Rigorous Cluster Analyses For

Prospective Player Evaluation In The

National Football League

Max Isaac Mulitz1

Brown University

December 2015

I wish to express my appreciation to my thesis advisor, Professor Francesco Di Plinio, for his guidance and support throughout the research process and to Professor Mark Dean who served as my second reader. I would also like to thank Dr. Kevin Dayaratna for his voluntary guidance and insights in discussing the issues addressed in this thesis. I also wish to thank those coaches and advisors that directed and assisted me toward this interest including: Coach Nelson Burton, Coach Tom Green, Katherine Russell, Frank

Costello, Coach Phil Estes and Brown University Football, and Coach Chip Kelly and the

Philadelphia Eagles Organization.

1

Abstract

This study uses principal component as well as k-means cluster analysis to evaluate prospects who enter the National Football League (NFL) draft. We also explore whether such analysis creates the opportunity to take advantage of inefficiencies in the NFL draft as a market. We find that for offensive tackles, both speed and explosiveness-based athleticism have a positive relationship with career performance, even after discounting for draft position. Our results have useful managerial implications, suggesting that many

NFL managers currently undervalue athleticism in the offensive tackle position when selecting players in the draft.

2

1. Introduction

The National Football League (NFL) is a multi-billion dollar business (Keenan,

2014). In principle, team quality influences the size of the teams fan base, which in turn sets the market for television rights, ticket sales and other moneys the team can make selling memorabilia, etc. Because of the hyper-competitive nature of the NFL, star players make close to 20 million per year and team salaries easily surpass $100 million per year.

Throughout the year, NFL teams are constantly assessing potential as well as current players for their rosters. Scouts, coaches, statisticians, general managers, and, occasionally, owners participate in the assessment and acquisition of players. Although there are multiple routes to becoming a player for the NFL, the predominant path is from a National Collegiate Athletic Association (NCAA) Division I college team to the NFL

Draft. Once drafted, the selectees must then make it through training camp without being cut from the roster and generally perform well during their initial game experiences.

Each team organization has its own approaches for scouting and evaluate future players. However, included in the mix of assessment tools are: college records and statistics; results of personal discussions and interviews with candidates and their coaches, and information collected through exercises known as “combines.” During combines, players are interviewed, subjected to medical, psychological, and intelligence

3 testing and participate in a host of activities designed to assess their athleticism. One attribute of the combines is that they produce a single set of data and information on each participating player that is available to each NFL team. In addition, unlike the data from each candidate’s college experience, each player participating in the combine is subjected to the same battery of tests in the same environment, at the same time, which gives the data greater utility for comparing players with each other: “The combine requires the players to display their talents by performing standardized tests under controlled conditions, thereby creating fair and unbiased assessment conditions.” (Kuzmits, 2008).

A detailed explanation of the Combine and the NFL Draft appear at Appendix I.

2. Previous Work

The Harvard Sports Analytics Collective has written two papers evaluating the effect of Combine performance on NFL success and found very little correlation between the two (Meers, 2015). The Harvard study, however, only looked at raw Combine data.

Many members of the sports analytics community believe that some adjustment to the raw Combine data yields a greater correlation between Combine results and NFL performance.

One example of such a study is Shawn Siegele’s work on agility score and running back elusiveness, in which he finds a relationship between the agility metrics and rushing yards before contact (Siegele, 2012). Similarly, Lyndon Plothow finds that the

Combine results measure “accurately skills and characteristics that are important for

NFL football players,” yet, he recognizes that “[i]nterviews, position specific drills, and intelligence tests all inform a team’s decision to draft a player.” (Plothow, 2010).

Another example is the analysts for Football Outsiders invented Speed Score in 2008,

4 which they used to demonstrate a stronger relationship between weight adjusted speed and running back performance than could be shown using a non-weight adjusted speed measurement. (Baier, 2015).

Recently, certain teams, including the Seattle Seahawks, have been using SPARQ, which essentially takes raw combine variables as data and transforms it into a single final athleticism score. (Kelly, 2015). Similarly, the Philadelphia Eagles also employ SPARQ in their assessment efforts (Mengels, 2015).

As discussed above, numerous studies suggest relationships between NFL combine scores and career performance. Each of these studies are based on some form of regression-based statistical analysis. It is this author’s view that regression analysis provides a reasonable measure of the correlation between combine and career performance. However, mathematical tools are available that present greater detail and precision in the analysis of correlations. Unlike regression analysis, Principal

Component Analysis (PCA) and k-means Cluster Analysis not only measure correlation, but also explain the relevant factors and provide or suggest a causal correlation.

Accordingly, this paper uses PCA and k-means, and therefore yields more precise analyses, which provide greater certainty to the overall conclusions drawn from the data.

3. Data

NFL Combine Data is widely available going back to 1999 online. (NFL

Combine Results, 2015). The sample data does not include information after 2011 because it is not possible to assess career performance of players that have not been in the league for more than three years. Accordingly, this paper used Combine data for the

1999 through 2011 seasons.

5 Our dependent measure is Career Approximate Value (AV) (Sports Reference,

2015). Although approximate value is not a perfect representation for career value, it is widely accepted as a reasonable proxy and, as a group, higher AV players playing a specific position have had better careers than lower AV players.

4. Methodology:

The analysis employs multiple methodologies to determine optimal methods of evaluating positions. First, PCA is used to find which skills yield the most direct correlation to NFL performance measured according to AV. Then the application of cluster analysis is used to determine whether there are player types or athletic profiles at different positions that outperform the other positions.

In addition to the combine numbers, we use speed score, which is a measurement of weight adjusted speed, and Explosion Score, which is the author’s own version of

Weight Adjusted Jumping, which has been demonstrated to be important for at least some positions. (Waldo, 2011). As discussed above, Football Outsiders demonstrated the strong relationship between Speed Scores and running back performance in comparison to speed or weight alone. Waldo showed that the predictive ability of weight-adjusted jumping scores exceeded that of just considering jumping scores. Greater weight may impede both speed and jumping ability. Therefore, adjusting speed and jumping metrics for weight produces better indications of future performance.

After performing the cluster analysis, we assess the performance of players, both before and after making an adjustment for draft position. The reason to adjust for draft position to some degree is because higher drafted players are given a greater opportunity to succeed and also because we are looking to see if players in a certain tier of athleticism

6 who are available later in the draft than their peers still actually outperform their expectation. To adjust for draft position, we compare the player’s data with the expected career AV of someone taken with at the same draft position. The expected Career AV will be tested using an online calculator (Rotoviz, Trade Calculator, 2015), which uses regression analysis. Because significant work has already been done on the quarterback, wide receiver, and running back positions, this work focuses on the offensive and defensive lines, which is somewhat uncharted territory. A better understanding of positions on the offensive and defensive lines should be of significant value to teams because the ultimate success of quarterbacks, wide receivers and running backs is largely dependent on the capabilities and performance of these supporting players.

5. Hypothesis

We hypothesize that the relationship between Combine performance and NFL career performance will vary depending on offensive or defensive line position. For example, there is an expectation that basic athleticism is a measurable asset for offensive tackles. On the other hand, guards and centers, who require less athleticism, are expected to show greater explosive strength, but less agility than offensive tackles.

For the defensive line, the success of interior players should, in principle, be strongly correlated to their explosive power as interior defensive line play is generally considered “trench warfare” strategically. For defensive ends, on the other hand, who are primarily valued as pass rushers, there is the expectation that both speed and power are manifested in successful players.

6. Principal Component Analysis

7 We compiled data from 1999 to 2011 from theNFL Combine Results website (NFL

Combine Results, 2015). To gain a better understanding of the variables associated with the NFL Combine on players’ career success, a principal components analysis (PCA) as well as a k-means cluster analysis were performed. PCA generally refers to a technique of data analysis that uses mathematical principles – usually linear algebra – to change a number of potentially correlated variables into a lesser number of variables from which to make statistical inferences. These lesser number of variables are referred to as “principal components.”

Using linear algebra, the PCA enables the de-correlation of the original data and decomposition of the initial data into independent components of declining variance.

Mathematically, the objective in PCA is to find, for an m x n matrix X, an m x m matrix

P, such that Y=PX. This linear mapping, represented by the matrix P, transforms the data into a different coordinate system that is ordered by projections of the data onto coordinates of declining variance.

Specifically, we establish an orthonormal matrix P, in which Y = PX and such

� that SY≡ �� is diagonalized. The rows of P are the principal components of X. ��

We applied PCA using the NFL Combine results and player measurements including height, bodyweight, number of bench press reps at 225 pounds, short shuttle time, three cone time, weight adjusted speed, and weight adjusted jumping. The player positions used for this PCA included centers, guards, tackles, defensive ends, and defensive tackles. For brevity, this writing contains the analysis for centers, guards, and tackles; the remaining analyses are available from the author upon request.

8 The plots below present the first four components, which explain over 95% of the variability of the data. For guards, we see in the First Principal Component, which explains 44.05 percent of the variability, we notice a clustering of Height, Short Shuttle,

Bench, and Three Cone. For tackles, we see a clustering of Three Cone, Short Shuttle,

Height, and Bench in the first component, explaining 48.63 percent of the position’s variability. For centers, we see a clustering of Height, Short Shuttle, Three Cone and

Bench in the first component, explaining 55.74 percent of the variability.

Guards - First Principle Component, Explains 44.0532% of Variability

Height Weight Bench Short shuttle Three cone Weight Adjusted Speed Weight Adjusted Jumping

-0.2 0 0.2 0.4 0.6 0.8 1 Principal Component Coefficients

9 Guards - Second Principle Component, Explains 39.0743% of Variability

Height Weight Bench Short shuttle Three cone Weight Adjusted Speed Weight Adjusted Jumping

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Principal Component Coefficients

Guards - Third Principle Component, Explains 12.0035% of Variability

Height Weight Bench Short shuttle Three cone Weight Adjusted Speed Weight Adjusted Jumping

-0.4 -0.2 0 0.2 0.4 0.6 0.8 Principal Component Coefficients

10 Guards - Fourth Principle Component, Explains 4.5801% of Variability

Height Weight Bench Short shuttle Three cone Weight Adjusted Speed Weight Adjusted Jumping

0 0.2 0.4 0.6 0.8 1 Principal Component Coefficients

Tackles - First Principle Component, Explains 48.6381% of Variability

Height Weight Bench Short shuttle Three cone Weight Adjusted Speed Weight Adjusted Jumping

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Principal Component Coefficients

11 Tackles - Second Principle Component, Explains 36.1753% of Variability

Height Weight Bench Short shuttle Three cone Weight Adjusted Speed Weight Adjusted Jumping

-0.4 -0.2 0 0.2 0.4 0.6 Principal Component Coefficients

Tackles - Third Principle Component, Explains 11.5129% of Variability

Height Weight Bench Short shuttle Three cone Weight Adjusted Speed Weight Adjusted Jumping

-0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 Principal Component Coefficients

12 Tackles - Fourth Principle Component, Explains 3.4217% of Variability

Height Weight Bench Short shuttle Three cone Weight Adjusted Speed Weight Adjusted Jumping

0 0.2 0.4 0.6 0.8 1 Principal Component Coefficients

13 Centers - First Principle Component, Explains 55.7456% of Variability

Height Weight Bench Short shuttle Three cone Weight Adjusted Speed Weight Adjusted Jumping

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Principal Component Coefficients

Centers - Second Principle Component, Explains 21.1736% of Variability

Height Weight Bench Short shuttle Three cone Weight Adjusted Speed Weight Adjusted Jumping

0 0.2 0.4 0.6 0.8 1 Principal Component Coefficients

14 Centers - Third Principle Component, Explains 17.0656% of Variability

Height Weight Bench Short shuttle Three cone Weight Adjusted Speed Weight Adjusted Jumping

-0.2 0 0.2 0.4 0.6 0.8 1 Principal Component Coefficients

Centers - Fourth Principle Component, Explains 5.5913% of Variability

Height Weight Bench Short shuttle Three cone Weight Adjusted Speed Weight Adjusted Jumping

-0.2 0 0.2 0.4 0.6 0.8 1 Principal Component Coefficients

15

7. k-means Clustering

Although these results are interesting, they are not particularly informative due to the fact that the variability is reasonably spread out amongst a variety of the principal components. To draw statistical inferences regarding the attributes of different players, we transformed the data by expressing it in terms of the basis generated by the PCA.

From this new dataset, a 3-dimensional k-means cluster analysis may be performed.

In clustering, a set of objects is grouped so that objects in a common group are more like each other than objects in other groups. These groups of similar characteristics are called “clusters.” “k-means clustering,” a vector quantization method, seeks to segregate or partition n observations into k clusters. The purpose or objective of k-means clustering is to partition n observations or data points into k clusters so that each data point or observation is associated with the cluster with the nearest mean, which acts as a prototype of the cluster. Given n observations, � = (�, �, … , �), where each observation is an m dimensional vector, we seek via k-means clustering to arrange our n

observations into k distinct sets � = {�}. Mathematically, we minimize the following sum of squares to do so:

Like PCA, this optimization can be performed in most standard statistical computing packages. The following results are based on the first three principal components from

16 our analysis in Section 6, which in each case, as discussed earlier, explain well over 90% of the variability:

17

18

Below are the coordinates of the centroids for the above plots:

Centroids for centers

First Second Third component component component Centroid 1 139.98 290.06 42.604 Centroid 2 158.05 288.67 37.487 Centroid 3 126.7 292.02 38.083

19 Centroids for guards

First Second Third component component component Centroid 1 247.1 216.54 45.663 Centroid 2 233.49 229.06 48.57 Centroid 3 261.91 237.07 48.623

Centroids for tackles

First Second Third component component component Centroid 1 316.94 130.66 50.784 Centroid 2 320.17 106.22 53.405 Centroid 3 301.37 120.63 55.712

Cluster results on a player-by-player basis are listed in Appendix II.

Our analysis illustrates well-defined clustering among the guards, centers

and tackles. These relationships are presented in the summary tables below.

TACKLE CLUSTER 1 DRAFT POSITION Top 50 Top 100 Top 150 Rest Total # of players 16 10 7 17 50 Expected AV 665.47 216.1 98.3 98.3 1147.06 Actual AV 705 301 95 87 1188 Average AV-Expected 2.47 8.49 -0.47 -4.72 0.82

20 TACKLE CLUSTER 2

DRAFT POSITION Top 50 Top 100 Top 150 Rest Total # of players 9 6 8 43 66 Expected AV 375.41 122.55 107.07 409.04 1014.07 Actual AV 327 94 156 269 846 Average AV-Expected -5.38 -4.76 6.12 -3.26 -2.55

TACKLE CLUSTER 3 DRAFT POSITION Top 50 Top 100 Top 150 Rest Total # of players 9 9 7 34 59 Expected AV 356.47 190.85 94.92 324.49 966.73 Actual AV 345 312 61 228 946 Average AV-Expected -1.27 13.46 -4.85 -2.84 -0.35

GUARD CLUSTER 1 DRAFT POSITION Top 50 Top 100 Top 150 Rest Total # of players 7 12 8 17 44 Expected AV 259.12 242.06 109.36 168.41 778.95 Actual AV 374 342 200 338 1254 Average AV-Expected 16.41 8.33 11.33 9.98 10.80

GUARD CLUSTER 2 DRAFT POSITION Top 50 Top 100 Top 150 Rest Total # of players 5 6 8 24 43 Expected AV 171.59 117.49 104.87 240.37 634.32 Actual AV 130 119 56 290 595 Average AV-Expected -8.32 0.25 -6.11 2.07 -0.91

21

GUARD CLUSTER 3 DRAFT POSITION Top 50 Top 100 Top 150 Rest Total # of players 6 4 5 6 21 Expected AV 215.08 77.69 67.69 59.07 419.53 Actual AV 227 98 39 50 414 Average AV-Expected 1.99 5.08 -5.74 -1.51 -0.26

CENTER CLUSTER 1 DRAFT POSITION Top 50 51-100 101-150 Rest Total # of players 3 3 3 13 22 Expected AV 101.63 71.25 43.26 130.07 346.21 Actual AV 115 102 19 255 491 Average AV-Expected 4.46 10.25 -8.09 9.61 6.58

CENTER CLUSTER 2 DRAFT POSITION Top 50 Top 100 Top 150 Rest Total # of players 1 3 2 8 14 Expected AV 27.99 67.27 27.99 82.91 206.16 Actual AV 39 56 31 67 193 Average AV-Expected 11.01 -3.76 1.51 -1.99 -0.94

22 CENTER CLUSTER 3 DRAFT POSITION Top 50 Top 100 Top 150 Rest Total # of players 3 4 6 1 14

Expected AV 108 88.73 82.46 9.1 288.29 Actual AV 162 162 84 17 472

Average AV- Expected 18.00 18.00 0.26 7.90 13.12

GUARD AVERAGES

Speed Jump Ht WT Bench Vert Broad Shuttle 3Cone 40 Score Score Cluster 1 76.02 303.91 5.14 27.27 30.30 106.09 4.59 7.69 87.50 97.92

Cluster 2 76.21 312.16 5.34 24.70 26.53 98.40 4.75 7.92 77.20 81.56

Cluster 3 76.24 334.14 5.30 28.62 28.31 99.24 4.76 7.99 85.07 93.90

An analysis of the cluster data for guards reveals that the Cluster 1 group out

performed the other two cluster groupings in each phase of the draft. In Cluster 1, the

guards’ performances collectively exceeded their draft positions by 10.80 Career AV

points. The guards grouped in Clusters 2 and 3 underperformed their expected Career

AB by less than a point. As one may expect, Cluster 1 Guards were proved to be the

most highly sought in the draft. These Cluster 1 guards garnered the greatest amount of

capital investment of all players for both the top fifty selections and for selection fifty-

one through 100.

23

With respect to measurements of athleticism among the guard clusters, Cluster 1

guards are shown to be the most athletic of the three cluster groups; Cluster 1 guards

recorded the best speed scores, jump scores and agility measurements. In addition, the

Cluster 1 guards weighed the least among the three clusters. Cluster 1 guards were the

lightest among the three groups by a significant amount, with an average weight of

303.91 pounds compared to 312.16 pounds for Cluster 2 guards and 334.14 pounds for

cluster 3 guards. These results suggest that weighing over 300 pounds may not provide

much benefit for offensive guards and that weight in excess of 300 pounds may hinder

athleticism. Furthermore, although athleticism is generally highly valued in the NFL

draft, it is still somewhat undervalued for guards, given that the most athletic cluster has

significantly overperformed their draft position when compared with less athletic players.

In other words, it appears that the NFL teams have placed a premium on size or weight

over measures of a combination of weight and athleticism. Furthermore, it appears that

the benefits of weight diminish for guards over 300 pounds.

TACKLE AVERAGES Speed Jump HT Weight 40 Bench Vert Broad Shuttle 3Cone Score Score CLUSTER 1 77.72 311.08 5.06 26.08 30.93 107.50 4.63 7.64 95.06 103.42

Cluster 2 77.67 306.95 5.29 22.48 26.47 99.59 4.76 7.95 78.66 80.91

Cluster 3 78.19 329.81 5.40 24.68 27.87 99.95 4.81 8.02 77.71 91.97

24 Cluster 1 tackles proved to be the most athletic group by a substantial margin and, overall, performed the best of the three groups, mainly due to their strong performance in the top 100 picks. Cluster 1 tackles dominated the top fifty draft selections. In addition, the Cluster 1 Tackles were the quickest during the Combine and have the best weight- adjusted athleticism of the three groups. This suggests that athleticism is undervalued at the tackle position, especially for the first 100 draft picks.

As a group, Cluster 3 tackles were less successful than their Cluster 1 counterparts; however, Cluster 3 tackles did outperform the players in Cluster 2. The defining features of this group were an acceptable Jump Score and very heavy weight.

Therefore, although this group of tackles failed to attain the highest measures of athleticism, they have realized a high degree of success based on strong jump scores and heavy weight. Therefore, if a tackle cannot attain an elite level of athleticism, he can still realize a high level of success if he is an extremely large player with solid leg power.

Cluster 2 tackles were the smallest group and had the lower scores for jumping and agility compared to Cluster 3 tackles; and the Cluster 2 tackles were, on average, twenty-five pounds lighter than the Cluster 3 tackles. Therefore, it appears that the NFL overvalues smaller, less athletic tackle prospects.

25 CENTER AVERAGES Speed Jump HT WT 40 Bench Vert Broad SS 3C Score Score CLUSTER 1 75.50 302.73 5.23 28.00 28.39 101.23 4.63 7.64 81.19 86.91

CLUSTER 2 75.64 302.43 5.30 23.14 25.25 95.86 4.67 7.77 76.94 73.20

CLUSTER 3 75.14 304.21 5.18 26.64 32.39 105.21 4.57 7.72 84.56 103.58

Cluster 3 centers outperformed their draft position by an average of 13.12 points of AV compared to Cluster 1 players. Cluster 1 centers bested their draft positions by an average of 6.58 points and Cluster 2 centers who underperformed their draft position by

.94 points.

With respect to athleticism, although all the groups of centers are similar in terms of height and weight, Cluster 3 centers are almost universally more athletic than Cluster 1 players, who are in turn far more athletic than Cluster 2 players. This is the most straightforward evidence yet that athleticism is undervalued at the center position in the

NFL.

7.1 The Kolmogorov-Smirnov Test and Statistical Significance of Differences Between the AV of Different Clusters

The tables below shows the results of a Kolmogorov-Smirnov test. We tested the null hypothesis that AV of Cluster i (in the left hand column) is less than or equal to the

AV of cluster j. To avoid redundancy we only needed to test three hypotheses per position, depending on the associated scatterplots.

26

Centers

Cluster 1 Cluster 2 Cluster 3

Cluster 1 N/A 0.0549 0.3603

Cluster 2 N/A N/A N/A

Cluster 3 N/A 0.1658 N/A

Guards

Cluster 1 Cluster 2 Cluster 3

Cluster 1 N/A 0.1918 N/A

Cluster 2 N/A N/A N/A

Cluster 3 0.1383 0.0964 N/A

Tackles

Cluster 1 Cluster 2 Cluster 3

Cluster 1 N/A 0.0084 0.7566

Cluster 2 N/A N/A N/A

Cluster 3 N/A 0.0078 N/A

For Tackles, using a significance level of .05, we notice that we can reject both null hypothesis that Cluster 1<=Cluster 2 and that Cluster 3<=Cluster 2. Further, we notice

27 that for Centers we can reject Cluster 1<=Cluster 2 at the .10 significance level and for

Guards we can reject Cluster 3<=Cluster 2 at the same level.

The KS tests illustrate that the clusters do not all elicit differences between AV.

This is expected and confirmation of the fact that players with similar athletic traits go on to have a wide spectrum of different career performances. Our analysis aims to provide a method of classifying players by means of their combine results, within a cluster of players with similar athletic traits, visualized and described in an aggregated way which explains most of the variability. This can be used as a simple yet effective classification tool of a player's athletic traits and career potential, according to which of the predefined clusters the player falls. Because AV for offensive linemen is largely (though not entirely) driven by playing time and team statistics, the statistic is included to aid in visualization of the range of players, not necessarily to show a statistically significant difference between the mean of the sub-clusters.

8. Conclusions and Future Research

This paper applied principal component analysis and k-means cluster analysis to reach a greater understanding of the variables associated with NFL Combine on payers’ career success. Focusing on the positions of guards, centers and tackles, we conclude that, based on NFL Combine scores and subsequent NFL career performance, the NFL teams generally under value athleticism in selecting players. The NFL teams in their selection of tackles also undervalue athleticism.

A significant conclusion inferred by this study is that the techniques of principal component and k-means cluster analyses provide an improvement in the certainty of results over mere regression analyses. The analytic techniques used in this paper may

28 serve as a basis for further exploration of other positions in football and potentially other sports to disclose opportunities to take advantage of inefficiencies in the selection of players as a market. Whether in baseball, basketball, football, or any other team sport where recruiting talent is considered important, we hope that this study provides a useful addition for athletics managers to use.

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33 APPENDIX I

The Combine

The predominant combine is the National Invitational Camp, more commonly known as the “NFL Scouting Combine” or the “NFL Combine.” Historically, subsets or groups of team scouts joined together to sponsor combines. However, in 1985, all of the then twenty-eight NFL teams agreed to participate in the Combine for the stated purposes of sharing costs. A significant potion of Combine costs is associated with medical assessments. For each player-participant in the Combine, a medical file is compiled and made available to the scouting teams. The Combine medical staff conducts medical and orthopedic physicals, X-rays, CT scans, and MRI scans and prepares a “medical risk analysis” for each Combine participant.2

Medical assessments are useful. If a player receives a “clean bill of health,” then his medical condition is a positive factor. If past injuries or other issues are disclosed, then the teams must determine whether other attributes of the player overcome the medical risks.

In addition to medical evaluations, the Combine administers the Wonderlic

Personnel Test (WPT) for assessing cognitive abilities. The value of cognitive ability testing is questionable. First, a “baseline” level of intelligence is established by NCAA

1 The medical team collects similar data on non-combine candidates, which information is included in the medical database made available to all NFL teams.

34 academic requirements.3 Second, three studies show no relationship between WPT results and future success in the NFL (Kuzmits, 2008).

Although there are regional combines in addition to the National Invitational

Camp, the NFL Combine is the main event. Participation by players in the NFL

Combine is by invitation only. Out of the approximately 10,000 football players, associated with 119 NCAA Division I teams, only 330 or so invitations are extended – slightly more than three percent of all Division I players. Although the medical and cognitive assessments comprise a large part of the Combine, it is the testing of athleticism that receives the greatest attention and may offer the greatest value to the NFL teams.

As it stands, there is publically available data on players’ height, weight, forty- yard dash, bench press, vertical leap, broad jump, short shuttle and three-cone drill from the players’ attendance at smaller camps other than the NFL Combine. For some players who attended the Combine but for various reasons (such as injury) skipped specific drills, results from other camps may be substituted.

The following chart presents examples of the Combine testing with brief descriptions of what is tested and to which positions the test result is most applicable:

(The Red Zone, 2009).

Test Description Attribute Tested Applicable Positions

Forty-yard dash, timed at Pure speed and acceleration. Offensive and ten yards, twenty yards, and Note: all athleticism tests are defensive linemen

2 The NCAA requires a minimum grade point average for eligibility to play.

35 forty yards performed indoors, on Astroturf,

without wearing football

equipment.

Bench press of a 225-pound Strength and conditioning Offensive and barbell – maximum defensive linemen; repetitions quarterbacks and wide

receivers exempt

Vertical jump Explosive leg power Receivers and

defensive backs

Broad Jump (from a Explosive leg power; overall Running backs, standing position) quickness and lateral power linemen and

linebackers

Twenty-yard shuttle – a Lateral speed; ability to change All positions timed test in which player direction; and overall moves five yards laterally coordination and ten yards back

Sixty-yard or Long shuttle Speed, endurance and overall All positions

conditioning

Three-cone drill – a speed Flexibility, speed, quickness, All positions test in which the player change of direction and body maneuvers around three control cones, five feet apart

Position specific drills Position dependent Each positions

36 Team interviews Varied questions All positions

Wonderlic Personnel Test Cognitive ability All positions

Measurements Weight, height, arm length, hand All positions

size, and, for linemen and

running backs, body fat

Cybex test Flexibility and joint movement All positions

Injury evaluation and urine Injury evaluation and substance All positions testing for substance abuse abuse

Although each year sportswriters prepare articles questioning the utility of

Combine results, there is no debate that Combine results are highly valued by NFL teams.

(Reuter, 2015; Gabriel, 2014; Chase, 2015). As suggested above, the Combine results provide a controlled data set of the top NFL prospects.

The NFL Draft

As stated earlier, the NFL draft is an intermediate step between college play and the NFL. Armed with results from the Combine for the most elite college players entering the draft, teams tend to initially focus on top performers from the Combine.

The NFL Draft is a three-day event consisting of seven rounds in which each of the thirty-two NFL teams have an opportunity to select a player from the pool of eligible participants who have entered the draft. (ESPN – NFL Draft 2015, 2015). Teams pick in reverse order of their record from the previous season, with the teams with least successful records choosing early in each round and the Super Bowl champion having the final pick of each round. Teams are permitted to trade draft picks with each other and

37 supplemental picks can be awarded to teams for losing players in free agency in order to try to maintain competitive balance in the league.

The NFL operates with an overall salary cap and a “rookie wage scale.” Because of the rookie wage scale, which limits what first-year players may earn, the NFL Draft represents the best opportunity for teams to find players at a price discounted from their true market value. This “discount” serves as an important concept in a sport with a

“hard” salary cap. This means that, unlike sports such as Major League Baseball, one cannot significantly outspend one’s competition.

This paper utilizes rigorous statistical methodologies to evaluate the strength of the relationship between a player’s NFL Combine performance and his professional performance. NFL teams can use this information to decide how to value prospective players in subsequent NFL drafts.

38

APPENDIX II

Below are the cluster results on a player-by-player basis, coupled with information about their draft positions and approximate values (AV):

Cluster Results for Guards

Draft Name Cluster Position AV Ben Hamilton 1 113 51 Justin Smiley 1 46 30 Michael Person 1 239 0 Logan Mankins 1 32 98 Trey Darilek 1 131 1 Julian Vandervelde 1 161 1 Dan Santucci 1 230 0 David Loverne 1 90 12 Cameron Spikes 1 145 13 Daniel Kilgore 1 163 5 Robert Hunt 1 226 0 Antoine Caldwell 1 77 11 Branden Albert 1 15 33 Reggie Wells 1 177 40 Kyle Kosier 1 248 54 Brandon Burlsworth 1 63 0 Chris Kuper 1 161 33 Jake Scott 1 141 58 John Welbourn 1 97 38 Scott Tercero 1 184 2 Shelley Smith 1 187 7 Rex Tucker 1 66 14 Eric King 1 220 0 Vince Manuwai 1 72 52 Andy Alleman 1 88 5 Jeb Terry 1 146 2 Clint Boling 1 101 21 Cooper Carlisle 1 112 53

39 Chris Snee 1 34 75 Travis Claridge 1 37 23 Matt Stinchcomb 1 18 19 Sean Mahan 1 168 26 Scott Wells 1 251 65 Randy Thomas 1 57 52 Steve Hutchinson 1 17 96 Rick DeMulling 1 220 31 Eric Heitmann 1 239 40 Fred Weary 1 66 19 Evan Mathis 1 79 40 Will Montgomery 1 234 33 Jeremy Zuttah 1 83 39 Roberto Garza 1 99 60 Victor Leyva 1 135 1 Scott Young 1 172 1 Richard Mercier 2 148 0 Tupe Peko 2 217 8 Mark Setterstrom 2 242 5 Zach Strief 2 210 35 Tutan Reyes 2 131 20 Tyrone Hopson 2 161 3 Floyd Wedderburn 2 140 15 Marcus Johnson 2 49 10 Tony Coats 2 209 0 Junius Coston 2 143 5 Quinn Ojinnaka 2 139 12 David Diehl 2 160 69 Joe Wong 2 244 0 Michael Toudouze 2 162 1 Seth Olsen 2 132 3 John Moffitt 2 75 7 Stephen Peterman 2 83 37 Oniel Cousins 2 99 9 Keith Williams 2 196 0 Darnell Alford 2 188 0 Kynan Forney 2 219 38 Dan Stevenson 2 205 0 Kendall Simmons 2 30 38 Jeno James 2 182 27 Marshall 2 169 23

40 Newhouse David Arkin 2 110 0 Jason Spitz 2 75 24 Lennie Friedman 2 61 19 Jeremy Bridges 2 185 23 Andrew Kline 2 220 0 Wes Sims 2 177 0 Rex Hadnot 2 174 36 Donald Thomas 2 195 14 Chilo Rachal 2 39 21 Danny Watkins 2 23 9 Ben Grubbs 2 29 52 Stephen Schilling 2 201 5 Pete Campion 2 213 0 Brian Rimpf 2 246 3 Shawn Lauvao 2 92 23 Cameron Stephenson 2 156 0 Justin Geisinger 2 197 0 Michael Moore 2 129 1 Kelvin Garmon 3 243 20 Steve Sciullo 3 122 12 Chris Kemoeatu 3 204 27 Chad Ward 3 170 0 Tony Pape 3 221 0 Deuce Lutui 3 41 35 Chris DeGeare 3 161 2 Mike Iupati 3 17 43 Todd Williams 3 225 1 Claude Terrell 3 134 6 Shawn Andrews 3 16 38 Max Jean-Gilles 3 99 14 Bobbie Williams 3 61 51 Taylor Whitley 3 87 4 Marques Sullivan 3 144 11 David Baas 3 33 36 Dan Buenning 3 107 10 Toniu Fonoti 3 39 18 Matt Johnson 3 138 0 Justin Blalock 3 39 57 Zach Piller 3 81 29

41

Cluster Results for Tackles

Draft Name Cluster Position AV Anthony Alabi 1 162 1 Selvish Capers 1 231 0 Tom Ashworth 1 263 21 Adam Koets 1 190 0 Mario Henderson 1 91 13 Seth Wand 1 75 10 Nate Solder 1 17 28 Daryn Colledge 1 47 59 Jim Molinaro 1 180 1 Doug Free 1 122 40 Gabe Hall 1 263 0 Dan Connolly 1 263 36 Jarriel King 1 263 0 Trent Williams 1 4 38 Eugene Monroe 1 8 29 Robert Gallery 1 2 39 Duane Brown 1 26 56 Chad Clifton 1 44 74 Wade Smith 1 78 43 Kenyatta Walker 1 14 29 John Welbourn 1 97 39 Lydon Murtha 1 228 0 Jarvis Borum 1 263 0 Guy Whimper 1 129 13 John Tait 1 14 50 Khalif Barnes 1 52 44 Xavier Fulton 1 155 0 Rodger Saffold 1 33 24 Joel Bell 1 263 0 William Beatty 1 60 32 Adrian Jones 1 132 12

42 Anthony Castonzo 1 22 29 Allen Barbre 1 119 7 Joey Chustz 1 123 0 Jordan Gross 1 8 70 Paul McQuistan 1 69 26 Scott Kooistra 1 215 6 Joe Thomas 1 3 71 Andrew Whitworth 1 55 60 Sam Young 1 179 5 Matt Stinchcomb 1 18 20 Jamon Meredith 1 162 14 Jared Veldheer 1 69 23 Jon Stinchcomb 1 37 44 Tony Washington 1 263 0 Luke Petitgout 1 19 45 Brandon Frye 1 163 3 Bruce Campbell 1 106 1 Stacy Andrews 1 123 22 Wayne Hunter 1 73 11 Demetrius Bell 2 219 16 Daniel Loper 2 150 7 Dan Dercher 2 263 1 Michael Thompson 2 100 3 Cleve Roberts 2 263 0 Harvey Dahl 2 263 33 Kris Comstock 2 263 0 Garry Johnson 2 263 0 Jason Watkins 2 263 0 Cornell Green 2 263 20 Jason Jimenez 2 263 0 Wes Shivers 2 237 0 Garrett Reynolds 2 156 16 Tutan Reyes 2 131 20 Matt Hill 2 171 3 Mike Otto 2 263 0 Mark Baniewicz 2 247 0 Jeremy Trueblood 2 59 37 Pete Lougheed 2 263 0 DeMarcus Curry 2 263 0 Jhari Evans 2 108 101 Kris Farris 2 74 1

43 Lance Nimmo 2 130 0 Troy Kropog 2 135 0 Michael Oher 2 23 39 Chris Williams 2 14 26 Josh Kobdish 2 263 0 Tim Provost 2 209 0 Quinn Ojinnaka 2 139 11 Doug Nienhuis 2 254 0 Jon Jansen 2 37 53 Ryan Harris 2 70 28 Frank Omiyale 2 163 15 Kevin Hughes 2 263 0 Chase Raynock 2 263 0 Sam Wilder 2 263 0 Corey Clark 2 234 0 Oniel Cousins 2 99 8 Reggie Wells 2 177 40 Will Ofenheusle 2 263 0 Gosder Cherilus 2 17 45 Tyler Polumbus 2 263 27 Derek Newton 2 214 19 Jeromey Clary 2 187 49 Eben Britton 2 39 14 Fenuki Tupou 2 159 0 Watts Sanderson 2 263 0 Sean Bubin 2 159 0 Ian Rafferty 2 263 0 Jeff Backus 2 18 63 Bryan Bulaga 2 23 22 Anthony Collins 2 112 16 Herb Taylor 2 196 1 Dan Lauta 2 263 0 Gerald Cadogan 2 263 0 Marek Rubin 2 263 0 Marko Cavka 2 178 0 DeMarcus Love 2 168 0 Kurth Connell 2 263 0 Corey Hilliard 2 209 9 Jerry Wisne 2 143 1 Joe Berger 2 207 20 John Greco 2 65 17

44 Michael Collins 2 263 0 Jason Smith 2 2 10 Jake Long 2 1 55 Jeremy Parquet 3 263 0 Damian Lavergne 3 263 0 Michael Roos 3 41 63 Elliot Silvers 3 132 0 Zach Strief 3 210 34 Tarlos Thomas 3 263 0 Lee Ziemba 3 244 1 Kareem McKenzie 3 79 64 Ramon Foster 3 263 34 Todd Frohbieter 3 263 0 Josh Parrish 3 263 0 Victor Rogers 3 259 0 Max Starks 3 75 46 Langston Walker 3 53 33 Chris Denman 3 214 0 Dustin Rykert 3 204 0 Kirk Chambers 3 176 9 L.J. Shelton 3 21 43 Greg Robinson- Randall 3 127 19 Derek Sherrod 3 32 2 Damion McIntosh 3 83 40 Tim Brown 3 263 0 Brad Lekkerkerker 3 263 0 Aaron Dalan 3 263 0 Kevin Boothe 3 176 28 Mark Wilson 3 151 0 Kyle Hix 3 263 0 Marvel Smith 3 38 47 Elliot Vallejo 3 263 0 Tyson Clabo 3 263 56 Phil Loadholt 3 54 39 Kevin Barry 3 263 8 James Brewer 3 117 4 Adam Grant 3 263 0 Calvin Armstrong 3 211 0 Wes Sims 3 177 0 Alan Reuber 3 263 0

45 Pete McMahon 3 214 0 Matt Anderle 3 178 0 Tony Pape 3 221 0 Nat Dorsey 3 115 7 Shawn Andrews 3 16 34 Franklin Dunbar 3 263 0 Jah Reid 3 85 4 Adam Kieft 3 153 0 Ken Shackleford 3 190 0 Marques Sullivan 3 144 11 Todd Wade 3 53 42 Joseph Barksdale 3 92 15 Marc Colombo 3 29 43 Willie Jones 3 263 2 Levi Brown 3 5 33 Carl Nicks 3 164 53 Brian Rimpf 3 246 3 Aaron Gibson 3 27 13 Jonas Jennings 3 95 29 Chris Hairston 3 122 10 Marcus Cannon 3 138 10 Leonard Davis 3 2 67

Cluster Results for Centers

Draft Name Cluster Position AV Austin King 1 133 3 John Sullivan 1 187 41 J.D. Walton 1 80 23 Nick Mangold 1 29 59 Louis Williams 1 211 0 Brandon Fusco 1 172 16 Geoff Hangartner 1 169 37 Jonathan Luigs 1 106 1 Marvin Philip 1 201 0 Drew Mormino 1 199 0

46 Dan Koppen 1 164 74 Ryan Cook 1 51 23 Greg Eslinger 1 198 0 Todd McClure 1 237 74 Stefen Wisniewski 1 48 24 Josh Sewell 1 190 0 Eric Wood 1 28 32 Doug Datish 1 198 0 A.Q. Shipley 1 226 10 Ryan Kalil 1 59 56 Joe Hawley 1 117 15 Eric Olsen 1 183 3 E.J. Whitley 2 224 0 Russ Hochstein 2 151 27 Nick Leckey 2 167 14 Grey Ruegamer 2 72 15 Max Unger 2 49 39 Steve Justice 2 201 1 Robert Hunt 2 165 0 Zack Quaccia 2 255 0 Josh Beekman 2 130 10 Ted Larsen 2 205 22 Matt Tennant 2 158 3 Rodney Hudson 2 55 16 Leroy Harris 2 115 21 Melvin Fowler 2 76 25 Jason Brown 3 124 31 Seth McKinney 3 90 21 Chukky Okobi 3 146 7 Samson Satele 3 60 48 Brad Meester 3 60 72 Dennis Norman 3 222 17 Damien Woody 3 17 58 Cody Wallace 3 107 5 Chris Spencer 3 26 37 Nick Hardwick 3 66 68 Matt Lehr 3 137 22 Dominic Raiola 3 50 67

47 Eric Ghiaciuc 3 119 18 Scott Peters 3 124 1

48