At 4.96 yards per carry (YPC), Jerick McKinnon leads all qualifying rookie running backs through Week 9, while the rookie rankings for touchdown rate (TD%) are currently led by Isaiah Crowell’s 7.69%. We can’t predict the future, but it would seem that these stats suggest McKinnon and Crowell are keepers in Minnesota and Cleveland, respectively…or do they? What if I told you that we’re nowhere near the point in their careers at which YPC and TD% tell us much about their “true” ability?

Chase Stuart — about whom I’m increasingly concerned about sharing my brain — has previously looked at the statistical farce of YPC, and found that it’s not a reliable indicator of RB skill, both from one half of a season to another and from one season to the next. To my knowledge, no one’s ever translated his results into a carry-by-carry number. And while Stuart’s extended his RB reliability research to success rates and expected points added, no one seems to have looked at TD% yet. Therefore, today’s post seeks to answer the following question: **How many carries do we need to observe before a RB’s YPC and TD% stabilize as measures of their “true” ability?**

### Methods

It’s been forever, so let’s recap my reliability analysis procedures:

- I collected data for all RBs that had at least 8 games played from 2007 to 2013.
- To control for team effects, I included only those RBs that played 8+ games
*for the same team*. - Starting with RBs that played 8+ games, I randomly selected two sets of 4 games for each RB, and calculated their YPC and TD% in both sets.
- For both of these metrics, I calculated its split-half correlation (
*r*) between the two randomly-selected sets of games. - I performed 25 iterations of Step 4 so that
*r*converged. - I repeated Steps 3-5, increasing the RB inclusion criteria in 8-game intervals, from 16+ games all the way to 72+ games.
- For each “games played” group, I calculated the number of games at which the variance explained in each metric,
*R*, would mathematically equal 0.5.^{2}^{1} - I calculated the “true” YPC and TD% for a hypothetical RB that’s had an observed performance of 5.00 YPC and 3.50% TD% through X number of games.
^{2} - I calculated a weighted average of the results from Steps 7 and 8.
^{3}

I’m obligated to mention one more methodological consideration. The definition of RB is a bit nebulous in today’s NFL. Fullbacks do still exist; but are they RBs? Situational personnel packages frequently involve all manner of positions lining up in the backfield; but are those players RBs? On both counts, my decision was to answer “no,” and restrict this analysis to only those players who fit a layman’s — admittedly fantasy football-driven — conceptualization of the RB position: Their primary responsibility is to gain yardage, not lead-block for the guys who gain yardage.

That said, I did take a liberal approach with respect to including big-back tweeners like LeRon McClain and Mike Tolbert, who over time have demonstrated the skill set to both lead-block and step in as a move-the-sticks yardage gainer when their teams’ primary bona fide RB gets hurt.^{4}

### Results

I’m a fan of suspense, so I’ll start with TD%. Here’s the familiar table:

Games | n | r | R = 0.50^{2} | Avg TD% | Obs 3.50% TD% |
---|---|---|---|---|---|

Wtd Average | 60 | 2.97% | 3.24% | ||

4 | 286 | 0.15 | 22 | 2.89% | 2.98% |

8 | 159 | 0.11 | 68 | 2.90% | 2.97% |

12 | 127 | 0.13 | 84 | 2.97% | 3.03% |

16 | 91 | 0.14 | 102 | 3.05% | 3.11% |

20 | 69 | 0.26 | 58 | 3.16% | 3.25% |

24 | 48 | 0.26 | 69 | 3.09% | 3.20% |

28 | 35 | 0.23 | 97 | 3.15% | 3.23% |

32 | 19 | 0.26 | 91 | 3.10% | 3.21% |

36 | 17 | 0.33 | 73 | 3.14% | 3.26% |

If you’re not familiar with how to comprehend the individual rows, there’s an archive of explanations on the front page, so let’s focus on the “Wtd Average” row, which tells us that **it takes 60 games for TD% to stabilize**. Using the weighted average number of carries per game (11.1), we can estimate that 60 games translates to 667 carries. The “Wtd Average” row also tells us that a RB with 3.50 TD% after 60 games (or 667 carries) has a True TD% of 3.24%.

One thing you might notice in the table — which hasn’t happened before in these reliability analyses — is that *r* never actually reaches 0.707 — and therefore *R ^{2}* never actually reaches 0.50 — in any row. Because of the equation that says when

*R*

^{2}*would*equal 0.50, it’s not a disaster, but this finding, coupled with the diminishing sample sizes as you move down the table, suggests it’s conceivable that TD% never stabilizes in real life for the average RB. Yes, the 667-carry figure means it has the potential to stabilize for a modern-day “workhorse” in about three full seasons-worth of carries, but it’s equally the case that a RB that gets 150 carries per season in the same offense — think Ronnie Brown — may move on to another team before he crosses the threshold. Returning to Crowell, 52 carries is — any way you slice it — a long way away from being a reliable indicator of his “true” TD-scoring ability.

Time for the main event:

Games | n | r | R = 0.50^{2} | Avg YPC | Obs 5.00 YPC |
---|---|---|---|---|---|

Wtd Average | 177 | 4.33 | 4.66 | ||

4 | 286 | 0.19 | 17 | 4.26 | 4.40 |

8 | 159 | 0.01 | 545 | 4.31 | 4.32 |

12 | 127 | 0.04 | 309 | 4.33 | 4.35 |

16 | 91 | 0.13 | 109 | 4.36 | 4.44 |

20 | 69 | 0.26 | 57 | 4.37 | 4.53 |

24 | 48 | 0.31 | 54 | 4.41 | 4.59 |

28 | 35 | 0.29 | 69 | 4.46 | 4.62 |

32 | 19 | 0.43 | 42 | 4.53 | 4.74 |

36 | 17 | 0.49 | 38 | 4.56 | 4.77 |

That’s right: **It takes 177 games for the average RB’s YPC to stabilize**. Translating that to number of carries, the vomit-inducing number is 1,978.^{5} So going back to McKinnon, 90 carries thus far in his Vikings career means that, in order to get a decent gauge on his True YPC, we have to hope that we get to see 168 games or 1,888 more carries from him in Minnesota. To put that in perspective, Frank Gore is easily the longest-tenured RB with his current team, and yet there’s this: a) He has yet to play 177 games in San Francisco, and b) it took him 10 seasons to reach 1,978 carries.

### DT : IR :: TL : DR

Although it may very well be the case that we’ll never know for certain, it takes at least 667 carries (or about three seasons) with the same team to get a decent gauge of a RB’s “true” TD-producing ability. With respect to YPC, we’re essentially talking about a bunkum stat.

The formula is

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

**[(Observed Performance * Observations) + (League-Average Performance * Stabilization Point)] / (Observations + Stabilization Point)**↩Weighted by group size. ↩

If you have trepidation about my decisions here, I’m happy to share the list of players I included and excluded. Just comment below or shoot an e-mail to danny@intentionalrounding.com. ↩

As somewhat of a numerologist, the fact that this is the year of my birth makes me sick. ↩

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I’m loving these sample size analyses, but I think the reason that people haven’t looked at TD% seriously is that it’s obviously heavily dependent on field position. Based on the play-by-play data, a rush from the team’s own 1 yard line has around a zero chance of getting a TD (something like 1 in 2000) and a rush from the opponents’ 1 is around 1 in 2.

Honestly, I’m impressed that TD% is so stable.

That’s an excellent point. The thing is that game situations are cooked into the books here: 1) It should (theoretically) wash out in the analyses themselves, especially in the larger-sample groups; and 2) It shouldn’t (theoretically) be too influential in application because guys seldom transition between “goal line back” and “non-goal line back” in their team-specific careers.

I should also add that, if you stay tuned, you’ll see that another RB stat is way less reliable than TD%, so its instability vis-a-vis YPC will look better by the time I’m done with this series.

With sufficient sample sizes, the laws of large numbers should defintely come into play.

It does seem like the weighted average is heavily influenced by the upper rows with that plummeting N – without that first row, the wtd average for the first table goes up to almost 80.

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This is amazing and thorough work. Bravo.

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