When Do YPRR, TPRR, and YPT Stabilize for Running Backs?

Among running backs (RBs) that have run at least 75 receiving routes so far this season,1  Roy Helu leads the NFL with 11.4 Yards per Target (YPT), while Darren Sproles’ 2.37 Yards per Route Run (YPRR) and Fred Jackson’s 27.4% Targets per Route Run (TPRR) sit atop the rankings for those advanced stat categories. But which of the three is most likely to still be No. 1 come seven weeks from now? Which is the least likely? If you’ve read my analogous posts for wide receivers (WRs) or tight ends (TEs), the answer(s) probably won’t shock you. What may shock you, however, is just how unreliable one of these stats actually is.

Methods

As always, here’s how my reliability analysis works:

  1. I collected data for all RBs that had at least 8 games played from 2007 to 2013.
  2. To control for team effects, I included only those RBs that played 8+ games for the same team.
  3. Starting with RBs that played 8+ games, I randomly selected two sets of 4 games for each RB, and calculated their YPT, YPRR, and TPRR in both sets.
  4. For both of these metrics, I calculated its split-half correlation (r) between the two randomly-selected sets of games.
  5. I performed 25 iterations of Step 4 so that r converged.
  6. I repeated Steps 3-5, increasing the RB inclusion criteria in 8-game intervals, from 16+ games all the way to 72+ games.
  7. For each “games played” group, I calculated the number of games at which the variance explained in each metric, R2, would mathematically equal 0.5.2
  8. I calculated the True YPT, True YPRR, and True TPRR for a hypothetical RB that’s had an observed performance of 7.00 YPT, 1.50 YPRR, and 20.0% TPRR through X number of games.3
  9. I calculated a weighted average of the results from Steps 7 and 8.4

Results

First up, it’s YPRR:

GamesnrR2 = 0.50Avg YPRRObs 1.50 YPRR
Wtd Average241.231.37
42860.15221.211.25
81590.24251.231.29
121270.38201.231.33
16910.37271.261.35
20690.47231.271.38
24480.49251.281.39
28350.43371.271.37
32190.59221.271.41
36170.61231.261.41

Getting down to brass tacks, the “Wtd Average” row tells us that YPRR takes 24 games to stabilize. Based on the weighted average of 13.1 routes run per game, a RB’s YPRR reaches half-skill/half-luck upon 308 routes run. Going back to the intro, Sproles has achieved his 2.37 YPRR on 103 routes run, which means that determining his True YPRR requires regressing his current YPRR 74.9% of the way towards the league average of 1.26.5

In a vacuum, 1.5 seasons’ worth of games may not seem all that reliable, but it’s (literally) light years earlier than determining a RB’s True YPT:

GamesnrR2 = 0.50Avg YPTObs 7.00 YPT
Wtd Average6.40
42860.05706.296.33
81590.023806.386.39
121270.13796.406.48
16910.072176.456.49
20690.121546.526.57
24480.054316.596.61
28350.122166.576.62
3219-0.066.57
3617-0.016.55

Well, this is troublesome: Not only does the RB position never cross the the .707 threshold for YPT’s split-half correlation; it never exceeds 0.13 in any group. Weirdest of all, unlike every reliability analysis I’ve published thus far, I encountered a group — actually two — for which a higher YPT in one set of games predicted a lower YPT in an equally sized set of other games. And most disconcerting of all, this phenomenon occurred for RBs with the most experience in their current offense.

In short, YPT takes anywhere from 70 games to the end of time to stabilize, with the erratic nature of group-specific results giving zero guidance as to where in that infinite range the “true” answer may lie. Essentially, Helu’s 11.4 YPT on an NFL field in 2014 is as indicative of his “true” receiving yardage ability as my 0.00 YPT is whilst sitting in front of a computer keyboard in my parents’ basement.6

Normally, this is the part where I would write something suggesting that TPRR is the reason for YPRR’s superior reliablity vis-à-vis YPT. With the utter failure of YPT, though, I’ll simply present the usual table wherein TPRR takes about half as many observations as YPRR to stabilize:

GamesnrR2 = 0.50Avg TPRRObs 20.0% TPRR
Wtd Average1219.3%19.6%
42860.251219.2%19.4%
81590.381319.2%19.5%
121270.491319.2%19.6%
16910.561319.5%19.8%
20690.651119.5%19.8%
24480.681119.4%19.8%
28350.641619.3%19.8%
32190.761019.3%19.8%
36170.781019.3%19.8%

Again, from the “Wtd Average” row we see that it takes 12 games for a RB’s TPRR to stabilize, which translates to 161 routes run. Unlike YPT, for which no RBs will reach the stabilization point even given an infinite-year career, 11 RBs have already run 161 routes in 2014 alone. Fred Jackson, the league leader in TPRR, is barely below that threshold at 157, but the reliability of this stat means that the league average accounts for far less of his True TPRR (about 50%) than it did for Sproles’ True YPRR (about 75%).

DT : IR :: TL : DR

In general, I’ve found that per-route metrics are more reliable than per-target metrics. For RBs, however, it’s not even a contest. It could very well take time immemorial to observe enough targets before a RB’s YPT represents half-skill/half-luck, whereas it appears to take less than two seasons for YPRR or TPRR to achieve same.

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  1. Routes run stats courtesy of Pro Football Focus

  2. The formula is (Observations/2)*[(1-r)/r]

  3. The formula is [(Observed Performance * Observations) + (League-Average Performance * Stabilization Point)] / (Observations + Stabilization Point)  

  4. Weighted by group size. 

  5. 103/(103 + 308) = 25.1% of the way toward 100% “true” ability. 

  6. Know that’s not technically true, but creative license, people. 

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