I know that some of you may be thinking that pro-bowl selection is SUCH a popularity contest. Yes, that may be true, but pro-bowl selection of a tight end is usually conditioned upon impressive season lines (receptions, yardage, and touchdowns) as well, so its an easy way to reduce three continuous variables to a binary outcome (Y/N to pro-bowl status).
Furthermore, the strength of using a binary outcome is that this fits nicely into the realm of a case-control study from epidemiology (my day job), so I can easily use the predicted log odds-ratios to estimate the probability (albeit badly as no model is perfect) of a player with a particular draft profile having played in at least one pro-bowl at some point in their career.
Using my factors (size-adjusted combine statistics) and outcome of interest (Pro-bowl appearance status), I began modeling. Bivariate analysis suggested that size adjusted 40 time, vertical leap, broad jump, and agility were all significantly different between eventual pro-bowlers and all yet-to-be-pro-bowlers. Correlation analysis suggested that size adjusted 40 time and broad jump were significantly correlated. Since 40 yard dash is completed by nearly all combine participants, it was decided to exclude size adjusted broad jump from the modeling. Finally, exploratory logistic regression methods (backwards and forward selection) were applied to the 1999-2011 combine data to approximate the odds of a player with the particular combine profile being selected to a pro-bowl (NOT a replacement) at some point in their career based on size adjusted 40 times, vertical leap, and agility times. Two-way interactions factors were also included as potential covariates.
The resulting logistic regression model depended primarily upon 2 factors:
1. Weight adjusted 40 yard Dash Time (Average Momentum)
2. Height complemented Vertical Leap (High Point Potential)
An ROC-curve analysis suggested that the best cutoff for predicting a legitimate pro-bowl appearance was a probability of 0.06, which ruled out 142 of the 188 (75.5% Specificity) combine tight-end hopefuls who never made it to a Pro-Bowl and correctly identified 9 (italics) of the 12 hopefuls who made it to a Pro-bowl (75% Sensitivity) listed below:
| Player Name | Prob(PB) |
| Vernon Davis | 66.2% |
| Jimmy Graham | 55.6% |
| Jordan Cameron | 27.4% |
| Greg Olsen | 24.6% |
| Marcedes Lewis | 18.3% |
| Dallas Clark | 16.1% |
| Jason Witten | 12.0% |
| Rob Gronkowski | 8.4% |
| Alge Crumpler | 7.8% |
| Julius Thomas | 4.2% |
| Todd Heap | 2.7% |
| Chris Cooley | 2.7% |
The remaining hopefuls is a bit too long to list, but still contains some notable names with their pro-bowl hopes alive (Virgil Green, Martellus Bennett, Owen Daniels), but many are either free agents or retired already. As a reference, I'll provide a nifty table for tabulation of the estimated probability of a pro-bowl based on high-point potential (vertical + height) and average momentum (Weight/Dash), but you can also access the interactive calculator to compute this Size-Adjusted Vertical and Velocity Athletic Greatness Estimate (SAVVAGE) for yourself:
| Wgt/40-yd Hgt+Vert |
45.0 | 46.0 | 47.0 | 48.0 | 49.0 | 50.0 | 51.0 | 52.0 | 53.0 | 54.0 | 55.0 | 56.0 | 57.0 | 58.0 | 59.0 | 60.0 |
| 100 | 0.0% | 0.0% | 0.0% | 0.0% | 0.0% | 0.0% | 0.1% | 0.1% | 0.2% | 0.3% | 0.5% | 0.9% | 1.5% | 2.6% | 4.3% | 7.1% |
| 101 | 0.0% | 0.0% | 0.0% | 0.0% | 0.0% | 0.0% | 0.1% | 0.1% | 0.2% | 0.4% | 0.7% | 1.2% | 1.9% | 3.3% | 5.4% | 8.9% |
| 102 | 0.0% | 0.0% | 0.0% | 0.0% | 0.0% | 0.1% | 0.1% | 0.2% | 0.3% | 0.5% | 0.9% | 1.5% | 2.5% | 4.2% | 6.9% | 11.2% |
| 103 | 0.0% | 0.0% | 0.0% | 0.0% | 0.0% | 0.1% | 0.1% | 0.2% | 0.4% | 0.7% | 1.1% | 1.9% | 3.2% | 5.3% | 8.7% | 14.0% |
| 104 | 0.0% | 0.0% | 0.0% | 0.0% | 0.1% | 0.1% | 0.2% | 0.3% | 0.5% | 0.9% | 1.4% | 2.4% | 4.1% | 6.7% | 11.0% | 17.3% |
| 105 | 0.0% | 0.0% | 0.0% | 0.0% | 0.1% | 0.1% | 0.2% | 0.4% | 0.6% | 1.1% | 1.9% | 3.1% | 5.2% | 8.5% | 13.7% | 21.3% |
| 106 | 0.0% | 0.0% | 0.0% | 0.1% | 0.1% | 0.2% | 0.3% | 0.5% | 0.8% | 1.4% | 2.4% | 4.0% | 6.6% | 10.7% | 17.0% | 25.8% |
| 107 | 0.0% | 0.0% | 0.0% | 0.1% | 0.1% | 0.2% | 0.4% | 0.6% | 1.1% | 1.8% | 3.0% | 5.1% | 8.3% | 13.4% | 20.9% | 31.0% |
| 108 | 0.0% | 0.0% | 0.1% | 0.1% | 0.2% | 0.3% | 0.5% | 0.8% | 1.4% | 2.3% | 3.9% | 6.4% | 10.5% | 16.6% | 25.4% | 36.6% |
| 109 | 0.0% | 0.0% | 0.1% | 0.1% | 0.2% | 0.4% | 0.6% | 1.0% | 1.8% | 3.0% | 5.0% | 8.2% | 13.1% | 20.5% | 30.5% | 42.7% |
| 110 | 0.0% | 0.1% | 0.1% | 0.2% | 0.3% | 0.5% | 0.8% | 1.3% | 2.3% | 3.8% | 6.3% | 10.3% | 16.3% | 24.9% | 36.1% | 49.0% |
| 111 | 0.0% | 0.1% | 0.1% | 0.2% | 0.4% | 0.6% | 1.0% | 1.7% | 2.9% | 4.8% | 8.0% | 12.8% | 20.1% | 29.9% | 42.1% | 55.3% |
| 112 | 0.1% | 0.1% | 0.2% | 0.3% | 0.5% | 0.8% | 1.3% | 2.2% | 3.7% | 6.2% | 10.0% | 16.0% | 24.4% | 35.5% | 48.4% | 61.5% |
| 113 | 0.1% | 0.1% | 0.2% | 0.3% | 0.6% | 1.0% | 1.7% | 2.8% | 4.7% | 7.8% | 12.6% | 19.7% | 29.4% | 41.5% | 54.7% | 67.3% |
| 114 | 0.1% | 0.2% | 0.3% | 0.4% | 0.8% | 1.3% | 2.2% | 3.6% | 6.0% | 9.8% | 15.6% | 24.0% | 34.9% | 47.8% | 60.9% | 72.6% |
| 115 | 0.1% | 0.2% | 0.3% | 0.6% | 1.0% | 1.6% | 2.8% | 4.6% | 7.6% | 12.3% | 19.3% | 28.9% | 40.9% | 54.1% | 66.7% | 77.4% |
| 116 | 0.2% | 0.3% | 0.4% | 0.7% | 1.2% | 2.1% | 3.5% | 5.9% | 9.6% | 15.3% | 23.5% | 34.4% | 47.2% | 60.3% | 72.1% | 81.5% |
| 117 | 0.2% | 0.3% | 0.6% | 0.9% | 1.6% | 2.7% | 4.5% | 7.4% | 12.0% | 18.9% | 28.4% | 40.3% | 53.5% | 66.2% | 76.9% | 85.0% |
| 118 | 0.2% | 0.4% | 0.7% | 1.2% | 2.1% | 3.5% | 5.7% | 9.4% | 15.0% | 23.1% | 33.8% | 46.5% | 59.7% | 71.6% | 81.1% | 88.0% |
| 119 | 0.3% | 0.5% | 0.9% | 1.6% | 2.6% | 4.4% | 7.3% | 11.8% | 18.5% | 27.9% | 39.7% | 52.9% | 65.6% | 76.5% | 84.7% | 90.4% |
| 120 | 0.4% | 0.7% | 1.2% | 2.0% | 3.4% | 5.6% | 9.2% | 14.7% | 22.7% | 33.3% | 45.9% | 59.1% | 71.1% | 80.7% | 87.7% | 92.4% |
For the purpose of model validation and the focus of a future post, we will look at a list of tight ends with scores greater than 0.06 from the 2012-2013 draft classes and track them forward in time to see if they reach a pro-bowl.
With many talented tight ends of recent years having a basketball background, we cannot rule out the possibility that a selection bias is driving this model. With the notable success of Tony Gonzalez and Antonio Gates paving the way for players like Jimmy Graham and Julius Thomas, it's possible that players with impressive athleticism for their size are becoming more and more popular in the time frame sampled. Opportunity breeds success, so this relationship may be correlation and not causation. However, for a Pro-bowl selection, a tight-end typically catches at least ten touchdowns and 1000 yards, so it's reasonable to think that impressive high-point potential and large average momentum over the 40 yard dash would give one an advantage in both of these football statistics.
