College Football by the Numbers: Recruiting and the Diversity Index

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Sunday, July 15, 2012

Recruiting and the Diversity Index

The Diversity Index is used to measure the diversity within in a population. Essentially it says, were we to select two random people from a population, what is the probability that they would be the same - what "same" means depends on what kind of diversity you are interested in: age, sex, race, eye color, favorite movie, college major, etc. I have applied the Diversity Index (DI) to college football rosters and the home state of college football players.

What's the point? If we assume that coaches would rather work local high schools than travel across many states to fill their rosters, we can conclude that the diversity index gives us some insight in to how hard it is for programs to recruit. This is muddled a bit because some coaches recruit more broadly because the program has a strong national presence. For example, Army, Notre Dame and Navy, the top three on the list, struggle with unique admission standards but also have relatively strong national presences. Wyoming, on the other hand, draws from a broader audience, not because of its national presence, but because Wyoming is not a hotbed of college football talent.

On the other hand, schools in Texas, California and Florida fill their rosters with in-state recruits - 22 of the 25 least geographically diverse programs come these three states.

Team	Rk	DI	Team	Rk	DI
Army	1	0.0432	Air Force	7	0.0920
Notre Dame	2	0.0594	Akron	73	0.2937
Navy	3	0.0644	Alabama	68	0.2723
Connecticut	4	0.0733	Arizona	46	0.2160
Boston College	5	0.0894	Arizona St.	76	0.3069
Duke	6	0.0896	Arkansas	27	0.1812
Air Force	7	0.0920	Arkansas St.	29	0.1857
Wyoming	8	0.0940	Army	1	0.0432
Vanderbilt	9	0.0990	Auburn	65	0.2659
West Virginia	10	0.1210	Ball St.	47	0.2175
Purdue	11	0.1212	Baylor	117	0.8098
Northwestern	12	0.1291	Boise St.	22	0.1665
Marshall	13	0.1374	Boston College	5	0.0894
New Mexico	14	0.1460	Bowling Green	70	0.2873
Syracuse	15	0.1492	Buffalo	20	0.1574
Memphis	16	0.1548	BYU	54	0.2403
Eastern Mich.	17	0.1549	California	87	0.3568
Mississippi	18	0.1553	Central Mich.	88	0.3952
Stanford	19	0.1574	Cincinnati	56	0.2479
Buffalo	20	0.1574	Clemson	58	0.2561
Southern Miss.	21	0.1634	Colorado	35	0.1932
Boise St.	22	0.1665	Colorado St.	25	0.1739
Iowa	23	0.1673	Connecticut	4	0.0733
Idaho	24	0.1730	Duke	6	0.0896
Colorado St.	25	0.1739	East Caro.	92	0.4091
Kansas	26	0.1808	Eastern Mich.	17	0.1549
Arkansas	27	0.1812	Fla. Atlantic	116	0.8017
Minnesota	28	0.1822	Florida	102	0.5601
Arkansas St.	29	0.1857	Florida Int'l	110	0.6967
Wake Forest	30	0.1858	Florida St.	101	0.5382
Western Mich.	31	0.1889	Fresno St.	120	0.8489
Western Ky.	32	0.1894	Georgia	105	0.5982
Middle Tenn. St.	33	0.1905	Georgia Tech	94	0.4234
Indiana	34	0.1906	Hawaii	80	0.3222
Colorado	35	0.1932	Houston	115	0.8002
Miami (Ohio)	36	0.1962	Idaho	24	0.1730
Northern Ill.	37	0.1968	Illinois	55	0.2450
Tulane	38	0.1980	Indiana	34	0.1906
Maryland	39	0.2033	Iowa	23	0.1673
Utah St.	40	0.2034	Iowa St.	50	0.2314
Kentucky	41	0.2048	Kansas	26	0.1808
Michigan	42	0.2072	Kansas St.	45	0.2141
Tennessee	43	0.2082	Kent St.	85	0.3506
New Mexico St.	44	0.2140	Kentucky	41	0.2048
Kansas St.	45	0.2141	La.-Lafayette	79	0.3213
Arizona	46	0.2160	La.-Monroe	57	0.2554
Ball St.	47	0.2175	Louisiana Tech	71	0.2913
Penn St.	48	0.2246	Louisville	51	0.2333
Oregon St.	49	0.2292	LSU	97	0.4358
Iowa St.	50	0.2314	Marshall	13	0.1374
Louisville	51	0.2333	Maryland	39	0.2033
Oregon	52	0.2340	Memphis	16	0.1548
UNLV	53	0.2364	Miami (Fla.)	96	0.4319
BYU	54	0.2403	Miami (Ohio)	36	0.1962
Illinois	55	0.2450	Michigan	42	0.2072
Cincinnati	56	0.2479	Michigan St.	77	0.3142
La.-Monroe	57	0.2554	Middle Tenn. St.	33	0.1905
Clemson	58	0.2561	Minnesota	28	0.1822
South Carolina	59	0.2580	Mississippi	18	0.1553
Nebraska	60	0.2581	Mississippi St.	93	0.4189
Utah	61	0.2606	Missouri	74	0.2991
UAB	62	0.2606	Navy	3	0.0644
Rutgers	63	0.2635	Nebraska	60	0.2581
Temple	64	0.2658	Nevada	107	0.6096
Auburn	65	0.2659	New Mexico	14	0.1460
Wisconsin	66	0.2692	New Mexico St.	44	0.2140
Troy	67	0.2723	North Carolina	82	0.3393
Alabama	68	0.2723	North Carolina St.	69	0.2772
North Carolina St.	69	0.2772	North Texas	109	0.6562
Bowling Green	70	0.2873	Northern Ill.	37	0.1968
Louisiana Tech	71	0.2913	Northwestern	12	0.1291
Tulsa	72	0.2927	Notre Dame	2	0.0594
Akron	73	0.2937	Ohio	78	0.3205
Missouri	74	0.2991	Ohio St.	95	0.4315
Washington St.	75	0.3039	Oklahoma	84	0.3405
Arizona St.	76	0.3069	Oklahoma St.	90	0.4053
Michigan St.	77	0.3142	Oregon	52	0.2340
Ohio	78	0.3205	Oregon St.	49	0.2292
La.-Lafayette	79	0.3213	Penn St.	48	0.2246
Hawaii	80	0.3222	Pittsburgh	83	0.3396
Toledo	81	0.3366	Purdue	11	0.1212
North Carolina	82	0.3393	Rice	112	0.7522
Pittsburgh	83	0.3396	Rutgers	63	0.2635
Oklahoma	84	0.3405	San Diego St.	111	0.7174
Kent St.	85	0.3506	San Jose St.	118	0.8212
Virginia	86	0.3546	South Carolina	59	0.2580
California	87	0.3568	South Fla.	114	0.7600
Central Mich.	88	0.3952	Southern California	103	0.5670
Virginia Tech	89	0.3986	Southern Methodist	99	0.4613
Oklahoma St.	90	0.4053	Southern Miss.	21	0.1634
Washington	91	0.4088	Stanford	19	0.1574
East Caro.	92	0.4091	Syracuse	15	0.1492
Mississippi St.	93	0.4189	TCU	108	0.6281
Georgia Tech	94	0.4234	Temple	64	0.2658
Ohio St.	95	0.4315	Tennessee	43	0.2082
Miami (Fla.)	96	0.4319	Texas	119	0.8308
LSU	97	0.4358	Texas A&M	113	0.7561
UCF	98	0.4374	Texas Tech	106	0.5987
Southern Methodist	99	0.4613	Toledo	81	0.3366
UTEP	100	0.5037	Troy	67	0.2723
Florida St.	101	0.5382	Tulane	38	0.1980
Florida	102	0.5601	Tulsa	72	0.2927
Southern California	103	0.5670	UAB	62	0.2606
UCLA	104	0.5808	UCF	98	0.4374
Georgia	105	0.5982	UCLA	104	0.5808
Texas Tech	106	0.5987	UNLV	53	0.2364
Nevada	107	0.6096	Utah	61	0.2606
TCU	108	0.6281	Utah St.	40	0.2034
North Texas	109	0.6562	UTEP	100	0.5037
Florida Int'l	110	0.6967	Vanderbilt	9	0.0990
San Diego St.	111	0.7174	Virginia	86	0.3546
Rice	112	0.7522	Virginia Tech	89	0.3986
Texas A&M	113	0.7561	Wake Forest	30	0.1858
South Fla.	114	0.7600	Washington	91	0.4088
Houston	115	0.8002	Washington St.	75	0.3039
Fla. Atlantic	116	0.8017	West Virginia	10	0.1210
Baylor	117	0.8098	Western Ky.	32	0.1894
San Jose St.	118	0.8212	Western Mich.	31	0.1889
Texas	119	0.8308	Wisconsin	66	0.2692
Fresno St.	120	0.8489	Wyoming	8	0.0940

BPR	A system for ranking teams based only one wins and losses and strength of schedule. See BPR for an explanation.
EPA (Expected Points Added)	Expected points are the points a team can "expect" to score based on the distance to the end zone and down and distance needed for a first down, with an adjustment for the amount of time remaining in some situations. Expected points for every situation is estimated using seven years of historical data. The expected points considers both the average points the offense scores in each scenario and the average number of points the other team scores on their ensuing possession. The Expected Points Added is the change in expected points before and after a play.
EP3 (Effective Points Per Possession)	Effective Points Per Possession is based on the same logic as the EPA, except it focuses on the expected points added at the beginning and end of an offensive drive. In other words, the EP3 for a single drive is equal to the sum of the expected points added for every offensive play in a drive (EP3 does not include punts and field goal attempts). We can also think of the EP3 as points scored+expected points from a field goal+the value of field position change on the opponent's next possession.
Adjusted for Competition	We attempt to adjust some statistics to compensate for differences in strength of schedule. While the exact approach varies some from stat to stat the basic concept is the same. We use an algorithm to estimate scores for all teams on both sides of the ball (e.g., offense and defense) that best predict real results. For example, we give every team an offensive and defensive yards per carry score. Subtracting the offensive score from the defensive score for two opposing teams will estimate the yards per carry if the two teams were to play. Generally, the defensive scores average to zero while offensive scores average to the national average, e.g., yards per carry, so we call the offensive score "adjusted for competition" and roughly reflects what the team would do against average competition
Impact	see Adjusted for Competition. Impact scores are generally used to evaluate defenses. The value roughly reflects how much better or worse a team can expect to do against this opponent than against the average opponent.

Total <=0	Percent of plays that are negative or no gain
Total >=10	Percent of plays that gain 10 or more yards
Total >=25	Percent of plays that gain 25 or more yards
10 to 0	Ratio of Total >=10 to Total <=0

Total <=0	Percent of plays that are negative or no gain
Total >=10	Percent of plays that gain 10 or more yards
Total >=25	Percent of plays that gain 25 or more yards
10 to 0	Ratio of Total >=10 to Total <=0

Total <=0	Percent of plays that are negative or no gain
Total >=10	Percent of plays that gain 10 or more yards
Total >=25	Percent of plays that gain 25 or more yards
10 to 0	Ratio of Total >=10 to Total <=0

3rdLComp%	Completion % on 3rd and long (7+ yards)
SitComp%	Standardized completion % for down and distance. Completion % by down and distance are weighted by the national average of pass plays by down and distance.
Pass <=0	Percent of pass plays that are negative or no gain
Pass >=10	Percent of pass plays that gain 10 or more yards
Pass >=25	Percent of pass plays that gain 25 or more yards
10 to 0	Ratio of Pass >=10 to Pass<=0
%Sacks	Ratio of sacks to pass plays
Bad INTs	Interceptions on 1st or 2nd down early before the last minute of the half

College Football by the Numbers

Sunday, July 15, 2012

Recruiting and the Diversity Index

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YPC1stD	Yards per carry on 1st down
CPCs	Conversions (1st down/TD) per carry in short yardage situations - the team 3 or fewer yards for a 1st down or touchdown
%Team Run	Player's carries as a percent of team's carries
%Team RunS	Player's carries as a percent of team's carries in short yardage situations
Run <=0	Percent of running plays that are negative or no gain
Run >=10	Percent of running plays that gain 10 or more yards
Run >=25	Percent of running plays that gain 25 or more yards
10 to 0	Ratio of Run >=10 to Run <=0

Conv/T 3rd	Conversions per target on 3rd Downs
Conv/T PZ	Touchdowns per target inside the 10 yardline
%Team PZ	Percent of team's targets inside the 10 yardline
Rec <=0	Percent of targets that go for negative yards or no net gain
Rec >=10	Percent of targets that go for 10+ yards
Rec >=25	Percent of targets that go for 25+ yards
10 to 0	Ratio of Rec>=0 to Rec<=0

NEPA	"Net Expected Points Added": (expected points after play - expected points before play)-(opponent's expected points after play - opponent's expected points before play). Uses the expected points for the current possession and the opponent's next possession based on down, distance and spot
NEPA/PP	Average NEPA per play
Max/Min	Single game high and low

Points/Poss	Offensive points per possession
EP3	Effective Points per Possession
EP3+	Effective Points per Possession impact
Plays/Poss	Plays per possession
Yards/Poss	Yards per possession
Start Spot	Average starting field position
Time of Poss	Average time of possession (in seconds)
TD/Poss	Touchdowns per possession
TO/Poss	Turnovers per possession
FGA/Poss	Attempted field goals per possession
%RZ	Red zone trips per possession
Points/RZ	Average points per red zone trip. Field Goals are included using expected points, not actual points.
TD/RZ	Touchdowns per red zone trip
FGA/RZ	Field goal attempt per red zone trip
Downs/RZ	Turnover on downs per red zone trip

EPA/Pass	Expected Points Added per pass attempt
EPA/Rush	Expected Points Added per rush attempt
EPA/Pass+	Expected Points Added per pass attempt impact
EPA/Rush+	Expected Points Added per rush attempt impact
Yards/Pass	Yards per pass
Yards/Rush	Yards per rush
Yards/Pass+	Yards per pass impact
Yards/Rush+	Yards per rush impact
Exp/Pass	Explosive plays (25+ yards) per pass
Exp/Rush	Explosive plays (25+ yards) per rush
Exp/Pass+	Explosive plays (25+ yards) per pass impact
Exp/Rush+	Explosive plays (25+ yards) per rush impact
Comp%	Completion percentage
Comp%+	Completion percentage impact
Yards/Comp	Yards per completion
Sack/Pass	Sacks per pass
Sack/Pass+	Sacks per pass impact
Sack/Pass*	Sacks per pass on passing downs
INT/Pass	Interceptions per pass
Neg/Rush	Negative plays (<=0) per rush
Neg/Run+	Negative plays (<=0) per rush impact
Run Short	% Runs in short yardage situations
Convert%	3rd/4th down conversions
Conv%*	3rd/4th down conversions versus average by distance
Conv%+	3rd/4th down conversions versus average by distance impact

Plays	Number of offensive plays
%Pass	Percent pass plays
EPA/Pass	Expected Points Added per pass attempt
EPA/Rush	Expected Points Added per rush attempt
EPA/Pass+	Expected Points Added per pass attempt adjusted for competition
EPA/Rush+	Expected Points Added per rush attempt adjusted for competition
Yards/Pass	Yards per pass
Yards/Rush	Yards per rush
Yards/Pass+	Yards per pass adjusted for competition
Yards/Rush+	Yards per rush adjusted for competition
Exp Pass	Explosive plays (25+ yards) per pass
Exp Run	Explosive plays (25+ yards) per rush
Exp Pass+	Explosive plays (25+ yards) per pass adjusted for competition
Exp Run+	Explosive plays (25+ yards) per rush adjusted for competition
Comp%	Completion percentage
Comp%+	Completion percentage adjusted for competition
Sack/Pass	Sacks per pass
Sack/Pass+	Sacks per pass adjusted for competition
Sack/Pass*	Sacks per pass on passing downs
Int/Pass	Interceptions per pass
Neg/Run	Negative plays (<=0) per rush
Neg/Run+	Negative plays (<=0) per rush adjusted for competition
Run Short	% Runs in short yardage situations
Convert%	3rd/4th down conversions
Conv%*	3rd/4th down conversions versus average by distance
Conv%+	3rd/4th down conversions versus average by distance adjusted for competition

PPP	Points per Possession
aPPP	Points per Possession allowed
PPE	Points per Exchange (PPP-aPPP)
EP3+	Expected Points per Possession
aEP3+	Expected Points per Possession allowed
EP2E+	Expected Points per Exchange
EPA/Pass+	Expected Points Added per Pass
EPA/Rush+	Expected Points Added per Rush
aEPA/Pass+	Expected Points Allowed per Pass
aEPA/Rush+	Expected Points Allowed per Rush
Exp/Pass	Explosive Plays per Pass
Exp/Rush	Explosive Plays per Rush
aExp/Pass	Explosive Plays per Pass allowed
aExp/Rush	Explosive Plays per Rush allowed

BPR	A method for ranking conferences based only on their wins and losses and the strength of schedule. See BPR for an explanation.
Power	A composite measure that is the best predictor of future game outcomes, averaged across all teams in the conference
P-Top	The power ranking of the top teams in the conference
P-Mid	The power ranking of the middling teams in the conference
P-Bot	The power ranking of the worst teams in the conference
SOS-Und	Strength of Schedule - Undefeated. Focuses on the difficulty of going undefeated, averaged across teams in the conference
SOS-BE	Strength of Schedule - Bowl Eligible. Focuses on the difficulty of becoming bowl eligible, averaged across teams in the conference
Hybrid	A composite measure that quantifies human polls, applied to converences

EPA	Expected points added (see glossary)
oEPA	Defense-independent performance

EP3	Effective points per possession (see glossary)
oEP3	Defense-independent offensive performance
dEP3	Offense-independent defensive performance
EPA	Expected points added (see glossary)
oEPA	Defense-independent offensive performance
dEPA	Offense-independent defensive performance
EPAp	Expected points added per play