It’s fun to play with weighted averages to see how the NFL has (or hasn’t) evolved. For example, the Giants led the league with interceptions: as a result, 5.8% of all interceptions thrown in the NFL last year were by Eli Manning or Curtis Painter. Since the Giants went 7-9 in 2013, that means 5.8% of all interceptions were thrown by a team that had a 0.438 winning percentage. Meanwhile, Kansas City and San Francisco each threw just 8 interceptions, or 1.6% of all NFL interceptions, and the Chiefs and 49ers had an average winning percentage of 0.719.

So while the average winning percentage of all NFL teams is of course 0.500, the average weighted (by interceptions) winning percentage of all NFL teams will be below .500 because bad teams tend to throw more interceptions than good teams. Last year, the averaged weighted winning percentage was 0.464 for all NFL teams.

What’s interesting is how little variation there has been over the years in weighted winning percentage. In fact, it’s been between 45% and 50% in just about every year since 1950:

What if we do the same anaylsis for touchdown percentage? Thanks to Peyton Manning, the Broncos were responsible for 6.8% of all touchdowns thrown in the NFL last year, and Denver won 81.3% of its games. Meanwhile, the Jets, Bills, Jaguars, and Raiders combined to throw just 7.7% of all touchdowns, and had an average (simple) winning percentage of just 0.344. As a result, the average weighted winning percentage for NFL teams, weighted by touchdown passes, tends to be above 0.500. Last year, it was 0.531, which also is pretty consistent with the last 64 years of pro football history:

What about doing the same analysis but using Net Yards per Attempt?

The numbers here are a little closer to .500 than the touchdown numbers, but that makes sense. Touchdowns lead directly to points, so while they may not be the most predictive stat, they will do a nice job of explaining prior winning percentage. But again we see very little fluctuation over the years.

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I think that the shape of these graphs (in particular, how far they are from 50%) depends on how the statistic is scaled. If the average on the stat is far from zero (as measured in standard deviations of that stat), then the value on this graph will tend to be close to 50%. That is why NY/A is close to 50%.

Let’s say that one stat has a mean of 10 and a stdev of 1. Then if a good team has an 11 and a bad team has a 9, the good team still only accounts for 55% of that stat.

Another stat has a mean of 3 and a stdev of 1. Then if a good team has a 4 and a bad team has a 2, the good team accounts for 67% of that stat.

Quite right. I think that’s one of the reasons the NY/A was a little higher during the dead ball era of the ’70s.

Quick note: on mobile safari at least all the AFL numbers are graphed from 1950 onwards, which I’m pretty sure is incorrect.

Hmm. Good to know, thanks.

Same is true on Firefox on Windows PC

I’m an idiot; I think I just put the AFL years at the end, so 1950 to 1959 for the AFL should be 1960 to 1969, obviously. D’oh!