FEI Week 13: Better To Be Lucky And Good

by Brian Fremeau

Notre Dame clinched its bid to the BCS national championship game on Saturday with a 22-13 victory over USC. As Matt Hinton described it, the victory was another "low scoring but utterly convincing victory" for the Irish, the culmination of an unexpected undefeated campaign led by an elite defense that won almost every battle in the red zone to carry the team to several close victories.

Are the Irish lucky to be undefeated? Certainly a missed chip-shot field goal by Pittsburgh in overtime would have derailed the championship run, and a play here and there in victories over Stanford, BYU, Purdue, and Michigan may have made the difference between victory and defeat. But there were blown opportunities by Notre Dame in each of those games that could have made each less of a nail-biter and allowed Notre Dame to win more comfortably. Are the Irish lucky to be undefeated or were several of their opponents lucky to hang in with the Irish?

That’s a complicated question, but we have some data points that can help answer it. First, we can use the mean wins calculation that I publish each week as a way to track what might be considered each team’s over-achievement or under-achievement this year. According to my analysis, the FEI rating and the strength of opposition faced produces an expected mean wins data point for each team: the average number of games a team with the given FEI rating would be expected to win against its entire FBS schedule. The difference between the team’s mean wins and its actual wins is one indicator of good or bad fortune over the course of the year.

Mean Wins at least 1.5 Games Over Actual Wins
FEI Rank	Team	Mean Wins	Actual Wins	Delta
114	East Carolina	3.5	7	+3.5
67	Middle Tennessee	6.2	8	+2.1
118	UTSA	2.0	4	+2.0
9	Ohio State	10.0	12	+2.0
87	Navy	4.7	6	+1.9
93	Duke	3.1	5	+1.9
121	Colorado State	2.1	4	+1.9
58	Ball State	7.3	9	+1.7
47	Kent State	8.7	10	+1.6
2	Notre Dame	10.4	12	+1.6
107	Wake Forest	2.5	4	+1.5
55	Washington	4.5	6	+1.5

Mean Wins at least 1.5 Games Under Actual Wins
FEI Rank	Team	Mean Wins	Actual Wins	Delta
68	South Florida	3.8	2	-1.5
70	Indiana	4.5	3	-1.5
74	Troy	6.6	5	-1.6
96	UTEP	4.7	3	-1.7
84	Florida International	4.8	3	-1.8
88	Boston College	2.8	1	-1.8
81	Western Michigan	5.0	3	-2.0
106	UNLV	4.1	2	-2.1
99	South Alabama	4.3	1	-2.6
115	Southern Mississippi	2.8	0	-2.8
101	Akron	3.4	0	-3.4

By this measure, Notre Dame has been one of the top beneficiaries of good fortune in 2012, but not exceptionally so. The undefeated Auburn Tigers were also +1.6 mean wins in 2010. The undefeated Alabama Crimson Tide were +1.5 mean wins in 2009. Top teams play games against top competition, and the probability of winning them all is rarely very high. Even teams that only play a few games against top-level competition are still statistically more likely to lose one than win them all. Is it a measure of good fortune that the Irish are undefeated? Yes, but it isn’t dumb luck. It’s well within the realm of probability.

There are 85 teams that have a record within one game of their mean wins expectation. The Irish finished last season with 0.9 wins below expectation, and they were 0.7 wins below expectation in 2010. That means that Brian Kelly’s three-year record of 28-10 is exactly what their FEI ratings over the last three years would have projected against their schedule. It doesn’t even out perfectly for all teams, but over the course of time, every program should probably play within a narrow range of their overall mean wins.

There are other ways to measure over-achievement and under-achievement. The "revisionist box scores" I publish each week are an attempt to identify the games in which turnovers, special teams, and field position were the difference between winning and losing. It isn’t as though teams aren’t deserving of close call victories due to those factors, but stripping away those factors does give us a better sense of which teams "played well enough to win." And it is another indicator of teams that have been the biggest beneficiaries of good fortune due to those elements.

Notre Dame did win one game in which the margin gained on turnovers exceeded the scoring margin in the game. Against Michigan, the Irish collected 12.7 points in total turnover value and won the game 13-6. But in most of their other victories this year, the Irish were overcoming turnover, special teams, or field position deficits.

Take the Pittsburgh game, for instance, the triple-overtime thriller against a mediocre opponent that nearly cost them a trip to Miami. The Irish gave up 14.0 points in turnover value in the game and still eked out a victory. In FBS games this year, only two teams overcame a larger turnover deficit and won. Duke beat Memphis despite an 18.8 point deficit in turnover value, and Virginia beat Penn State despite a 15.7 point deficit in turnover value.

The Irish won twice in 2012 despite losing the field position, turnover, and special teams battles in a single game: close victories over Purdue and BYU. Over the course of the season, Notre Dame won 10 games in which it had a deficit in at least one of those three factors, and 8 games in which it had a deficit in at least two of those factors. No other team overcame as many combined field position, turnover, and special deficits as Notre Dame. Does that make them lucky?

From the perspective of FEI, these elements are actually a big reason why the Irish are considered one of the best teams in the country, not one of the luckiest. Notre Dame’s opponent-adjusted offense is ranked eighth, and its opponent-adjusted defense is ranked second. It’s the non-offensive and non-defensive stuff like special teams (88th) that are holding back the Irish from passing the eye test in more people’s eyes. These might be the factors that hold the Irish back from winning the BCS title game as well, but it shouldn’t be a reason to knock them for what they have accomplished to date.

Week 13 Revisionist Box Scores

This weekly feature identifies the games played each week that were most impacted by turnovers, special teams, field position, or some combination of the three. The neutralized margin of victory is a function of the point values earned and surrendered based on field position and expected scoring rates.

Week 13 Games In Which Total Turnover Value Exceeded Non-Garbage Final Score Margin
Date	Winning Team	Non-Garbage Final Score	Losing Team	TTV +	TTV -	TTV Net	TO Neutral Score Margin
11/22	TCU	20-13	Texas	13.6	4.1	9.5	-2.5
11/23	Arizona State	41-34	Arizona	15.0	7.5	7.5	-0.5
11/23	East Carolina	65-59	Marshall	11.6	0.0	11.6	-5.6
11/23	LSU	20-13	Arkansas	7.8	0.0	7.8	-0.8
11/23	Utah	42-35	Colorado	17.3	4.3	13.0	-6.0
11/24	Baylor	52-45	Texas Tech	18.1	0.0	18.1	-11.1
11/24	Florida	30-20	Florida State	17.3	3.7	14.6	-4.6
11/24	Louisiana Monroe	23-17	Florida International	11.9	3.5	8.4	-2.4
11/24	Middle Tennessee	24-21	Troy	28.1	7.8	20.3	-17.3
11/24	Ohio State	26-21	Michigan	13.9	7.3	6.6	-1.6
11/24	Penn State	24-21	Wisconsin	3.9	0.0	3.9	-0.9
11/24	SMU	35-27	Tulsa	10.1	0.0	10.1	-2.1

Week 13 Games In Which Special Teams Value Exceeded Non-Garbage Final Score Margin
Date	Winning Team	Non-Garbage Final Score	Losing Team	STV +	STV Neutral Score Margin
11/23	LSU	20-13	Arkansas	7.5	-0.5
11/23	Washington State	31-28	Washington	5.8	-2.8
11/24	Connecticut	23-20	Louisville	4.1	-1.1
11/24	Middle Tennessee	24-21	Troy	5.6	-2.6
11/24	Oklahoma	51-48	Oklahoma State	3.6	-0.6
11/24	UTSA	38-31	Texas State	10.1	-3.1
11/24	Western Kentucky	25-24	North Texas	1.3	-0.3

Week 13 Games In Which Field Position Value Exceeded Non-Garbage Final Score Margin
Date	Winning Team	Non-Garbage Final Score	Losing Team	FPV +	FPV -	FPV Net	FPV Neutral Score Margin
11/23	East Carolina	65-59	Marshall	39.1	27.5	11.6	-5.6
11/23	Utah	42-35	Colorado	39.6	30.5	9.1	-2.1
11/23	Miami	52-45	Duke	28.2	20.1	8.1	-1.1
11/24	Middle Tennessee	24-21	Troy	36.8	24.8	12.0	-9.0
11/24	Oklahoma	51-48	Oklahoma State	31.7	27.6	4.1	-1.1
11/24	UTSA	38-31	Texas State	29.3	19.3	10.0	-3.0
11/24	Western Kentucky	25-24	North Texas	29.3	25.8	3.5	-2.5

2012 totals to date:

• Net Total Turnover Value was the difference in 110 of 678 FBS games (16.2 percent)
• Net Special Teams Value was the difference in 53 of 678 FBS games (7.8 percent)
• Net Field Position Value was the difference in 66 of 678 FBS games (9.7 percent)
• Turnovers, Special Teams and/or Field Position was the difference in 153 of 678 FBS games (22.6 percent)

2012 Game Splits for all teams, including the offensive, defensive, special teams, field position, and turnover values recorded in each FBS game are provided here.

FEI Week 13 Top 25

The Fremeau Efficiency Index (FEI) rewards playing well against good teams, win or lose, and punishes losing to poor teams more harshly than it rewards defeating poor teams. FEI is drive-based and it is specifically engineered to measure the college game. FEI is the opponent-adjusted value of Game Efficiency (GE), a measurement of the success rate of a team scoring and preventing opponent scoring throughout the non-garbage-time possessions of a game. FEI represents a team's efficiency value over average.

Other definitions:

• SOS Pvs: Strength of schedule to date, based on the likelihood of an elite team going undefeated against the given team's schedule to date.
• SOS Tot: Strength of schedule, based on the likelihood of an elite team going undefeated against the given team's entire schedule. Conference championship games and bowl games are not yet included.
• FBS MW: Mean Wins, the average number of games a team with the given FEI rating would be expected to win against its entire schedule.
• FBS RMW: Remaining Mean Wins, the average number of games a team with the given FEI rating would be expected to win against its remaining schedule.
• OFEI: Offensive FEI, the opponent-adjusted efficiency of the given team's offense.
• DFEI: Defensive FEI, the opponent-adjusted efficiency of the given team's defense.
• STE: Special Teams Efficiency, the scoring value earned by field goal, punt and kickoff units measured in points per average game.
• FPA: Field Position Advantage, the share of the value of total starting field position earned by each team against its opponents.

These FEI ratings are a function of results of games played through November 24th. The ratings for all FBS teams, including FEI splits for Offense, Defense, and Special Teams can be found here. Program FEI (five-year weighted) ratings and other supplemental drive-based data can be found here.

Rk	Team	FBS Rec	FEI	LW	GE	GE Rk	SOS Pvs	Rk	SOS Tot	Rk	FBS MW	FBS RMW	OFEI	Rk	DFEI	Rk	STE	Rk	FPA	Rk
1	Oregon	10-1	.292	3	.342	2	.264	54	.264	58	9.9	-	.487	10	-.573	8	.807	40	.542	16
2	Notre Dame	12-0	.284	2	.193	10	.142	27	.142	31	10.4	-	.510	8	-.742	2	-.768	88	.495	67
3	Alabama	10-1	.275	1	.352	1	.298	60	.211	45	10.5	0.7	.328	20	-.573	9	2.486	8	.566	3
4	Kansas State	9-1	.272	4	.242	6	.139	26	.116	19	9.0	0.8	.330	19	-.577	7	4.279	1	.587	1
5	Oklahoma	8-2	.270	5	.175	13	.126	20	.092	11	8.7	0.7	.520	5	-.518	13	1.406	27	.520	41
6	Florida	10-1	.262	7	.143	19	.131	23	.131	28	9.0	-	.113	48	-.767	1	3.165	2	.548	10
7	Texas A&M	8-2	.245	6	.212	8	.189	38	.189	40	8.2	-	.677	2	-.271	31	-.595	83	.505	59
8	Stanford	10-2	.225	10	.134	22	.069	4	.061	4	9.9	0.8	.121	45	-.715	3	1.758	19	.556	6
9	Ohio State	12-0	.220	9	.153	18	.248	51	.248	54	10.0	-	.518	6	-.466	17	-.551	81	.505	58
10	Nebraska	9-2	.205	11	.093	35	.152	29	.123	25	8.8	0.7	.494	9	-.486	15	-1.620	106	.459	106
11	Georgia	10-1	.204	14	.258	3	.305	62	.166	36	9.6	0.3	.376	16	-.434	22	.423	52	.530	26
12	Oklahoma State	6-4	.193	15	.112	28	.114	14	.085	9	7.5	0.6	.532	3	-.277	30	1.781	17	.484	81
Rk	Team	FBS Rec	FEI	LW	GE	GE Rk	SOS Pvs	Rk	SOS Tot	Rk	FBS MW	FBS RMW	OFEI	Rk	DFEI	Rk	STE	Rk	FPA	Rk
13	South Carolina	9-2	.192	16	.177	12	.163	32	.163	34	8.4	-	.140	41	-.589	6	-.201	72	.504	60
14	LSU	9-2	.190	13	.126	27	.118	16	.118	20	8.0	-	.131	42	-.547	11	1.973	14	.553	8
15	Oregon State	8-3	.177	8	.076	38	.121	17	.121	21	7.5	-	.396	14	-.337	27	.134	56	.499	65
16	Florida State	8-2	.175	12	.220	7	.439	83	.422	83	8.9	0.8	.083	53	-.517	14	1.718	20	.546	13
17	Texas	8-3	.169	17	.095	33	.188	37	.088	10	8.0	0.2	.346	18	-.149	42	2.336	11	.555	7
18	Cincinnati	6-3	.144	24	.129	25	.585	105	.563	105	7.8	0.8	.180	37	-.593	5	.455	50	.532	25
19	Wisconsin	6-5	.144	19	.108	29	.174	35	.123	24	7.6	0.3	.110	50	-.470	16	.057	60	.542	17
20	TCU	6-4	.143	37	.020	57	.159	30	.102	16	6.5	0.3	-.143	81	-.546	12	-.073	65	.520	42
21	Michigan	8-4	.142	22	.132	23	.060	3	.060	3	7.5	-	.288	25	-.403	23	.614	46	.483	82
22	Northwestern	8-3	.140	25	.069	41	.236	50	.236	53	7.6	-	.269	27	-.142	43	3.058	4	.532	23
23	Baylor	5-5	.138	31	.047	46	.103	12	.082	7	6.2	0.4	.821	1	.419	107	-1.373	100	.508	54
24	UCLA	9-3	.135	18	.093	34	.310	63	.180	38	8.8	0.2	.265	28	-.341	26	-.847	89	.545	14
25	USC	7-5	.134	20	.102	31	.084	7	.084	8	7.3	-	.279	26	-.174	37	1.540	22	.519	43