat_B = 5 +(1/7)(80 - 40 + 30 - 10 - 45) = 5 + 15/7 = 7.14
new_rat_C = -20 +(1/7)(10 + 80 + 30 - 10 - 45) = -20 + 65/7 = -10.71
new_rat_D = 30 +(1/7)(-20 - 90 + 40 + 5 - 20) = 30 - 85/7 = 17.85
new_rat_E = -10 +(1/7)(60 - 90 + 40 + 5 - 20) = -10 - 5/7 = -10.71
new_rat_F = -45 +(1/7)(60 - 20 + 40 + 5 - 20) = -45 + 65/7 = -35.71

and so forth. Of course, the linear algebra method is much more attractive, particularly with 100+ game schedules and 30+ teams.

This type of rating doesn't have to be based off of net points: it can be net yards, for example, or a net measure of some type of advanced stat. It's also general: it doesn't rely on the specifics of any given sport.

Football Outsiders

I of course have to link to the site that inspired my interest in sabermetrics.

(Like every red-blooded American, that love was really spawned by reading Bill James; my dad taught me arithmetic back when the Pirates were good (believe me, I can't remember it) and at that point, why not compute some sabermetrics and create a game called "Spinner Baseball" that relied on a spinner for randomness and a lot of pie charts. But the problem there is the next dozen years were enough to convince me that any passion about baseball was far more likely to bring me sorrow than joy. So I took refuge in the Steelers.)

So if you haven't already read Football Outsiders, please do. The central element of their sabermetrics is a statistic called DVOA, a stat generated by comparing a team's perfomance, say, converting third and six on its own twenty to the league's performance in that same situation, then normalizing for the defense it faced (and analogous comparisons for offense). This is a good system for giving you an idea of how strong a team is in an abstract sense; this system can further be used to predict game outcomes by prioritizing certain phases of the game: perhaps red zone offense and third downs, perhaps fourth quarter performance (since old defenses can get tired and really go belly-up in the fourth quarter, as I learned painfully this year).

It predicts game winners pretty well in its raw form; throwing a couple of coefficients and varying them to maximize correspondence to known wins and losses can only improve it, right?

Anyway, this is a pretty great system on this level. One of the problems is that it attempts to produce individual statistics even though the system is so inherently dependent on the team as a whole. Was that Shaun Alexander (2005 edition) twenty-seven yard run on third and three so much better than the expected league performance because Shaun Alexander (2005 edition) is such a god of a running back, or is it because he has the best offensive line in the game? To a certain extent they tease out offensive line statistics and create metrics that estimate how much of a run owes to line work. But I don't know to what extent, if any, they're applied to individual running back DVOA. (And certainly the degree to which the defense was playing the pass because Peyton Manning was in the building isn't incorporated.)

So I'd really like to see them do more to de-couple offense and defense and different parts of the offense and defense (if they're going to try to produce ratings for players and for different aspects of the offense and defense, they'd better). At the moment, though, they're certainly the highest-quality football sabermetrics available.