2011 in Review: Pythagorean Expectation and What It Can Tell Us



Ace Ventura and Roger Podacter think the Dolphins were better than their record last year.

Pythagorean expectation is a way to calculate a team's "expected" wins and losses.  The concept takes a team's margin of victory over the course of a season into account, weighing big wins and losses heavily and discounting closer margins.  Consider the example of the following 2 teams over 4 games:


Team A:
Week 1: Win, 21-20
Week 2: Win, 24-23
Week 3: Win, 27-24
Week 4: Win, 9-7

Team B:
Week 1: Win, 35-7
Week 2: Loss, 24-23
Week 3: Win, 17-7
Week 4: Loss, 21-17

Team A's record is 4-0, while Team B's is 2-2.  But who's really the stronger team?  Pythagorean expectation would tell us it's Team B.  The formula is:

Expected wins = 
((Points Scored)^2 / ((Points Scored)^2 + (Points Given Up)^2)) x # of Games Played

Team A would have 2.2 expected wins for the 4 game stretch, while Team B would have 3.1.  Pythagorean expectation is a bit flawed in football, given the low number of games in a season (it's much more applicable to baseball and its 162 game regular season), and it obviously discounts the merits of success in close-game situations, but it's instructive nonetheless in football.

After the jump, we'll look at the 32 teams and how their expected records compare with their actual records.

2011 NFL Records and Expected Records, Ranked by Expected Wins

	Team	W	L	PF	PA	Exp. W	Exp. L.	Delta: W - Exp. W	Playoffs and seed?	Playoffs if Expected Wins instead of Actual Wins
1	Niners	13	3	380	229	11.7	4.3	+1.3	NFCW Champ, 2 seed	NFCW Champ, 1 seed
2	Saints	13	3	547	339	11.6	4.4	+1.4	NFCS Champ, 3 seed	NFCS Champ, 2 seed
3	Packers	15	1	560	359	11.3	4.7	+3.7	NFCN Champ, 1 seed	NFCN Champ, 3 seed
4	Patriots	13	3	513	342	11.1	4.9	+1.9	AFCE Champ, 1 seed	AFCE Champ, 1 Seed
5	Steelers	12	4	325	227	10.8	5.2	+1.2	AFC Wild Card, 5 seed	AFCN Champ, 2 seed
6	Ravens	12	4	378	266	10.7	5.3	+1.3	AFCN Champ, 2 seed	AFC Wild Card, 5 seed
7	Texans	10	6	381	278	10.4	5.6	-0.4	AFCS Champ, 3 seed	AFCS Champ, 3 seed
8	Lions	10	6	474	387	9.6	6.4	+0.4	NFC Wild Card, 6 seed	NFC Wild Card, 5 seed
9	Eagles	8	8	396	328	9.5	6.5	-1.5	Missed playoffs	NFCE Champ, 4 seed
10	Falcons	10	6	402	305	9.1	6.9	+0.9	NFC Wild Card, 5 seed	NFC Wild Card, 6 seed
11	Chargers	8	8	406	377	8.6	7.4	-0.6	Missed playoffs	AFCW Champ, 4 seed
12	Bengals	9	7	344	323	8.5	7.5	+0.5	AFC Wild Card, 6 seed	AFC Wild Card, 6 seed
13	Cowboys	8	8	369	347	8.5	7.5	+0.5	Missed playoffs	Missed playoffs
14	Dolphins	6	10	329	313	8.4	7.6	-2.4	Missed playoffs	Missed playoffs
15	Jets	8	8	377	363	8.3	7.7	-0.3	Missed playoffs	Missed playoffs
16	Bears	8	8	353	341	8.3	7.7	-0.3	Missed playoffs	Missed playoffs
17	Titans	9	7	325	317	8.2	7.8	+0.8	Missed playoffs	Missed playoffs
18	Seahawks	7	9	321	315	8.2	7.8	-1.2	Missed playoffs	Missed playoffs
19	Giants	9	7	394	400	7.9	8.1	+1.1	NFCN Champ, 4 seed	Missed playoffs
20	Panthers	6	10	406	429	7.6	8.4	-1.6	Missed playoffs	Missed playoffs
21	Cardinals	8	8	312	348	7.1	8.9	+0.9	Missed playoffs	Missed playoffs
22	Bills	6	10	374	434	6.8	9.2	-0.8	Missed playoffs	Missed playoffs
23	Raiders	8	8	359	433	6.5	9.5	+1.5	Missed playoffs	Missed playoffs
24	Broncos	8	8	309	390	6.2	9.8	+1.8	AFCW Champ, 4 seed	Missed playoffs
25	Redskins	5	11	288	367	6.1	9.9	-1.1	Missed playoffs	Missed playoffs
26	Vikings	3	13	340	449	5.8	10.2	-2.8	Missed playoffs	Missed playoffs
27	Jaguars	5	11	243	329	5.6	10.4	-0.6	Missed playoffs	Missed playoffs
28	Browns	4	12	218	307	5.4	10.6	-1.4	Missed playoffs	Missed playoffs
29	Chiefs	7	9	212	338	4.5	11.5	+2.5	Missed playoffs	Missed playoffs
30	Bucs	4	12	287	494	4.0	12.0	0	Missed playoffs	Missed playoffs
31	Colts	2	14	243	430	3.9	12.1	-1.9	Missed playoffs	Missed playoffs
32	Rams	2	14	193	407	2.9	13.1	-0.9	Missed playoffs	Missed playoffs

Some observations:

1. By this metric, the Broncos and the Super Bowl champion Giants look somewhat like flukes.  Using Expected Wins rather than actual wins, neither would have even made the playoffs.  The Giants were "really" a .500 team that was 1.5 games worse than the Eagles, and the Broncos were "really" a 6-win team.  (The Giants, to be fair, were ravaged with injuries throughout the season, so the team that played in the playoffs was different than the one that played in the regular season.)

2. The Eagles and Chargers "should" have been playoff teams (division champs, in fact).  The Eagles were a full 1.5 games below expectation -- the 4th "unluckiest" team in the league.  The Chargers weren't quite as far off of expectation but were hurt by the division rival Broncos being so far above their expectation.

3. The Dolphins and Vikings were the only teams more than 2 games below expectation, making them the "unluckiest" teams in the league.  The 6-10 Dolphins "should" have been a .500 team, and the 3-13 Vikings "should" have been 6-10.

4. No team had expected wins over 12, yet 6 teams had 12 or more wins (Pythagorean expectation would call each of the 6 "lucky").  Mathematically, a team has to score twice as many points as its opponents to have a win expectation of 12 or higher.  It's only happened twice since 2002 -- the '05 Colts (12.2 expected wins, 14-2) and the '07 Pats (13.2 expected wins, 16-0).  Notably, neither won the Super Bowl.  The 2011 Packers (15-1) were "actually" only an 11.3-win team.

5. The Saints and Steelers would have gotten byes using Expected Wins, while the Ravens and Packers would have had to play the first weekend.  Would that have impacted the playoffs?  One can only speculate.

6. The "luckiest" teams of 2012?  In order, the Packers, Chiefs, Pats, and Broncos (although the Packers and Pats still should have won their divisions).  The unluckiest?  The Dolphins and Vikings (as noted in #3 above), the lowly Colts, who should have only lost 12 games rather than 14, and the Panthers, who were really a .500 team instead of a 6-10 one.

Over the next several weeks, we'll be combining the expected wins concept with our draft rankings, as well as several other elements, as we try to come up with an intelligent view on each team heading into 2012.  Stay tuned.

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