Which backs and receivers, based on their combine metrics and a little math, have a higher probability of hitting in this year's NFL Draft?

Every year in February, a group of NFL front office personnel, scouting organizations, media members, and the nation's top collegiate athletes get together for the NFL Combine. In this weeklong event, players hoping to make the leap to the NFL are measured, analyzed, and scrutinized by the movers and shakers of the league. Yet, many have wondered whether these movement tests performed in sterile conditions -- in shorts and t-shirts, free of helmets and pads -- have any validity in predicting future NFL performance.

With a large coffee in one hand and the combine results for all 1,091 wide receivers and running backs from the past 16 seasons (courtesy of mockdraftable.com) on my computer in front of me, I decided to tackle the task of assimilating the vast metrics measured at the combine for each player and converting this information into an actionable predictor of NFL potential.

The Math

When we glance at combine numbers, our intuition gives us a general sense of a "good" combine performance versus a "bad" one. But these are subjective measures. Can we define these in a quantitative manner? First, I asked, "What exactly constitutes a 'good' combine performance? What separates the 'good' from the 'great', and the 'great' from the 'elite'?"

I decided to define the quality of an athlete's combine performance as the fold increase above what would be expected for an NFL hopeful of that athlete's size to produce. I chose to normalize everything to size to take into account a condition that makes intuitive sense: if two athlete's both run a 4.4 40-yard dash, but one athlete weighs 265 pounds and the other weights 190 pounds, we would consider the performance by the 265 pound athlete much more impressive. Therefore, I thought that rather than compare performances at face value, our analysis should somehow factor in player size.

So from the large set of historical data at my disposal, I was able to derive a set of equations to determine an athlete's expected combine numbers based on that athlete's size (specifically, weight), which served as the baseline from which I then assessed that player's actual combine performance:

Estimated 40 = (.0022 x Weight) + 4.0726

Estimated Bench = (.1313 x Weight) - 9.825

Estimated Vertical = (-.0102 x Weight) + 37.264

Estimated Broad = (-.0244 x Weight) + 124.08

Estimated 3-Cone = (.004 x Weight) + 6.1036

Estimated 20ss = (.0026 x Weight) + 3.688

So a fair question to ask would be: "Just how valid are these equations in predicting combine performance?" To test this, I took the average weight of all 1,091 running backs and wide receivers (206.6 pounds) and calculated what the combine performances would be for players of this size. I then compared these numbers to the actual average of the combine performances for all players from the last 16 seasons weighing either 205, 206, or 207 pounds (n = 63 players). The results are listed below:

Weight 40-yd Bench Vert Broad 3Cone 20ss Predicted 206.6 4.527 17.301 35.157 119.039 6.957 4.225 Actual (Avg.) 205.9 4.534 18.861 35.402 118.982 7.018 4.215

From the data above, we see that these equations do an excellent job of predicting combine performance for a given player's size. Using these equations, I was then able to assess how well a player's actual performance differed from their predicted performance. Players performing better than their expected combine numbers in a given event received a positive score for that event (weighted according to the dynamic range of the particular skill being measured), and conversely, players performing worse than their expected combine numbers for a given event received a negative weighted score for that event. Specifically, the scores for each player for any particular event was obtained using the following formulas:

40 = -(Observed - Expected)/(Range)

Bench = (Observed - Expected)/(Range)

Vertical = (Observed - Expected)/(Range)

Broad = (Observed - Expected)/(Range)

3-Cone = -(Observed - Expected)/(Range)

20ss = -(Observed - Expected)/(Range)

Range is defined as the upper limit of all combine performances for all wide receivers and running backs subtracted by the lower limit for a given event.

Wide Receiver and Running Back Ranks According to PACE

Taking the average scores across all events, I then obtained what I call my Performance Above Combine Expectations (PACE) score. This allowed me to rank all 1,091 wide receivers and running backs from 1999-2015 on the basis of their combine performances, with some of the notable names at the top five percent of all-time PACE scores listed below:

All-Time Top 50 Â Â Â Â Year Name Position PACE Score All-time Rank 2007 Calvin Johnson WR 0.432 1 2001 Chris Chambers WR 0.355 2 2003 Justin Fargas RB 0.3428 3 1999 Edgerrin James RB 0.288 6 2001 Santana Moss WR 0.275 8 2010 Demaryius Thomas WR 0.244 11 2014 Jerick McKinnon RB 0.243 12 2013 Christine Michael RB 0.221 14 2010 Ben Tate RB 0.213 16 2008 Chris Johnson RB 0.212 17 2015 Jaelen Strong WR 0.206 20 2004 Kevin Jones RB 0.205 24 2015 Chris Conley WR 0.200 27 2015 Ameer Abdullah RB 0.196 29 2011 Julio Jones WR 0.187 37 2010 C.J. Spiller RB 0.186 38 2008 Donnie Avery WR 0.186 39 2015 Sammie Coates WR 0.185 40 2003 Andre Johnson WR 0.179 44 2012 Ryan Broyles WR 0.175 46 2013 Cordarrelle Patterson WR 0.174 48

Not surprisingly, Calvin Johnson was the top performer according to the PACE metric, achieving a score of 0.43, a figure nearly 25% greater than the second-best performer, wide receiver Chris Chambers.

Some other notable names at the top of this list include athletic freaks who have emerged recently as stars in the NFL, including Demaryius Thomas, Julio Jones, and C.J. Spiller, veterans that have shown long-term productivity in the league including the Colts franchise leader in rushing yards, Edgerrin James, Pro Bowl wideouts Santana Moss and Andre Johnson, and 2014 breakouts including Jerick McKinnon.

Predictive Value of the PACE Metric

To further test the validity of the PACE metric as a predictor of on-field success, I decided to do a case study of the 2011 rookie class. I chose this class because we have four seasons worth of statistics for this group of players that we can then use to assess the relationship between NFL productivity and combine metrics. I ranked every wide receiver and running back participating in at least four events of the 2011 combine by PACE score, and assessed their productivity for the past four seasons using Total Net Expected Points (NEP).

Below is the list of the top 25 players of the class of 2011 as ranked by the PACE metric, along with their total NEP for each season from 2011-2014, their average NEP per season, and their positional rank (percentile) according to NEP per season:

Â Year Name Pos PACEÂ Score '11Â NEP '12Â NEP '13Â NEP '14Â NEP AvgÂ NEP RBÂ Rk WRÂ Rk Â 2011 GregÂ Little WR 0.1905 55.92 54.72 30.49 8.16 37.32 - 77.8% Â 2011 JulioÂ Jones WR 0.1875 81.10 105.55 39.34 141.72 91.93 - 94.4% Â 2011 TorreyÂ Smith WR 0.1593 75.36 76.45 97.73 80.96 82.63 - 91.7% Â 2011 JordanÂ Todman RB 0.1563 0.00 -2.02 1.90 6.89 1.69 72.4% - Â 2011 AldrickÂ Robinson WR 0.1503 0.00 24.16 31.45 0.48 14.02 - 61.1% Â 2011 AnthonyÂ Allen RB 0.1460 -0.45 2.44 0.00 0.00 0.50 65.5% - Â 2011 EdmondÂ Gates WR 0.1440 2.45 20.76 6.83 0.00 7.51 - 38.9% Â 2011 DeMarcoÂ Murray RB 0.1305 22.51 3.21 39.45 23.54 22.18 96.6% - Â 2011 DeloneÂ Carter RB 0.1190 -25.36 8.46 0.00 0.00 -4.23 24.1% - Â 2011 JonÂ Baldwin WR 0.1139 21.46 25.17 2.14 0.00 12.19 - 55.6% Â 2011 TerranceÂ Toliver WR 0.1056 - - - - - - 0.0% Â 2011 RyanÂ Whalen WR 0.1033 1.92 4.89 0.00 0.00 1.70 - 22.2% Â 2011 RicardoÂ Lockette WR 0.0908 8.52 0.00 6.55 12.15 6.81 - 36.1% Â 2011 MarioÂ Fannin RB 0.0811 - - - - - 0.0% - Â 2011 RyanÂ Williams RB 0.0771 0.00 -16.20 0.00 0.00 -4.05 27.6% - Â 2011 CecilÂ Shorts WR 0.0769 4.67 85.41 62.43 37.19 47.42 - 83.3% Â 2011 KendallÂ Hunter RB 0.0735 10.78 13.00 -4.13 0.00 4.91 82.8% - Â 2011 NilesÂ Paul WR 0.0735 4.32 10.01 3.33 34.10 12.94 - 58.3% Â 2011 GregÂ Salas WR 0.0692 16.20 0.00 11.48 17.17 11.21 - 52.8% Â 2011 AustinÂ Pettis WR 0.0581 17.94 30.61 46.51 13.74 27.20 - 75.0% Â 2011 DerrickÂ Locke RB 0.0567 - - - - - 0.0% - Â 2011 RoyÂ Helu RB 0.0552 4.05 0.65 13.57 25.29 10.89 89.7% - Â 2011 A.J.Â Green WR 0.0529 100.46 111.17 127.49 78.94 104.52 - 97.2% Â 2011 ShaneÂ Vereen RB 0.0522 2.40 18.27 37.55 29.61 21.96 93.1% - Â 2011 DaneÂ Sanzenbacher WR 0.0451 27.17 1.01 7.21 6.01 10.35 - 50.0%

10 out of the top 25 players as ranked by PACE score had four-year NEP averages that placed them in the top 25th percentile of the 2011 class, including Pro Bowlers Julio Jones, A.J. Green, and DeMarco Murray, along with established starters such as Torrey Smith, Shane Vereen, and Cecil Shorts.

Conversely, 16 out of the bottom 25 players as ranked by PACE score had four-year NEP averages that placed them in the bottom half of the 2011 class:

Â Year Name Pos PACEÂ Score '11Â NEP '12Â NEP '13Â NEP '14Â NEP AvgÂ NEP RBÂ Rk WRÂ Rk Â 2011 OwenÂ Spencer WR 0.0013 - - - - - - 0.0% Â 2011 GraigÂ Cooper RB -0.0074 - - - - - 0.0% - Â 2011 StephenÂ Burton WR -0.0111 3.36 3.87 3.73 0.00 2.74 - 25.0% Â 2011 StevanÂ Ridley RB -0.0130 2.44 13.11 -13.28 -1.38 0.22 58.6% - Â 2011 TitusÂ Young WR -0.0150 56.55 35.31 0.00 0.00 22.96 - 69.4% Â 2011 DarrenÂ Evans RB -0.0355 - - - - - 0.0% - Â 2011 ToriÂ Gurley WR -0.0386 0.00 0.00 3.24 0.00 0.81 - 19.4% Â 2011 ShaunÂ Draughn RB -0.0399 0.00 2.59 -1.54 -4.11 -0.76 44.8% - Â 2011 AllenÂ Bradford RB -0.0446 -1.14 0.00 0.00 0.00 -0.29 51.7% - Â 2011 JerrelÂ Jernigan WR -0.0455 0.00 1.80 33.47 0.59 8.97 - 47.2% Â 2011 VincentÂ Brown WR -0.0484 29.50 0.00 41.05 7.74 19.57 - 63.9% Â 2011 VaiÂ Taua RB -0.0494 - - - - - 0.0% - Â 2011 EvanÂ Royster RB -0.0495 18.68 1.50 -2.29 0.00 4.47 79.3% - Â 2011 DeAndreÂ Brown WR -0.0510 - - - - - - 0.0% Â 2011 TandonÂ Doss WR -0.0511 0.00 10.98 22.50 0.00 8.37 - 41.7% Â 2011 ArmonÂ Binns WR -0.0518 0.00 19.82 0.00 0.00 4.96 - 30.6% Â 2011 DionÂ Lewis RB -0.0545 1.62 5.10 0.00 0.00 1.68 69.0% - Â 2011 JohnnyÂ White RB -0.0557 -4.50 -1.23 0.00 0.00 -1.43 41.4% - Â 2011 DwayneÂ Harris WR -0.0632 0.00 17.39 8.88 8.37 8.66 - 44.4% Â 2011 O.J.Â Murdock WR -0.0714 - - - - - - 0.0% Â 2011 RandallÂ Cobb WR -0.0730 31.46 98.04 40.95 118.03 72.12 - 88.9% Â 2011 JacquizzÂ Rodgers RB -0.1161 3.90 6.47 7.97 3.53 5.47 86.2% - Â 2011 LestarÂ Jean WR -0.1302 0.00 14.06 7.85 0.00 5.48 - 33.3% Â 2011 MarkÂ Ingram RB -0.1441 0.27 -6.87 -2.99 7.10 -0.62 48.3% - Â 2011 MattÂ Asiata RB -0.1877 0.00 -2.00 -1.84 11.45 1.90 75.9% -

Only four players, Randall Cobb, Matt Asiata, Jacquizz Rodgers, and Evan Royster, had four-year NEP averages placing them in the top 25th percentile of the 2011 class. To further emphasize the predictive value of the PACE metric to player performance, six of the players from this group actually failed to ever see regular season playing time in the NFL.

A closer look at the data reveals that 17 out of the top 25 players as ranked by the PACE metric ranked in the top half of their class according to their four-year average NEP score. In contrast, only 9 of the bottom 25 players achieved this same feat. For these bottom 25 players, there was instead an enrichment for those ranking in the bottom half of their class according to NEP per season, with 16 of these players clustering into this group:

Percentile Rank (Pos) Â Â Â Â Â 100-75th 75-50th 50-25th 25-0 PACE Score Top 25 10 7 3 5 PACE Score Bottom 25 4 5 9 7

In addition, the average NEP scores over the 2011-2014 seasons for the top 25 players as measured by PACE nearly tripled the average NEP scores for the bottom 25 players (23.7 vs. 8.7):

Group Four Year Avg. of Total NEP PACE Score Top 25 23.7 PACE Score Bottom 25 8.7

Through this analysis of the 2011 rookie class, we can see at multiple levels that players ranking near the top of the list according to PACE score have a strong tendency to have productive NFL careers, whereas players ranking near the bottom of this list (with a few rare exceptions) have a strong tendency to have either lackluster or even non-existent NFL careers.

Using the PACE Score to Assess the Incoming Class of 2015

So how does the running back and wide receiver class of 2015 stack up when we rank them based on the PACE metric? Below is the list of players clustering into the top 20 (or roughly top 25% of all skill position players) according to PACE score:

Rookie Class of 2015 Top 20 Â Â Â Â Year Name Pos PACE Score 2015 Rk 2015 Jaelen Strong WR 0.206064702 1 2015 Chris Conley WR 0.199988665 2 2015 Ameer Abdullah RB 0.195970932 3 2015 Sammie Coates WR 0.184831338 4 2015 David Johnson RB 0.163048363 5 2015 Tevin Coleman RB 0.1492875 6 2015 Kevin White WR 0.124324899 7 2015 Antwan Goodley WR 0.121578947 8 2015 Kenny Bell WR 0.110632442 9 2015 Geremy Davis WR 0.105123048 10 2015 Amari Cooper WR 0.104148538 11 2015 Rannell Hall WR 0.10350315 12 2015 Ty Montgomery WR 0.088294351 13 2015 Tre McBride WR 0.082919086 14 2015 DeVante Parker WR 0.08162597 15 2015 Phillip Dorsett WR 0.081148093 16 2015 Melvin Gordon RB 0.063459594 17 2015 Jay Ajayi RB 0.056708064 18 2015 Devin Smith WR 0.047593305 19 2015 Michael Dyer RB 0.042384857 20

We see the appearance of some familiar, highly-touted NFL draft prospects on this list including Fred Biletnkoff Award winner Amari Cooper, Doak Walker Award winner Melvin Gordon, and projected first-rounders Kevin White and Jaelen Strong. But where it gets interesting is the presence of names on this list projected to be drafted in the fifth round or later, including Georgia Bulldog wideout Chris Conley and Louisville running back Michael Dyer. These players represent excellent value picks for NFL teams willing to take a chance on them in the upcoming draft.

If history serves as a guide for us, the players on this top 20 list have a high probability of being impact players for the NFL teams that draft them this upcoming April. And, in particular, a few of these aforementioned players -- who have all the athletic skills necessary to succeed at the NFL level -- may represent overlooked candidates with the potential to have careers that vastly outperform their NFL draft position.