Sunday, February 28, 2010

What Passer Rating Can Tell Us About Expected Wins

Somewhat surprisingly, quite a bit.

I started by considering how a team's passer rating was reflective of its performance. While it did seem to show a positive correlation (unsurprisingly) it really was only predictive within the context of a single team. In other words, a team passer rating of 80.0 could have been very good for some teams and very poor for others. It meant 13 win seasons for the Ravens and 8 win seasons for the Bills.

This is actually pretty useful as it can reveal outlying seasons. For example, in 2008 Green Bay won 6 games with a team passer rating of 93.3. As this was the worst win total by a team with a rating over 90 this decade (and probably ever) it was easy to predict a significant improvement in 2009, which we saw. Other measurements such as pythagorean win total supported this as well.

Once again, not very surprising.

But anyhow, the obvious thing to do at this point was look at the delta instead. What is the difference between a teams passer rating, and passer rating allowed?

The fit here is really tremendous.

Here's the ten year win total versus the ten year delta for each team:

Sorry for the fuzzy graph and huge gap in text. Excel --> Paint --> Blogger doesn't translate very well.

Anyhow, the fit appears to be very good. What interests me here is that the error bars appear to be logarithmic. Around the zero point there is a great deal of variance in win totals, however at the extremes the fit is much better. Granted, there are only a few datapoints at the extremes so this could easily be coincidence.

Perhaps the most interesting number from this graph is that Chicago managed a league-average 81 victories over the last 10 years despite having the third worst delta at -90.

Taking this a step further, here are is the full data from the ten year graph (318 datapoints):
This also demonstrates much of what we would already expect. The zero win Detroit Lions were really just an unlucky 2 win team. Most of the 1 win teams really should have landed more in the 4-5 win range. And so on.

But still, the scatter plot seems to be highly predictive, with a significant error bar. The trend line crosses the zero point right at 8 victories, exactly as we would expect.

So what does this mean? That passer rating delta can probably be very predictive in terms of regression. For example, in 2008 the Dolphins went from 1 win to 11. How much of the 11 wins were due to luck and how much due to a vast improvement in both passing and pass defense?

At -20 in 2007, Miami really was more like a 5 win team that got terribly unlucky. At +20 in 2008 was, in fact, exactly an 11 win team.

If we use those numbers as averages (and they do seem to be), then every 7 points in delta is equivalent to 1 victory in expectation. A team at +7 would be expected to win 9 games. A team at +14, 10. And so on.

There is also some evidence that this is no longer a linear relationship at the extremes, but since there are only a few extremes to look at it cannot really be determined whether this is so. Mostly though, from eyeballing the chart we see that teams with negative deltas tend to fall below the trendline while teams with positive deltas above.

Other notable outliers from the last couple of years: Carolina's 12 win season in 2008 in which they only had a +3 delta. They very predictably returned to average in 2009 at 8 wins and -1.2. We mentioned Green Bay in '08. They had a +21 delta and won 6 games. Their 11 wins in '09 were exactly in line, but there might be something going on with that team, considering their +33 in '09 should have been more like 13 wins. Washington underperformed their expectation in '09 with 4 wins and virtually no delta. Kansas City has a combined 10 victories the last 3 years where their expectation would have put them at 20.

I will probably continuing some of this over the next while as there is a lot of data to parse, however here's a first run at predicting victories in 2010. This is entirely based on recent trends based on PR delta and does not reflect coaching or personnel changes:

Denver 8
Miami 7
Indianapolis 11
New York Jets 7
Buffalo 8
New England 10
Tennessee 8
Baltimore 9
Pittsburgh 11
Jacksonville 8
Cincinnati 7
Cleveland 5
Oakland 6
Kansas City 6
Seattle 7
San Diego 10
New York Giants 8
Philadelphia 9
Washington 9
Dallas 10
Arizona 8
Minnesota 8
Tampa Bay 8
Green Bay 12
Detroit 3
Chicago 7
New Orleans 10
St. Louis 4
Carolina 8
San Francisco 7
Atlanta 7
Houston 8


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