Margins Matter (More than Straight Ws and Ls)

Wins and losses are all that matter. Margin of victory isn’t important.

Hm. Hmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmm.

Context

Emeryville Public Market. Lunch. Football. The San Francisco 49ers. It started when I expressed a nagging concern about losing to the Raiders in Week 14. Because you know, $*!% happens.

Why are you worried about the Raiders? They’ve lost 16 games in a row!

I know. That is a lot of games to lose. The Raiders are bad at football. I expect the 49ers to beat them; and given the respective current states of each team, I would expect these 49ers to beat these Raiders…90% of the time, or something. But half of the Raiders losses have been by 7 points or fewer; that means they are 0-5 in games decided by a touchdown (/one possession) or less. They lost 14-19 on the road to the Jets, 9-16 on the road to the Patriots, 28-31 at home to the Chargers, 24-30 on the road to Seattle, and 6-13 on the road to the Chargers this past weekend.

Does that matter?

Yes. Look at this Bill Barnwell piece from 2012:

In last year’s primer, I highlighted five teams that had particularly good records in close games in 2011: the Raiders (7-2 in close games in 2011), Packers (5-1), Saints (4-1), 49ers (6-2), and Steelers (5-2). In 2012, despite the presence of several star quarterbacks on their respective rosters, those same five teams went a combined 16-16-1 in games decided by one touchdown or less.

A team’s record in close games looks an awful lot like a random variable, and winning or losing a high percentage of close games in the past does not suggest that a team will continue that clip in the future. Rather, in close games teams tend to balance out around a .500 winning percentage. #regressiontothemean

Think about this conceptually. All else equal, would you rather play a team that had lost 10 games by 20 points each, or a team that had lost 10 games by 1 point each? Presumably the second team, with the much narrower margin of defeat, is a tougher opponent. Next, would you rather play a team that had lost 9 games by 20 points each and won 1 game by 1 point, or a team that had lost 10 games by 1 point each? The second team has the worse record; the first team has the worst point differential. All else equal, despite their worse record, the second team is still presumably a tougher opponent than the first team. This is because wins and losses are an imperfect measure of pure performance. Think about how these imaginary teams “performed”. The first team was dominated 9 times out of 10. The second team has been rather competitive with every opponent, only losing by one point. Context matters!

I think this is about where we came in.1

Wins and losses are all that matters. Margin of victory isn’t important.

Obviously, in a sense that is true. The teams with the most wins make the playoffs. But purely in terms of predicting how well a team will play (say, against the 49ers in Week 14), margin of victory matters a great deal. In fact, margin of victory is a better predictor of a team’s future chances than victory itself.

How can that be? Reducing a game purely to a win, a loss, or a tie for each team is not very useful. Not all wins are created equal.2 If Team A beats Team C by 1 point, and Team B beats Team C by 20 points, while Teams A and B are equal in wins, B certainly seems stronger than A. Turns out, there is a way to quantify such measures, aggregating across many games and years.

Pythagorean wins is an estimate of what a team’s expected record should be, based on their point differential. The formula is as follows:

Pythagorean Wins = [(Points Scored ^ 2.37) / {(Points Scored ^ 2.37) + (Points Allowed ^ 2.37)}] * 16 games per season

I have gathered the wins, losses, ties, points for, and points against for all teams for each year from 2002-2013.3 The 2008 Detroit Lions went a historic 0-16. Yet their point differential (268 for, 517 against) maps to 2.8 Pythagorean wins. They may not have counted in the score book, but perhaps it is some comfort to Lions fans that their winless season was only the 8th worst in the sample, by Pythagorean standards. The 2007 New England Patriots, meanwhile, went an equally historic 16-0. Their point differential (589 for, 274 against) is in fact the very best of any team since 2002. Yet in 2007 they totaled 13.8 Pythagorean wins. To be sure, that is a lot4, but short of the 16 actual wins they achieved.

So what?

The whole point here is gauge a team’s likely future performance. What do you think is the better indicator of a team’s record next season: their actual record from the year before, or their Pythagorean record from the year before? (Hint: It’s the Pythagorean record. I didn’t write this for no reason.)

Oversimplifying5, a win in a given season amounts to .28 more wins in the next season; there is a positive correlation of 28%.6 And similarly, a loss in a given season amounts to .28 more losses in the next season. However, a Pythagorean win in a given season amounts to .38 more (actual) wins in the next season; there is a positive correlation of 38%. All else equal, Pythagorean wins say more about a team’s future than actual wins. Margins–of victory, and defeat–matter.

Graphs

WinsPythagorean_Wins


  1. I spent roughly 35 minutes looking for a clip of that quote from the end of Fight Club on YouTube. It’s not there. F@%^ you, YouTube. F@$% you. 
  2. In addition to margin of victory, think location (home vs road vs neutral), strength of opponent, weather, etc. The others are important too, but they are not included here because #toomuchwork. 
  3. Why 2002? That is the first year under the NFL’s current number of teams (32) and divisional alignment (8 divisions of 4 teams each). 
  4. I believe the official term is “f^&*ton”. 
  5. Ie, without explaining what a regression is. Please Google if you’re curious. Regressions were simple and limited to one independent variable, but coefficients were found to be significant. 
  6. Again, simplifying. 
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