A Power Ranking System that Ranks Detroit 9th (Adjusted Win Probabilities)

The first regular feature I post every week after the games is the expected win probabilities for each game given the box score stats (i.e. in-game only performance of both teams). These probabilities are the result of a logistic regression model trained on the 1996-2006 seasons.

P(team X wins | box score)=99.9% means that team X completely dominated the game statistically. It is easier to dominate the 49ers than the Steelers. Therefore, I tried adjusting the win probabilities for each game based on opponent expected win percentage. The method for opponent adjustments is similar to what I use for adjusting the VOLA stats seen on the site. A concrete example follows the math...



adjXWinProb(team, opponent) = unadjXWinProb(team,opponent) * .5 / (1 - unadjXWinPercentage(opponent))

The win probability can also be interpreted as an expected number of wins (if the matchup were played 1000 times, the expected number of wins would be 1000 * P(win), but it's only played once so 1*P(win)=P(win)).

Example: The Colts had a 77.43% probability of beating the Pats in their meeting this season given the box score. The Patriots have an .8314 expected winning percentage this year. So the Colts' adjusted probability of winning the game is:
.7743 * .5/(1-.8314) = 2.2963 (adjusted expected wins)

Obviously, a 229.63% probability of winning is impossible, but the system gives Indianapolis a lot of credit for performing so well against New England. Similarly, New England is heavily penalized for nearly losing to Baltimore, accruing only .2498 adjusted expected wins. Although one or two games can get weighed very heavily by the adjustment process, the results do not look terribly out of whack.

Below is a table of every team's adjusted expected win total prorated to a 16-game season ranked in order of wins.

Rank	Team	Unadj. Expected Wins	Adj. Expected Wins
1	IND	13.5230	16.0278
2	NE	13.3027	14.7816
3	DAL	12.7584	12.9264
4	PIT	11.1355	11.2092
5	GB	10.9467	10.4008
6	JAX	10.3409	10.1535
7	TB	10.4636	9.8695
8	SEA	11.2993	9.7173
9	DET	8.0443	9.1228
10	PHI	8.4323	8.9552
11	TEN	7.7004	8.6468
12	MIN	8.8850	8.2582
13	KC	6.6498	8.0524
14	WAS	7.3755	7.9169
15	NYG	7.9746	7.5721
16	DEN	8.1019	7.4848
17	SD	8.3092	7.4617
18	CIN	7.7629	7.3479
19	ARI	6.5629	7.2998
20	ATL	6.9780	7.1539
21	CLE	7.6921	7.0279
22	NO	7.3527	6.9686
23	BUF	6.7337	6.5243
24	HOU	7.2044	6.5216
25	BAL	5.9070	6.5084
26	NYJ	5.4645	5.4883
27	MIA	5.1138	5.1293
28	CAR	5.8493	4.9563
29	OAK	5.4123	4.9256
30	STL	5.9473	4.9045
31	CHI	4.3431	4.5478
32	SF	2.4330	2.1388

For most teams, their ranking ends up similar to what's seen in my other power ranking system with a few noticable exceptions.

Kansas City moves up from 27 to 13, thanks largely to its performance against Indy in week 11.
San Diego moves down from 10 to 17 with their most valuable win coming against Denver (1.0128 expected wins). Wins against Baltimore, Kansas City, and Tennessee are devalued by the opponent adjustments.

And then there's Detroit. They gained 2.0234 adjusted expected wins for their performance against Dallas. Strong performances against Tampa Bay, Minnesota, and Denver also help. Of the teams in the NFC wild card chase, Detroit comes out on top because they were the most impressive against tougher opponents.