Thursday, December 9, 2010

Skinning the NFL cat

by Bruce D

We've all heard the saying "there's more than one way to skin a cat", and that's what I've attempted to do. Skin the same "cat" as Brian Burke attempts to, but in a totally different way.

In this case the "cat" is the value, power, efficiency, likely hood to win, whatever you want to call it, of each NFL team. As I see it, Mr. Burke uses sophisticated statistical analysis and analyzes pertinent information in pertinent situations, such as tracking the success and efficiency of individual plays outside of the "garbage time" and odd-ball situations during NFL games. He strives to "eliminate the noise" and get to the truth about a team's true ability to score points, prevent points, and win games.

I'm totally with Brian on that goal, but I don't have Brian's statistical skill set (I spend too much time on wikipedia just looking up some of the words he uses as it is), and I really don't trust anything or anyone(except Brian at this point) that I can't prove to myself. So I have to do it the old fashioned, "empirical" way (I learned that big word on this web-site, had to look it up on wikipedia, did I use it in the right way?). In my analysis I came up with a simple formula that virtually anyone would agree with.

In any NFL game, if Team A scores more points than team B scores, team A wins.

So team A can win by any positive combination of scoring points and preventing team B from scoring points.

So its points. More points you win, less points you lose. I'll state it again, "its points". So that's what I use, because nothing else allows a team to win. I use points for, points allowed, and then pull out a portion of "lucky" points for each lucky play, and give a portion of "unlucky" points back to a team in random unlucky plays. The same sort of goal that Brian has, yet I look at the actual results data rather than what should be expected. The following is an example of what I've come up with. Here's an excerpt from my web-site that shows my version of team efficiency, power, ability to win, whatever you may call it, that Brian and I are trying to determine.

The power rankings and ratings listed to the left is a new feature to be posted each week. Power is derived by calculating each team's offensive and defensive points production and prevention for each game, comparing it to the league average each week, and then adjusting for strength of opponent. For each game calculated, there is a MAX and a MIN power that a team cannot go beyond, so a blow out win is great, but it can't become unrealistically excessive, likewise, getting shut out can't give a team a 0 power rating for offense or defense.

Next, all lucky type plays, good or bad, such as interceptions, fumbles lost, blocked punts, kick off return touchdowns, missed field goals etc. are valued, and each team's power is adjusted by a portion of this luck value (about half seems to be appropriate to distinguish between aggressive or sloppy team play vs dumb luck). If a team has been overly lucky, their power will be adjusted lower due to the fact that they can't be expected to continue to be so lucky. For the same reasons, an unlucky team's power will be increased.

A power rating of 1 is considered league average, so a team with a rating of 1.2 can be thought to be 20% better than the average team, and a team with a rating of .85 can be thought to be 15% worse than average.

A few things to keep in mind about the ratings. This is average power year to date, so a "hot" team won't jump above a consistently good team, all power is based on the ability to score and prevent points, so wins have no affect on the ratings, and player and coaching changes are not factored in.

You may also want to consider that a ranking system of 1 to 32 can be misleading. Rank and rating are 2 different things. You can see that the power rating of some teams are equal and/or very similar to the group of teams they're listed close to. A team ranked at #5 could have a rating that is virtually identical to a team ranked #10, yet a 5 rank difference infers a large difference. In other words, I'd pay more attention to the ratings than the rankings.

One last thing. In the 2010 NFL season, home advantage looks to be about 4% as far as these ratings go. In a match-up/prediction situation, I'd add about .04 to the home team's power rating.

So I put my calculated power ratings up against my NFL hero Mr. Burke's, and I was amazed. The expected results are pretty damn close to actual results.

What do I deduct from this? To me, its proof that Brian was right all along, its proof that Brian is a very smart "out of the box" NFL analyst, and that I never would have come up with my formulas if it weren't for this web-site.

In my humble opinion, this is "the" web-site for NFL statistical analysis.


Brett said...

Great job, Bruce! I refer to your power rating method as "subtractive synthesis" as opposed to Brian's method of "additive synthesis." Since the goal is to predict future outcomes and future outcomes are based on talent and luck (with luck being unknowable), then talent is what we are really trying to measure. Brian attempts to do this by adding together all the team stats that are caused by talent. Your method is just as valid if we assume TALENT = PAST OUTCOMES - LUCK and you are accurately measuring both PAST OUTCOMES and LUCK. The fact that your ratings are so close to Brian's shows that you have probably subtracted just the right amount of luck and Brian has added just the right amount of talent.

My only criticism of your results is that your scale has all the teams rated too close to average. I believe the Packers are more than 17% above average, and the Cardinals are more than 15% below average. You can test this by converting your ratings to expected point values and comparing them to the Vegas lines. Since your average rating is 1.0, just multiply each team's rating by the average team score per game (22.25 points). Doing this gives the top-ranked Packers a point-rating of 26.01 and the bottom-ranked Cardinals a rating of 19.02, a difference of only 7 points. In reality, the Packers would probably be favored by 13-14 points on a neutral field. You can fix this by raising your ratings to the power of 1.8. This will adjust the scale to match the expected point-spread values. According to this adjusted scale, the Packers would have a rating of 1.32, and the Cardinals 0.75, which seems more accurate to me.

Bruce D. said...


I absolutely see(and have seen) your point about looking too close to average.

I had to "guestimate" the cut-off for MIN and MAX power per game.

The MIN is .4, the MAX is 2(offense points above average and defense points below average per week/game). My reasoning is, no team can be more than 5 times better than another, even in one odd-ball game, and IMO there really is a fair amount of parity in the NFL.

This kind of penalizes good teams that consistently blow out other teams, and boosts shut-out teams by not allowing a 0 offense rating.

I'll change the cut-offs. and see if I can't get closer to realistic vegas odds.

I'll post it here when done.

Bruce D. said...


Thought a lot about your post.

Reran power without the MIN MAX limits, not much different at all.

So since power is the average of offense and defense, we can assume it reacts on points scored and given up, so maybe:

Using the GB ARI examples, first we can calculate against an average NFL team the following way.

GB offense at 1.169 is 16.9% better, so .169 * 22(avg points score)= +3.7 points(above avg) for GB, or 25.7 points(22+3.7)
GB defense at 1.169 is 16.9% better, so .169 * 22(avg points score)= -3.7 points(below avg) for AVG TEAM, or 18.3 points(22-3.7)

So against an average team, GB should win by 6.4 points(25.7-18.3).

ARI offense at .855 is 14.5% worse, so .145 * 22(avg points score)= -3.19 points(below avg) for ARI, or 18.81 points(22-3.19)
ARI defense at .855 is 14.5% worse, , so .145 * 22(avg points score)= +3.19 points(above avg) for AVG TEAM, or 25.19 points(22+3.19)

So against an average team, ARI should lose by -6.89 points(25.19-18.81).

Now take the difference between +6.4 and -6.89, and GB should win over ARI by 13.29 points.

Looks better.

Or simply take the difference in power (1.169-.855)=.314, so GB is 31.4% better than ARI, on offense AND defense.

So the total of the average points gained and average points given up in each game is 44(22+22)

44 *.314(better %) = 13.8 points.

That seems to fall in line with real world expectations.

Thanks for the push to figure it out.

Also, home advantage this season seems to be about .02, not the .04 as stated above.

Brett said...


I think you're right. I was using team totals instead of combined totals which would make more sense.

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