NFL's FARCE Ratings and Week 13 Predictions Using Them

I've been continually tinkering with the FARCE system, both the formulae in the calculations and the averaging of the week-by-week ratings. Every change I made still left FARCE with one glaring hole: Philadelphia inside the top three.

(Skip to the table and predictions if you don't want to read about the changes being made to FARCE.)

In the first article explaining FARCE, I said at the end that one change that I was thinking of making was changing the 2.37 exponent in the "win score" formula to three, in order to give more benefit to winning, and the downgrade the effects of a blowout win.

Doing so would, for example, make a 21-17 win worth .653 instead of .622. It would also in turn lower the effects of a blowout win (by upgrading close wins). This is why the first change I made to FARCE was make the "win score" exponent three instead of 2.37.

The second change I made was towards the "expected win score" formula. Previously it had been (Rating — Opp. Rating)/250 + 0.5 . The downside of this was that the exp. score didn't stray too much from 0.5—using last week's ratings, the Tennessee Titans would have been "expected" to win just 12.6 games in a 16-game season against the Lions, who were the second-worst team according to FARCE.

Knowing this, I changed the 250 denominator to 150. This would make the Titan's "expected wins" to 15.7 wins. That number may seem high, but if you use the formula for the "win score" with a three exponent, the .984 win percentage needed for the 15.7 wins is equivalent to a 28-7 win, extremely probably if the Titans and Lions played each other.

Both of these changes made week-by-week ratings less volatile than before. Why is this important? Because the new formulae spit out reasonable year-to-date rankings by looking at just one week, whereas looking at one specific week before would show the best teams for that week only.

The Week 12 ratings had the Titans at No. 4 and the Saints at No. 6. I felt these were a little bit too off, so I had to include the average weekly ratings somehow. I concluded that the best way to rate all teams thus far was to find the average of each weekly rating, then average that with the Week 12 rating.

Here are the top teams so far using the "adjusted average" method, along with the Week 12 rating. Like last week, all ratings are subtracted from 1000, the starting score.

Week 12 NFL FARCE Ratings

Rank		Team	Adj_Avg	Week 12
1		New York Giants	35.3	47.7
2		Tennessee Titans	26.0	22.9
3		Baltimore Ravens	23.4	32.9
4		New York Jets	23.2	38.8
5		Tampa Bay Buccaneers	18.3	19.6
6		Arizona Cardinals	15.6	16.3
7		New England Patriots	12.6	17.2
8		Green Bay Packers	11.8	14.2
9		Pittsburgh Steelers	11.3	10.4
10		New Orleans Saints	10.9	17.8
11		Philadelphia Eagles	10.3	2.7
12		Carolina Panthers	8.1	5.6
13		Dallas Cowboys	8.0	7.3
14		Indianapolis Colts	7.7	14.3
15		Minnesota Vikings	6.6	13.4
16		Atlanta Falcons	6.1	11.2
17		San Diego Chargers	3.6	0.4
18		Chicago Bears	3.0	-1.6
19		Buffalo Bills	-2.8	-7.6
20		Houston Texans	-3.6	4.1
21		Washington Redskins	-4.7	-10.1
22		Miami Dolphins	-9.4	-16.0
23		Oakland Raiders	-12.8	-10.1
24		Jacksonville Jaguars	-13.1	-18.3
25		Cleveland Browns	-14.1	-20.7
26		San Francisco 49ers	-17.9	-18.9
27		Denver Broncos	-17.9	-25.7
28		Seattle Seahawks	-19.4	-22.2
29		Kansas City Chiefs	-26.5	-31.3
30		Detroit Lions	-28.8	-31.5
31		Cincinnati Bengals	-31.2	-35.7
32		St. Louis Rams	-35.8	-47.0

So, now the good part. How can we use those ratings to predict weekly matchups? In the first article explaining FARCE, I said that subtracting 960 from a team's rating (or adding 40 to the ratings shown above) could show the odds of one team beating another.

But that's no good—whatever team has a higher rating would be projected to win, of course.

I found a way to use the FARCE ratings in order to predict a game's final score, which can be used to pick against the spread.

(Major number alert. Skip down if you don't want to comprehend all of this.)

If Vegas has the Titans as 11-point favorites against the Lions, and the over/under is 45, then you can use that to find Vegas' predicted score. In this case, Tennessee would be projected to win 28-17, a difference of 11 points and a sum of 45. Using the formula for "win score" with an exponent of 2.37, the Titans are predicted to have a 0.765 winning percentage or win score.

Now, why an exponent of 2.37 and not three? The formula I use for "expected win score" has correlated better with actual win score with an exponent of 2.37 than 3 this year.

If we use the formula for expected win score, using the Titans' and Lions' FARCE ratings, the Titans are predicted to have a .865 win percentage, a tenth of a point better than Vegas. Now we know the Titans should cover the Vegas spread...but why stop there?

We can compute the predicted score of this game using the "expected win score" and a 2.37 exponent if we use Vegas' over/under as a given. The "solve for x and y" equations would be

x^2.37/(x^2.37 + y^2.37) = .865

x + y = 45

where x is the amount of points the Titans should score and y is the amount of points Detroit would score. This comes out to be a 31-14 game. Add 1.5 to the home and subtract 1.5 points from the away team for home field advantage, and the Titans are still over Vegas' spread, winning 29.5-15.5.

Using all this, here are the Week 13 predictions against the spread. All spread and over/under data is using MGM Mirage's lines found here , with Leroy's being used for the Miami/St. Louis game.

Home team in CAPS. (Don't forget that when I say "over," I mean the winner after the spread is added, not the straight up winner. Some scores may not add up the Vegas over/under due to rounding issues.)

Titans over LIONS, 29.5-15.5. Vegas spread: Titans -11

Seahawks over COWBOYS, 19.5-26.5. Vegas spread: Cowboys -12.5

Cardinals over EAGLES, 22.5-24.5. Vegas spread: Eagles -3.5

JETS over Broncos, 28.5-18.5. Vegas spread: Jets -7.5

49ers over BILLS, 18.5-23.5. Vegas spread: Bills -7

BUCCANEERS over Saints, 26.5-21.5. Vegas line: Bucs -3.5

PACKERS over Panthers, 23.5-19.5. Vegas line: Packers -3

REDSKINS over Giants, 19.5-22.5. Vegas line: Giants -3.5

RAMS over Dolphins, 21.5-22.5. Vegas line: Dolphins -8

BENGALS over Ravens, 16.5-20.5. Vegas line: Ravens -7

BROWNS over Colts, 22.5-22.5. A tie! Vegas line: Colts -4.5

Falcons over CHARGERS, 25.5-23.5. Vegas line: Chargers -5

PATRIOTS over Steelers, 21.5-18.5. Vegas line: Patriots -3

RAIDERS over Chiefs in a must-see, 23.5-18.5. Vegas line: Raiders -3

Bears over VIKINGS, 19.5-22.5. Vegas line: Vikings -3.5.

TEXANS over Jaguars, 26.5-22.5. Vegas line: Texans -3.5

Home teams are predicted to go 10-6 against the spread and 10-5-1 straight up this week.