Those Other Guys

I am not a mathemetician.

However, after 20 years of debates and reading to understand how computer ranking systems work, and after hearing all the arguments about how margin of victory is either vitally important (“a 37-10 win isn’t the same as a 28-27 win!”) or totally unfair (“you’re encouraging poor sportsmanship and running up the score!”)… I think I have finally hit on it.

Bill James came up with a method of determining when, precisely, a basketball game was truly “over” based on the lead held by the winning team compared to the time remaining in the game.  Baseball has similar methods based on outs remaining to the trailing team vs odds of the leading team adding to their advantage; it’s a completely different paradigm, but the core idea is the same.  We have oodles of data we can mine, and the question we need to answer is simple:

At what point, mathematically, can a football game be said to be over with some agreed-upon level of certainty?

Podunk State beat Big City Tech 52-20?  Well, at some point during that game, depending on how the scoring went, we can be reasonably assured that Podunk State was essentially certain to win, mathematically.  Maybe it wasn’t until seven minutes remained, and Podunk State extended a 31-20 lead to 48-20 by scoring a touchdown, then recovered a fumble on the ensuing kickoff to score again.  Maybe it was with five minutes to go in the second quarter, when they went up 52-0 and put in the scrubs.  Maybe it was somewhere in the third quarter.  The point is, this right here is the thing.  It doesn’t matter how badly you beat the opponent in terms of the final score; what matters is when did you reach the point at which victory was certain?

As an aside, this value can change if you screw up and let a team get back into the game once you’ve already triggered it.  Winning 52-0 at halftime, and then suddenly you find yourself leading 52-45 with six minutes left?  Reset, buddy.  The other team actually has gotten back in the contest, and has erased your certainty.

Anyway, once we’ve come up with a formula to compare lead vs time and determine the “this game is over” curve, then any given game can be assigned a value based on how much time remained in the game.  That value can then be safely used by computer ranking systems to assign weight to “margin of victory” without promoting unsportsmanlike humiliation of another team just to earn style points.  The differences between computer models would largely rest on how much weight they choose to give the new MoV component and in how the MoV component interacts with the strength of the opponent.  (Ultimately, the best result would be for each game to have a score based on both components, so that the value of one win could simply be compared to the value of another win to see which was more impressive, at least within that system.  Systems aren’t going to agree all the time, of course, but that’s what makes life fun.)

Now, it might change the way some teams operate early in a game, as they might go all-0ut to try and put a game away in the second quarter rather than deciding to hold steady and put it away in the third, but I don’t actually see this as a big problem (especially in an environment where teams are currently plodding around aimlessly in the first half and going to the locker room losing to teams from lower levels anyway).  But here’s the secondary benefit: once a coach is sure a game’s in the bag, and knows that they’ve received all the benefit they’re going to get from having won the game, the starters are coming off the field.  No coach will ever risk starter injury in such a situation ever again, because people are going to know: This game was over, coach, and you opted to keep running it up.

Math wonks: get on this.  Figure it out, and we can finally start mathematically distinguishing a team which wins in dominating fashion from a team which squeaks by every week.