FARCE: A New Type Of NFL Power Ratings

Zach FeinAnalyst INovember 7, 2008

I swear it's not a farce. It's purely coincidental that the name also matches the word that means "a ridiculous sham," according to Dictionary.com.


What is FARCE?

I've been wanting to make my own set of NFL power ratings for a while now, trying everything from a simple add-subtract-multiply formula using season stats, to a long, week-by-week breakdown. Little did I know that a simple three-letter word would make it so much easier for me.


The Elo Rating System, used mostly in chess to rate individual chess players, allows to track a player's (or in this case, a team's) progress through week-by-week wins and losses against opponents of various skill levels. The formula uses three simple sources of data: Current rating, the strength of your opponent, and whether you won or lost your last game.

Now, FARCE—which stands for Football Analysis Replicating Chess' Elo—is more complicated than that, but it still follows the basic steps of Elo.


How is FARCE calculated?

In simplest terms, and you'll need the Elo link I embedded above to follow: First, start every team at 1000. Then instead of using a one or zero for "score" (whether you won or lost), I use the Pythagorean winning percentage for that matchup, using points scored and allowed, and a 2.37 exponent.

I adjust points scored and allowed based on home field advantage before that, too. Home teams outscored their opponents by about 2.85 points per game last year, so I subtract 1.43 points from the home team and add 1.43 to the away team.

My first time trying this out, I used the same formula supplied on the Web site, with the exception of the "score." After seeing the end results, I decided to change the "expected score" numbers. Why? Because almost every team fell within 30-or-so points from each other.

Because of that, all expected scores were between .40 and .60, give or take a few, when in reality it should be higher. So the new formula for expected score is (Rating—Opp. Rating)/250 + 0.5 . I also set a maximum of one and minimum of zero for the expected score, but it's unnecessary because no expected score goes within about 0.15 of one or zero.

(One quick note: When I say "rating," I mean the rating from the week before. I change the definition of it later on, but for now when I say "rating," that's what I mean.)

(One more note: The constant stays at 30 throughout because I started all teams at only 1000.)

Understand so far? Good, because that's all there is to the formula for now. Just plug in all of the above into the formula and you're good to go.


How FARCE applies to the NFL

Because FARCE puts heavy weighting on the most recent game, using a one-week FARCE is no good in ranking teams. What's best is to average a team's weekly rating output and use that figure.

The following table shows each team's average weekly rating, their non-skewed rating (average rating without the highest and lowest weekly scores), and their opponents' average ratings, or strength of schedule.


  FARCE ratings  
Tennessee TitansW1029.71031.7997.2
Philadelphia EaglesW1019.91019.01002.9
New York GiantsW1018.91018.4993.2
Tampa Bay BuccaneersW1018.31019.3997.0
Arizona CardinalsW1016.31016.51002.1
Pittsburgh SteelersW1015.51014.71000.0
Chicago BearsW1013.51013.4995.7
Buffalo BillsL1010.91011.8996.0
Dallas CowboysL1010.81011.21005.2
Carolina PanthersBYE1009.01009.51005.7
San Diego ChargersBYE1008.31008.41004.2
Baltimore RavensW1008.11009.21000.8
New England PatriotsL1006.11006.2995.2
Green Bay PackersL1005.21005.01007.1
New Orleans SaintsBYE1004.21003.11001.7
Washington RedskinsL1002.11001.61000.4
New York JetsW1000.51000.9992.3
Atlanta FalconsW999.2999.2998.1
Miami DolphinsW997.4998.51000.6
Minnesota VikingsW997.3997.71000.6
Indianapolis ColtsW996.9996.31004.7
Denver BroncosL995.9997.1995.2
Jacksonville JaguarsL992.6992.5992.6
Cleveland BrownsL989.7990.41006.4
Oakland RaidersL986.6987.71003.2
Houston TexansL986.4985.8991.2
San Francisco 49ersBYE986.2987.2995.4
Seattle SeahawksL982.9982.41000.7
Kansas City ChiefsL974.9973.51008.5
St. Louis RamsL974.4975.41009.0
Detroit LionsL973.8972.11001.2
Cincinnati BengalsW972.0971.91000.0

Why is Philadelphia so high, and why is Washington so low?

Philadelphia is high because of their schedule. In their five wins, they've outscored opponents by 16 points per game, and in their three losses—which were against the Giants, Steelers, and Cowboys, mind you—they've lost by only five points per game.

In Washington's case, they did very poorly in a four-game stretch against the Rams, Browns, Lions, and Steelers. They went 2-2 and were outscored 62-70. Needless to say, that hurt their rating substantially, both due to the fact that they barely outscored the Rams, Browns, and Lions combined, and the fact that they lost 23-6 at home—they started that stretch with a 1017 rating and ended it with a 995 rating.


How can the FARCE ratings be used to predict individual matchups?

I have done no testing on this whatsoever, but by trying out a few different methods, I think I found one that works, sort of.

Subtract 960 points from all teams' ratings.

There you go. You can then use that to find a team's winning percentage against another should they play each other by using the formula (Team Adj. Rating) / (Team Adj. Rating + Opp. Adj. Rating). For example, the Giants would have a 56.5 percent chance of beating the Packers, which seems about right.


There might be a few tweaks here and there with FARCE (primarily with the first step of finding the "score"—I was thinking of making the exponent higher, to 3 or 3.5, in order to give real benefit to the actual winner or downgrade the actual loser of a game more than there is at the moment), but overall, I like the way it looks as is.


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