Analysis of Collegiate Football Rivalries at the Aggregate Level

Rivalry games are an occasion for hate for college football fans and their silent, meticulous superstitions. Many hold a degree granted by the name on the front of the jersey, conferred upon them after four or five years of personal growth and diligent pupilage. It was during these years that many fans learned to hate whereas others, who may never have enrolled, will, throughout the life course, continually refine a hate acquired in early childhood. Not all rivalries are vicarious campaigns of hatred staged in the last week before post-season play. Not all rivalries are staged annually. Sometimes, members of the opposing student body are abducted and ransomed; occasionally, a festivity such as homecoming is borne some  existed prior to statehood;  yet others are simply old.

Perhaps meta-rivalries emerge when considering the most preeminent rivalries. Indeed, a Google search will reveal countless lists. A recent study concluded that the Auburn-Alabama football rivalry is the greatest in sports, based on a thorough analyses of troves of fanbases’ Twitter activities.  The conclusion seems reasonable and surely other empirical analyses exist but I am too lazy to perform a more thorough lit review.

Let us consider the characteristics of a rivalry based on how the matchups have played out because fans are wonderfully delusional. Data were extracted from the CFB SR Rivalry Finder and include only rivalries in which ≥50 matchups were available with both parties classified as major college teams. Included in the analyses were 116 rivalries from 1891 through 2015, a total of 9499 games.

The characteristics below are essential in my estimation. I intend to revisit this subject to analyze rivalries on a game-by-game basis but for this analysis, we will examine rivalries using summary statistics of the entire history of each rivalry.

• Frequency: because absence makes the heart grow fonder
• How often rivals play, we'll call this regularity, as measured by dividing the age of the rivalry (in years) by the quantity of matchups
• Lesser values indicate greater frequency
• The length of the longest span (of years) between matchups
• Lesser values indicate greater frequency
• Competitiveness: because there are no moral victories
• How often a winning/losing streak was ended divided by the quantity of matchups, we'll call this streaks ending
• Higher values indicate higher competitiveness
• Team A winning one year and team B winning the next would produce two ended-streaks
• The length of the longest streak
• Smaller values indicate higher competitiveness
• How close is the series overall, we'll refer to this as closeness and it is computed by (win% team A to-date)² * (win% team B to-date)² * 16;
• Value will be ≤1 and ≥0.
• Greater values indicate higher competitiveness
• if each team won 50% of all games (i.e., no ties), this value will equal 1
• Arithmetically, this value will be inflated for rivalries with fewer or no ties because imagine if the Big-10 declared a tie at the end of regulation in the OSU-UM game last week
• Margin of Victory: because, for the fanatics there is always a thirst for additional goblets of enemy blood but for the enthusiasts and executives there is a preference for games decided in the fourth quarter. Indeed, there is likely collinearity between margin of victory and competitiveness but margin of victory provides additional nuance. For instance, BYU-Utah St. rivalry is 47-35-3 but 54.1% of the matchups have been blowouts—or 54.1% of matchups have been boring for unemotional audiences. Closeness ranks BYU-USU higher than the Colorado-Utah rivalry which is 29-28-3 although only 28.3% of the games have been blowouts.
• How often matchups are close-scoring, as measured by the quantity of matchups in which the margin of victory is ≤ 7 points divided by total quantity of matchups
• Greater value indicates higher competitiveness
• How often matchups are blowouts, as measured by the quantity of matchups in which the margin of victory is ≥ 17 points divided by total quantity of matchups
• Lesser values indicate higher competitiveness
• How often matchups end in ties, as measured by the quantity of ties divided by the quantity of matchups
• Greater values indicate more tie-games
• Ties suggest a competitive game but have not occurred since 1995, thereby penalizing or rewarding rivalries with more games prior to 1996. Inherently, rivalries with more ties will be rewarded by several (likely collinear) variables described above. Moreover, winning is the only thing. Thusly, ties will be penalized slightly.
• Home invasion: because magic moments are made winning in front of the fans but few spoils of battle are more savory than the arrangement of the muscles on the faces of enemies defeated in their own territory
• How often matchups are won by the road team, as measured by the quantity of matchups in which the road team was victorious divided by the quantity of matchups not played at a neutral site
• Greater values indicate more road wins

I debated including age (in years) and the quantity of matchups but decided against it. The inclusion/exclusion criteria of ≥50 matchups as major college teams excluded Kent St.-Akron or Harvard-Yale and would unfairly penalized included rivalries such as Cinci-Miami(OH) who had matched-up 120 times as of 2015 but only had 54 of those included in the analysis.

Once the foregoing values were obtained for each rivalry, the values of each variable were standardized using the entire sample of rivalries (mean=0, SD=1). A number of standardized scores were inverted to ensure those scores entered a purely additive equation positively; for instance, higher regularity values would yield a positive standardized score instead of the negative score yielded directly from the raw values. The percentage of tie games was inverted but the inversion was weight as to reduce the direct penalty to ties (i.e., standard score multiplied by -0.5). Finally, all standard scores were summed yielding a rivalry rating with a mean of 0 and a SD of 1 across the sample.

WVU-Penn St. came out as the lowest rated rivalry and, thankfully, it has been on hiatus since 1992. Notre Dame-Navy was rated only slightly less uninteresting. Despite an historical dearth of competitiveness in both, Auburn-Miss. St. and LSU-Miss. State are the most average rivalries. Florida St.-Miami was the highest rated rivalry. The rivalry was 29-29-0 until earlier in the 2016 season when FSU took control. Having played 58 games in 60 seasons, there has been no ties, no neutral sites, and 44.8% of matchups were decided by ≤7 points. Although 32.8 of games were decided by ≥17 points, visiting teams won 58.6% of matchups. The rivalry approached or surpassed 1 SD above average in all variables except for ending streaks, in which it was average; the rivalry has been streaky. Summarily, at the close of the post there is a massive table with the summary statistics (raw values) for the 116 rivalries included in the analysis. It is not sortable but it is searchable—indeed, we here at POTH bring our readership the foremost developments in information technology.

We should also consider how this rivalry rating is associated with the raw values used in its imputation and some others. Doing so provides some insight into rivalry ratings  This can be seen in the table below. I also included the proportions of games with total scores within each rivalry that were ≤25th or ≥75th percentiles of total game scores for 5 years before and after a game. All p-values < .05.

Variable		r
History
	Matches	0.319
	Age	-0.103
Frequency
	Longest Hiatus	-0.378
	Age / Matchups	-0.478
Competitiveness
	Closeness	0.634
	Longest Streak	-0.662
	Streaks End %	0.706
Margin of Victory
	Margin of Victory ≤ 7pts	0.719
	Margin of Victory ≥ 17	-0.678
	Ties	0.181
Home Invasion
	Visiting Team Wins	0.369
Inferred Style of Play
	Total Pts ≤ 25th%ile	0.244
	Total Pts ≥ 75th%ile	-0.178

 I made no a priori suggestions about the valence each variable should contribute statistically to the rivalry rating. Other than the adjustment to ties (and while excluding age and matchup quantity), the rating was computed by a simple summation of standardized scores. So, in the future, when I elect to revisit this topic and perform a game-level analysis, I have some prior notions on how the  model model be constructed and tested for validity.

	History					Frequency		Competitiveness			Margin of Victory
	Rivalry	Matchups	First-Latest	W-L-T	Neutral Site%	Max Hiatus	Regularity	Closeness	Max Streak	Streaks End%	≤ 7 %	≥ 17 %	Road Team Win%	Rating
1	Florida State-Miami (FL)	58	1955-2015	29-29-0	0.000	3	1.034	1.000	7	0.397	0.448	0.328	0.586	8.977
2	Auburn-Georgia	111	1902-2015	50-55-6	0.351	3	1.018	0.797	9	0.495	0.432	0.297	0.583	7.85
3	Texas-Oklahoma	100	1903-2015	53-42-5	0.950	6	1.120	0.793	8	0.440	0.46	0.32	0.6	7.015
4	Oregon State-Oregon	99	1916-2015	43-50-6	0.061	3	1.000	0.770	8	0.465	0.414	0.293	0.559	6.751
5	Florida-Miami (FL)	55	1938-2013	26-29-0	0.109	14	1.364	0.994	7	0.400	0.418	0.255	0.531	6.428
6	Cincinnati-Miami (OH)	54	1962-2015	26-27-1	0.019	1	0.981	0.927	11	0.444	0.444	0.333	0.453	6.243
7	Clemson-South Carolina	107	1909-2015	63-40-4	0.000	1	0.991	0.775	7	0.486	0.374	0.393	0.561	5.902
8	Michigan-Ohio State	99	1904-2015	47-48-4	0.000	14	1.121	0.848	7	0.525	0.384	0.273	0.485	5.716
9	UCLA-Southern California	85	1929-2015	30-48-7	0.000	6	1.012	0.636	8	0.494	0.459	0.329	0.541	5.425
10	Oregon-Washington	96	1916-2015	40-52-4	0.000	3	1.031	0.815	12	0.438	0.469	0.323	0.479	5.4
11	Kansas-Missouri	110	1901-2011	48-54-8	0.145	2	1.000	0.734	5	0.573	0.427	0.345	0.404	5.325
12	Washington-Washington State	96	1917-2015	62-30-4	0.000	3	1.021	0.652	8	0.510	0.406	0.333	0.49	5.236
13	Southern California-Stanford	91	1922-2015	57-31-3	0.011	4	1.022	0.728	12	0.352	0.396	0.308	0.622	5.22
14	Baylor-Texas Christian	103	1903-2015	46-52-5	0.097	11	1.087	0.813	8	0.524	0.398	0.369	0.538	5.201
15	Texas A&M-Texas Tech	69	1932-2011	36-32-1	0.188	10	1.145	0.937	6	0.449	0.449	0.377	0.446	5.114
16	Indiana-Purdue	112	1899-2015	40-66-6	0.018	3	1.036	0.709	10	0.420	0.464	0.348	0.536	5.078
17	Toledo-Bowling Green State	54	1962-2015	27-26-1	0.000	1	0.981	0.927	7	0.463	0.352	0.315	0.389	4.981
18	Kentucky-Vanderbilt	82	1916-2015	42-36-4	0.000	9	1.207	0.809	7	0.463	0.439	0.293	0.463	4.909
19	Georgia-Georgia Tech	105	1902-2015	61-39-5	0.000	9	1.076	0.745	8	0.381	0.438	0.295	0.514	4.491
20	North Carolina-North Carolina State	95	1902-2015	57-34-4	0.021	15	1.189	0.738	9	0.411	0.453	0.305	0.548	4.409
21	Duke-North Carolina	95	1922-2015	33-58-4	0.000	1	0.979	0.720	13	0.379	0.453	0.347	0.526	4.403
22	Illinois-Northwestern	109	1892-2015	55-49-5	0.009	7	1.128	0.823	7	0.486	0.413	0.413	0.509	4.358
23	Louisiana State-Mississippi	99	1902-2015	57-38-4	0.010	5	1.141	0.781	8	0.485	0.424	0.364	0.459	4.347
24	California-Stanford	95	1918-2015	39-50-6	0.000	4	1.021	0.747	7	0.453	0.421	0.379	0.505	4.344
25	Iowa State-Kansas	94	1916-2015	39-49-6	0.000	3	1.053	0.748	7	0.521	0.351	0.34	0.479	4.326
26	Iowa State-Missouri	103	1908-2011	33-61-9	0.000	2	1.000	0.576	10	0.466	0.398	0.282	0.524	4.203
27	Army-Navy	112	1891-2015	49-56-7	0.804	7	1.107	0.766	14	0.491	0.438	0.277	0.455	4.169
28	Ohio-Miami (OH)	54	1962-2015	24-29-1	0.000	1	0.981	0.912	6	0.389	0.389	0.407	0.444	4.119
29	Arkansas-Mississippi	62	1908-2015	33-28-1	0.242	11	1.726	0.924	6	0.500	0.435	0.323	0.426	3.833
30	Georgia-Florida	94	1904-2015	49-43-2	0.872	11	1.181	0.910	7	0.415	0.394	0.404	0.5	3.496
31	Illinois-Purdue	90	1892-2015	43-41-6	0.000	12	1.367	0.758	6	0.511	0.4	0.389	0.544	3.395
32	Florida-Florida State	60	1958-2015	34-24-2	0.033	1	0.950	0.822	9	0.383	0.367	0.35	0.448	3.379
33	Wisconsin-Minnesota	123	1892-2015	58-57-8	0.000	2	1.000	0.764	12	0.455	0.431	0.358	0.439	3.278
34	New Mexico State-Texas-El Paso	76	1935-2015	26-49-1	0.000	4	1.053	0.778	8	0.382	0.461	0.355	0.368	3.198
35	Rice-Southern Methodist	90	1916-2012	41-48-1	0.000	5	1.067	0.944	10	0.422	0.333	0.344	0.411	3.069
36	Memphis-Southern Mississippi	50	1963-2012	17-32-1	0.000	2	0.980	0.758	7	0.380	0.42	0.38	0.4	3.03
37	Iowa-Wisconsin	88	1906-2015	42-44-2	0.000	7	1.239	0.911	10	0.443	0.352	0.352	0.443	2.787
38	Alabama-Louisiana State	78	1902-2015	49-24-5	0.013	14	1.449	0.598	11	0.474	0.397	0.346	0.623	2.565
39	Mississippi-Mississippi State	108	1902-2015	61-42-5	0.324	4	1.046	0.772	12	0.472	0.361	0.444	0.507	2.282
40	Notre Dame-Southern California	87	1926-2015	46-36-5	0.000	4	1.023	0.766	11	0.414	0.402	0.368	0.437	2.133
41	Arizona-Arizona State	79	1931-2015	39-39-1	0.000	4	1.063	0.950	11	0.392	0.316	0.405	0.456	2.131
42	Syracuse-West Virginia	60	1945-2012	33-27-0	0.033	9	1.117	0.980	8	0.433	0.317	0.4	0.397	2.088
43	Baylor-Texas A&M	102	1903-2011	29-64-9	0.010	5	1.059	0.509	13	0.441	0.451	0.333	0.495	2.023
44	Virginia Tech-Virginia	92	1902-2015	55-32-5	0.250	18	1.228	0.692	12	0.478	0.435	0.359	0.493	1.865
45	Auburn-Florida	84	1904-2011	44-38-2	0.024	10	1.274	0.898	7	0.488	0.393	0.357	0.305	1.747
46	Texas A&M-Texas	109	1903-2011	36-69-4	0.046	4	0.991	0.699	10	0.486	0.349	0.376	0.385	1.71
47	Arkansas-Texas A&M	71	1910-2015	40-28-3	0.099	18	1.479	0.790	9	0.479	0.423	0.366	0.469	1.642
48	Notre Dame-Michigan State	63	1918-2013	34-28-1	0.000	30	1.508	0.921	8	0.429	0.413	0.349	0.492	1.567
49	Southern Methodist-Texas Christian	93	1916-2015	38-48-7	0.011	4	1.065	0.712	15	0.376	0.376	0.344	0.533	1.555
50	Colorado State-Wyoming	101	1905-2015	52-45-4	0.000	5	1.089	0.842	10	0.426	0.297	0.416	0.495	1.505
51	New Mexico-Utah	52	1939-2010	17-33-2	0.019	15	1.365	0.689	5	0.462	0.442	0.404	0.412	1.158
52	North Carolina-Virginia	110	1902-2015	61-45-4	0.018	3	1.027	0.823	9	0.382	0.391	0.436	0.398	1.097
53	Auburn-Tennessee	51	1929-2013	27-21-3	0.039	17	1.647	0.760	6	0.471	0.471	0.333	0.388	0.978
54	Air Force-Colorado State	54	1957-2015	32-21-1	0.000	3	1.074	0.850	7	0.407	0.296	0.5	0.463	0.759
55	Maryland-Virginia	78	1919-2013	44-32-2	0.026	12	1.205	0.857	16	0.385	0.333	0.346	0.487	0.668
56	Arkansas-Texas	75	1906-2014	22-53-0	0.040	9	1.440	0.687	12	0.480	0.36	0.453	0.486	0.588
57	North Carolina-South Carolina	55	1903-2015	32-19-4	0.018	16	2.036	0.646	5	0.491	0.418	0.291	0.481	0.525
58	Alabama-Tennessee	97	1903-2015	53-37-7	0.000	14	1.155	0.695	11	0.381	0.402	0.371	0.505	0.487
59	Kansas-Kansas State	104	1912-2015	57-42-5	0.000	1	0.990	0.784	11	0.394	0.337	0.481	0.471	0.411
60	Southern California-California	96	1922-2015	67-25-4	0.000	2	0.969	0.529	13	0.333	0.323	0.375	0.531	0.264
61	Michigan-Michigan State	90	1918-2015	53-33-4	0.000	7	1.078	0.746	10	0.389	0.289	0.356	0.444	0.158
62	Mississippi State-Auburn	88	1910-2015	27-58-3	0.000	8	1.193	0.654	11	0.307	0.42	0.364	0.443	0.009
63	Mississippi State-Louisiana State	106	1902-2015	34-69-3	0.000	4	1.066	0.698	14	0.358	0.377	0.396	0.425	-0.027
64	California-UCLA	86	1933-2015	32-53-1	0.000	1	0.953	0.841	18	0.395	0.302	0.43	0.419	-0.109
65	Oklahoma-Nebraska	86	1912-2010	45-38-3	0.035	7	1.140	0.855	16	0.360	0.372	0.419	0.446	-0.267
66	Pittsburgh-West Virginia	93	1909-2011	55-35-3	0.000	4	1.097	0.793	15	0.419	0.323	0.462	0.462	-0.29
67	Iowa-Minnesota	108	1901-2015	45-61-2	0.000	4	1.056	0.886	11	0.389	0.315	0.472	0.38	-0.635
68	Brigham Young-Utah	90	1922-2015	30-56-4	0.011	4	1.033	0.688	9	0.322	0.4	0.467	0.427	-0.641
69	Arkansas-Louisiana State	60	1906-2015	21-37-2	0.433	26	1.817	0.745	7	0.450	0.417	0.317	0.412	-0.732
70	Baylor-Texas	104	1903-2015	25-74-5	0.010	4	1.077	0.468	16	0.462	0.356	0.413	0.437	-1.125
71	Baylor-Texas Tech	72	1932-2015	34-37-1	0.111	8	1.153	0.942	15	0.347	0.347	0.444	0.391	-1.128
72	Arizona-New Mexico	50	1931-2015	31-17-2	0.020	10	1.680	0.711	10	0.340	0.34	0.34	0.49	-1.267
73	North Carolina-Wake Forest	101	1908-2015	67-32-2	0.050	4	1.059	0.707	16	0.366	0.356	0.455	0.417	-1.343
74	Brigham Young-Utah State	85	1922-2015	47-35-3	0.035	4	1.094	0.829	10	0.388	0.306	0.541	0.451	-1.346
75	Penn State-Pittsburgh	89	1905-2000	43-42-4	0.000	16	1.067	0.832	14	0.416	0.348	0.438	0.416	-1.364
76	Alabama-Auburn	74	1902-2015	43-30-1	0.676	41	1.527	0.888	9	0.446	0.392	0.365	0.417	-1.48
77	Wisconsin-Ohio State	80	1913-2014	17-58-5	0.013	8	1.263	0.380	21	0.413	0.413	0.325	0.481	-1.611
78	Missouri-Oklahoma	93	1912-2011	22-66-5	0.022	3	1.065	0.451	14	0.430	0.301	0.409	0.462	-1.689
79	Pittsburgh-Syracuse	71	1916-2015	37-31-3	0.028	25	1.394	0.828	11	0.352	0.394	0.38	0.435	-1.865
80	New Mexico-New Mexico State	82	1931-2015	59-21-2	0.000	4	1.024	0.543	18	0.305	0.39	0.427	0.451	-1.908
81	Notre Dame-Purdue	83	1899-2014	56-25-2	0.024	13	1.386	0.661	11	0.434	0.301	0.458	0.469	-2.07
82	Georgia-South Carolina	63	1903-2015	44-17-2	0.000	17	1.778	0.568	10	0.397	0.397	0.365	0.46	-2.12
83	Oklahoma State-Tulsa	58	1917-2011	34-22-2	0.000	16	1.621	0.791	5	0.466	0.293	0.328	0.293	-2.223
84	Colorado-Utah	60	1905-2015	29-28-3	0.000	49	1.833	0.814	9	0.383	0.467	0.283	0.467	-2.285
85	Utah-Utah State	98	1912-2015	68-26-4	0.000	3	1.051	0.542	12	0.388	0.296	0.439	0.418	-2.303
86	Penn State-Syracuse	71	1922-2013	43-23-5	0.042	18	1.282	0.616	16	0.352	0.408	0.366	0.471	-2.415
87	Texas-Texas Tech	64	1934-2015	48-16-0	0.000	8	1.266	0.563	8	0.375	0.281	0.453	0.406	-2.666
88	Virginia Tech-West Virginia	50	1915-2005	21-28-1	0.060	35	1.800	0.885	7	0.440	0.3	0.32	0.404	-2.683
89	Kent State-Bowling Green State	53	1962-2015	9-44-0	0.019	2	1.000	0.318	14	0.264	0.264	0.396	0.5	-2.939
90	Maryland-West Virginia	52	1919-2015	22-28-2	0.038	24	1.846	0.830	7	0.404	0.327	0.462	0.5	-3.1
91	Tennessee-Vanderbilt	105	1902-2015	75-26-4	0.000	3	1.076	0.501	22	0.286	0.371	0.429	0.486	-3.257
92	Mississippi-Vanderbilt	86	1902-2015	49-35-2	0.105	9	1.314	0.860	15	0.314	0.302	0.419	0.39	-3.26
93	Missouri-Nebraska	95	1901-2010	33-59-3	0.011	9	1.147	0.745	24	0.316	0.347	0.389	0.426	-3.304
94	Tennessee-Kentucky	99	1915-2015	73-18-8	0.000	3	1.010	0.288	26	0.333	0.394	0.374	0.515	-3.564
95	Mississippi-Tulane	62	1902-2012	39-23-0	0.000	10	1.774	0.871	11	0.290	0.29	0.419	0.403	-4.01
96	Air Force-Army	50	1959-2015	35-14-1	0.040	4	1.120	0.615	8	0.480	0.2	0.54	0.333	-4.216
97	Georgia Tech-Clemson	79	1902-2015	50-27-2	0.013	10	1.430	0.749	15	0.380	0.38	0.418	0.256	-4.426
98	Texas A&M-Texas Christian	89	1903-2001	54-28-7	0.056	6	1.101	0.583	24	0.315	0.326	0.427	0.5	-4.536
99	Michigan-Minnesota	102	1892-2015	74-25-3	0.000	9	1.206	0.506	16	0.294	0.314	0.48	0.49	-4.59
100	Texas Christian-Texas	82	1904-2015	23-58-1	0.000	12	1.354	0.630	24	0.378	0.268	0.476	0.512	-4.85
101	Iowa-Iowa State	60	1899-2015	41-19-0	0.000	43	1.933	0.749	15	0.367	0.367	0.367	0.483	-5.059
102	Utah State-Wyoming	65	1912-2015	36-25-4	0.000	23	1.585	0.726	10	0.415	0.277	0.431	0.415	-5.217
103	Clemson-Georgia	59	1902-2014	16-39-4	0.119	10	1.898	0.514	10	0.441	0.356	0.407	0.346	-5.426
104	Oklahoma State-Oklahoma	102	1914-2015	18-77-7	0.069	1	0.990	0.284	19	0.343	0.284	0.529	0.537	-5.429
105	Indiana-Michigan State	61	1927-2015	13-46-2	0.000	12	1.443	0.413	8	0.393	0.262	0.541	0.459	-5.815
106	Louisiana State-Tulane	90	1904-2009	63-20-7	0.000	7	1.167	0.387	18	0.378	0.244	0.478	0.489	-6.276
107	Nebraska-Minnesota	56	1900-2015	23-31-2	0.000	21	2.054	0.827	16	0.321	0.357	0.464	0.446	-6.563
108	Georgia-Vanderbilt	72	1903-2015	53-17-2	0.000	20	1.556	0.483	11	0.333	0.264	0.486	0.486	-6.598
109	Alabama-Mississippi State	96	1902-2015	77-16-3	0.000	5	1.177	0.286	22	0.229	0.333	0.427	0.438	-6.986
110	Wisconsin-Michigan	64	1892-2010	13-50-1	0.031	16	1.844	0.403	14	0.313	0.281	0.422	0.468	-7.21
111	Nebraska-Colorado	68	1902-2010	48-18-2	0.000	41	1.588	0.559	18	0.368	0.25	0.412	0.471	-8.6
112	Kentucky-Florida	66	1917-2015	16-50-0	0.000	11	1.485	0.540	30	0.258	0.288	0.5	0.409	-9.818
113	Georgia Tech-Tulane	50	1916-2015	37-13-0	0.000	32	1.980	0.592	14	0.240	0.26	0.44	0.4	-10.637
114	Washington State-Idaho	63	1917-2013	53-8-2	0.063	24	1.524	0.183	21	0.190	0.254	0.444	0.508	-11.521
115	Navy-Notre Dame	89	1927-2015	12-76-1	0.360	1	0.989	0.212	43	0.202	0.281	0.562	0.404	-13.236
116	West Virginia-Penn State	55	1909-1992	9-44-2	0.018	14	1.509	0.274	25	0.273	0.236	0.545	0.389	-13.283

Hand Size, Arm Length, and Drop Rate among NFL Receivers

Although it is not evident here, I have been exploring the influence of physical attributes on in-game performance in gridiron football. Physical attributes include anthropometrics such as height and weight as well as assessments of athleticism such as the 40-yard dash and standing vertical jump. In this post I focus on hand size and drop rates in NFL receivers. By receivers I refer broadly to any eligible pass catcher; specifically, WRs, TEs, and RBs. 

At least one other author has examined the influence of hand size on WR performance. Joe Redemann at numberFire explored relationships between hand size, several standard statistics, and “a player’s contribution to his team”, NEP, across multiple seasons. A mild relationship between hand size and catch rate (receptions / targets rate) was discernible (r = .17). Ultimately, Redemann demonstrated that the performance of elite WRs was relatively unrelated to hand size whereas a stronger—but still mild—relationship evidenced between the performance of ordinary WRs and hand size. 

We should expect then to find that larger hands predict in fewer drops. We should also expect a minimal reduction in drops offered by larger hands. We shall extend the analysis by including TEs and RBs in addition to WRs. 

NFL Combine data were procured from NFL Savant and passes dropped were extracted from Sporting Charts. Drop data were gathered for WRs, TEs, and RBs from the 2009-15 seasons. Combining Combine and drop data yielded 604 player-seasons from 238 players without checking for spelling inconsistencies between the two data sets. As regular readers know, I am lazy, so I pressed onward with this sample. Player height and arm length were included because of my intuition that doing so would better isolate the effect, if any, of hand size by isolating the effect of atypically large hands given medium or small stature. 

Table 1. Targets, Drops, and Anthropometrics for NFL WRs, TEs, and RBs, 2009-15

	Totals			Medians
	Seasons	≥ Median Targets	Players	Handsize	Arm Length	Height	Drop %	Targets
RB	123	65	63	9.25	31	71	0.051	28
TE	103	52	42	9.875	33.125	77	0.046	35
WR	378	194	133	9.25	32.1	73	0.043	67
TOTAL	604	311	238
MEDIAN				9.375	32	73	0.045	53

Table 1 displays basic information about the players within our sample. Medially, TEs presented with the largest hands and, for the included seasons, WRs dropped fewer passes while being targeted more frequently. Thus, position should be accounted for in the analysis. Also, we will need to account for season to season variability within players. 

I constructed several models. For each model, the count of drops for each player-season was the dependent variable (actually, the rate of drops, or, drops / targets). Hand size, arm length, height, and position were predictor, independent, or explanatory variables—whichever jargon you prefer. Players were included as a random effect to account for each player’s variability in drops between seasons. Random effect also means that the models are constructed accounting for the differences between players that we are not measuring in this analysis; for instance, a factor as relevant but complex as coverages faced or as esoteric as blood type. 

Three models were constructed. Excluded here, there is a table at the bottom of the page with pertinent model data.

• The first model included all 604 player seasons. In short, increased hand size predicted fewer drops; being a WR decreased drops.
• The second model included 311 player seasons from 127 players who accumulated ≥ median targets at their positions. Again, larger hands and being WRs predicted fewer drops. Interestingly, greater arm length predicted greater drops.
• In the third model, I included all 604 player seasons while accounting for whether ≥ median targets were accumulated in a given player-season (via dummy coding). Again, being a WR and having larger hands predicted fewer drops.
  

Figure 1. Expected Drops by hand size for NFL receivers.

For convenience, the p-values for hand size in models 1, 2, and 3 were .07, .05, and .10, respectively. So, the statistical significance of hand size in explaining drop rates hovers slightly above the conventional cutoff of .05.  But how does hand size actually impact drops? Probably minimally, as can be seen in Figure 1. Arm length and height held constant, for WRs, 3 inches of greater hand size equates to about 1 less drop per season; for RBs and TEs 3 inches of greater hand size equates to about half a drop per season.

Why though would greater arm length predict more dropped passes in the group of receivers targeted at or above the median? It might be a spurious finding, but, perhaps players with longer arms drop errant passes at the fringes of their catch radii, passes beyond the range of players with shorter arms. 

Alternatively, RBs are known to exhibit the highest drop rate. Likewise, consider that RBs are often catching passes coming out of the backfield where more defenders may be lurking; perhaps RBs are targeted with more less accurate passes due to their being a check down or hot receiver targeted when the QB is hurried; or by releasing from his blocking assignment into the flats, knowing a pass is coming, and having to reorient his body to catch. The process of reorienting with multiple proximal defenders might be more difficult for larger RBs, with longer arms. Unsurprisingly then, within each position, only for RBs is the raw correlation between drop rate and arm length appreciable—although this may be the result of small sample sizes:

• WR: r = .014, p = .805, n = 315
• TE: r = .133, p = .311, n = 60
• RB: r = .369, p = .004, n = 58
  

Summarily, the effects of hand size and subsequently arm length on drop rates in NFL WRs, TEs, and RBs were examined in this analysis. Although the effect of hand size was in a significant range, the ecological impact of hand size is irresolute because, with all else held constant, 1 inch of hand size was worth about 1/3 of a drop per season for WRs. Additionally, if you are managing NFL offensive personnel and you rely on RBs in your passing game, the present results suggest it may be advisable to cultivate a smaller RB with shorter arms to specialize in pass catching.

Technical supplement. For GLMMs 1-3

Variable	Fixed-Effects
	Estimate	SE	z	p
Model 1: AIC = 2216.4		Player Var & SD = .039, 0.197
Intercept	-2.940	0.085	-34.400	0.000
Hand	-0.065	0.036	-1.790	0.073
Height	-0.002	0.056	-0.030	0.978
Arm	0.067	0.051	1.330	0.185
TE	-0.113	0.142	-0.800	0.425
WR	-0.172	0.093	-1.840	0.066
Model 2: AIC = 1298		Player VAR & SD = .037, 0.193
Intercept	-2.974	0.101	-29.350	0.000
Hand	-0.0840	0.0422	-1.990	0.047
Height	0.112	0.064	1.760	0.079
Arm	0.028	0.067	0.420	0.674
TE	-0.239	0.166	-1.440	0.149
WR	-0.199	0.111	-1.790	0.074
Model 3: AIC = 2207.2		Player Var & SD = .039, 0.197
Intercept	-2.786	0.094	-29.570	0.000
Hand	-0.058	0.035	-1.670	0.095
Height	0.070	0.049	1.430	0.153
Arm	0.003	0.054	0.050	0.960
≥ Median Targets	-0.199	0.059	-3.410	0.001
TE	-0.131	0.137	-0.960	0.340
WR	-0.189	0.091	-2.090	0.036

Note: R v3.3.1 console used for analysis. The glmer function within the lme4 package was employed in the GLMM. A Poisson distribution was specified; a negative binomial distribution yielded essentially identical results but the models did not converge. Data and R code available upon request, of course.

Field Position Part II

In a previous post I discussed how INTs and INT return yardage influenced starting field position (SFP). I will extend that discussion to include each of the other events that directly result in SFP: turnover-fumble returns, kick and punt returns, and missed field goals by opponents. As an aspiring defensive back, I of course took great care discussing interceptions. I will devote little discussion here to fumble recoveries and missed field goals. I will harp on kick-off returns but refrain from discussing punt returns at any depth.

Let me first state that my play-by-play (PBP) data differs slightly from the official record. I excluded yardage gained on returns for TDs in the analysis because a TD precludes SFP. Excluded also was return yardage gained prior to a turnover-fumble.

Concerning INTs, I emphasized that ending opponents’ possessions is most salient and that INT return yardage is a somewhat superfluous stat. INT return yards may be useful to compare playmaking abilities between DBs, although statisticians, teams, and observers might be better served knowing the SFP that resulted from an interception. This notion is definitely applicable for fumble returns where, again, the ending of opponents’ possession is most salient.

Likewise, it is also relevant for rating punt returners. For instance, a player fair catching a punt at his own 9-yard line would be recorded as a fairly unremarkable zero yards (i.e., it is counted in his average PRY). However, the fair catch was probably initiated in the presence of proximal defenders who could have disrupted the impetus of the punted ball at say, the 2-yard line had the returner declined to fair catch. Thus, by fair catching—despite accruing zero yards—the returner in the example would improve his team’s SFP by 7 yards (of course, the defense downing the ball is hypothetical).

The foregoing notion of field position in lieu of yardage is applicable to kick returns as well. For example, let us review the 2014 NFLleading kick-returners by average yards per return. I have Bruce Ellington of the 49ers at 24 returns for 25.9 yards per return;^c.f. he ranks about ninth in KR yards. However, Ellington gives his offensive teammates an average starting FP at the ~23-yard line—18^th on my list of qualifying players. It may be poor decision making on his behalf or poor block execution behalf of his teammates or that he generally fields kickoffs from superior kickers but we must acknowledge Ellington’s average catch-spot (CS) on KRs was nearly 3-yards into the endzone, ranking third-deepest on my list of qualifying players.¹

Although this post is about SFP, the above anecdotes underscore the entanglement of variables involved in appraising performances with yardage accrued. However, Ellington still gained those yards. If we are comparing players (or even coverage units), perhaps, Ellington does rank ninth in KR yards. However, football is about team success and on a given drive, a team is increasingly inclined to success the closer it begins to its opponent’s endzone. Conversely, Ellington’s team did start 3 yards closer to the endzone then would result from him taking more touchbacks.

Moving on, for all teams in the 2014-15 NFL season, I obtained all non-TD turnover-fumble returns, interceptions, kick and punt returns, and field goals missed by opponents using the Pro-Football Reference PBP searchtool. Opponents’ missed FGs include blocks but excludes blocks returned for TDs. For all plays except opponents’ missed field goals, I extracted [a] the spot of the INT, fumble recovery, or catch and [b] the spot at which the player was downed following the return. Computed with those values were [c] return yards or 20 for a touchback and [d] the SFP of the player’s offensive teammates. SFP was scaled such that teams’ own goal lines equaled zero and opponents’ goal lines equaled 100; greater yards indicate better SFP.

Table 1. Counts, Average SFP, and Average Return Yards for Events Resulting in SFP, NFL 2014-15

TEAM	TOTAL EVENT COUNTS						AVERAGE STARTING FIELD POSITION BY EVENT							AVERAGE RETURN YARDS BY EVENT
	KR	PR	FR	INT	oMFG		SFP	KR	PR	FR	INT	oMFG		KR	PR	FR	INT
KAN	68	76	5	5	5		29.3	25.4	28.7	22.4	44.0	23.6		25.4	8.6	0.0	15.2
CIN	78	74	5	19	5		30.3	24.7	30.3	27.4	50.8	26.0		24.9	8.4	0.0	9.2
NWE	68	64	7	16	5		30.6	22.7	32.0	36.9	51.8	29.6		22.1	7.5	0.4	11.7
DAL	75	66	12	16	2		28.9	21.1	26.9	35.5	43.3	21.0		22.3	7.3	2.6	9.3
TAM	81	63	11	11	7		26.6	20.7	25.3	30.1	48.8	32.6		21.6	7.2	1.3	6.9
IND	79	88	13	11	4		28.7	22.5	28.4	30.3	43.2	24.0		24.3	7.0	2.6	8.7
BAL	68	73	12	10	6		28.7	23.3	30.4	32.9	48.2	27.8		22.9	6.9	4.3	9.1
JAX	92	74	12	5	4		25.7	22.1	21.5	24.3	51.0	31.8		21.9	6.4	0.8	13.0
PHI	83	85	16	9	5		30.0	22.9	28.8	33.8	41.6	23.4		20.9	6.2	6.3	6.2
MIN	73	74	4	11	6		27.3	25.0	25.5	15.3	49.0	30.3		21.9	6.2	0.0	8.2
STL	79	74	11	10	1		28.0	22.1	28.8	32.4	42.1	35.0		22.9	5.9	3.3	10.8
BUF	71	86	8	18	7		30.2	21.3	27.0	25.5	60.4	26.9		20.6	5.9	4.4	19.2
OAK	94	81	4	9	5		24.2	19.9	24.7	26.0	61.9	24.2		21.4	5.7	5.3	8.4
CHI	97	49	8	13	6		25.9	21.1	27.0	15.9	43.6	23.8		20.5	5.6	2.4	10.9
SDG	81	66	8	6	2		26.4	21.3	26.5	24.1	31.7	33.5		21.1	5.5	0.0	12.0
SFO	70	74	5	21	0		27.8	22.6	28.3	16.2	48.0	-		22.9	5.5	0.0	18.8
ATL	89	55	7	15	4		26.5	22.4	25.7	32.3	40.5	27.5		22.5	5.4	5.6	6.9
MIA	82	57	10	11	6		31.1	24.2	25.5	21.3	50.6	23.5		23.9	5.3	0.0	17.1
DEN	75	84	5	16	5		28.9	22.6	28.2	26.0	54.4	25.2		21.4	5.3	0.4	10.8
TEN	89	72	6	11	5		25.8	23.2	24.8	38.8	52.7	31.0		22.5	5.2	7.2	10.8
ARI	76	77	5	15	4		26.9	19.6	24.8	20.8	51.3	32.5		20.2	5.1	1.8	10.3
NYJ	85	79	7	6	5		27.8	22.5	26.6	31.4	35.0	24.0		22.1	5.1	0.3	9.0
PIT	86	66	10	7	2		25.7	20.7	24.9	32.5	48.9	29.5		21.1	5.0	3.9	18.1
NYG	87	74	9	16	2		28.2	20.7	23.7	31.6	62.1	24.0		21.1	4.9	1.5	16.6
GNB	79	60	7	15	1		28.5	20.1	27.0	37.4	54.7	29.0		20.3	4.8	0.0	15.2
CAR	83	69	13	10	4		27.7	21.8	25.5	32.5	45.2	25.8		21.0	4.5	2.8	19.0
SEA	62	81	9	11	2		30.5	22.4	27.7	29.0	58.2	32.5		21.4	4.2	0.0	14.2
CLE	72	83	7	18	3		26.8	22.6	24.9	27.7	54.1	34.0		22.8	4.2	4.9	14.4
WAS	85	80	9	6	3		25.1	21.4	22.7	29.0	45.5	18.0		20.8	4.0	2.1	5.0
HOU	71	82	10	16	2		27.7	20.4	23.5	31.9	60.6	26.5		20.7	3.8	8.7	16.6
DET	70	81	7	18	4		29.9	21.1	29.4	32.9	59.2	27.3		21.8	3.8	1.8	18.7
NOR	86	62	6	12	0		25.5	22.2	22.0	18.5	42.9	-		22.3	3.0	0.0	12.5
League	Event Counts						Average Field Position by Event							Average Return Yards by Event
AVG	79	73	8	12	4	AVG	27.9	22.0	26.5	29.1	50.5	27.2	AVG	22.0	5.6	2.3	12.3
SD	9	10	3	4	2	SD	1.8	1.4	2.5	6.4	7.6	4.2	SD	1.3	1.3	2.4	4.2

Table 1 contains 2014-15 distributions, NFL team average SFP and yards gained for each event, and League averages thereof. KRY and PRY are computed with touchbacks equal to 20 yards and no return equal to zero yards. Neither New Orleans’ nor San Francisco’s opponents missed FGs, apparently. There is nothing particularly noteworthy in the table, otherwise.

I also can tell you several things. INTs have the largest impact on the next-SFP when statistically controlling for the initial play spot, the spot at which an INT, fumble recovery, or kick/punt catch occurred, and the yardage gained on the return.² I can also tell you that for all NFL teams, the majority of SFP yardage is derived from either KR yards or PR yards. Table 2 provides some insight into why this is.

Table 2. Characteristics of NFL Based on Majority of SFP

	Majority of Team SFP From
VARIABLE	KR	PR
Teams Count	11	21
avg SFP	27	28
avg SFP Unproductive Drives	24	24
avg KR-SFP	22	22
avg Unproductive Drive Yards	17	16
avg Punt Yards	45	45
Opp avg Punt Return Yards	9	9
avg Def. SFP After Unproductive Drive	24	23
Opp avg Unproductive Drive Yards	16	16
Opp avg Punt Yards	45	45
avg Punt Return Yards	5	6
% All Drives Turnovers	14%	11%
Opp % All Drives Turnovers	12%	12%
% All Drives End w/ Score	32%	35%
Opp % All Drives End w/ Score	39%	32%
win%	35%	58%

NOTE: Unproductive drives are defined as those that end without a score.
Scoring drives are those that ended in TDs or FGs.

In Table 2 we see that the two types of teams perform similarly in most situations. Notably, teams whose majority of SFP is derived from KRs commit TOs slightly more frequently. As an aside, this might suggest that while essentially random, a modicum of TOs may be attributable to offensive ineptitude (albeit, in single season sample). Those teams’ opponents also end drives by scoring considerably more frequently—23% more—than teams whose majority of SFP is derived from PRs. The PR-teams score slightly more frequently.

Most striking in Table 2, though, is the disparity in win percentage. The KR-teams can be expected to win 5.6 games whereas PR-teams can be expected to win 9.3 games. Thus, I conclude that, despite the indelible impact of Devon Hester or the ’84 Seahawks’ 3-4 monster, ultimately, SFP is largely the result of an ungenerous defense supplemented by relatively consistent and careful offensive play.

Summarily, the impact of various events on starting field position was examined using data from the 2014-15 NFL season. Although INT yards are most impactful on SFP in isolation, when statistically controlling for event-spot and return yardage, the majority of SFP is derived from either KR or PR yards. Likewise, winning teams garner most of their from PR yards. I concluded that this effect is likely due to defensive stops and consistent, careful offensive play.

---

¹ Minimum 1 KR per game scheduled.

² To accomplish this, SFP was regressed on to play start spot, event spot, and yards gained. The residuals were saved. An ANOVA was performed with those residuals as the dependent variable and event type as the independent variable. A significant effect of event type was found, F(4, 5641) = 17.422, p < .001. Roughly, planned post hoc comparisons indicate the effect of event on SFP could be ranked as INT > FUM > PR > MFG > KR.