# Mandatory Minimum: ANY/A

Last week, I found that quarterbacks (QBs) need 109 pass attempts in order for us to reliably compare their Passer Ratings (PR) — not the NFL-standard 224.1 Today, I’ll report the mandatory minimum for Adjusted Net Yards per Attempt (ANY/A).

### Methods

Once again, here was the procedure I used to calculate the mandatory minimum:

1. I collected data for all QBs with at least 200 total dropbacks for the same team from 2002 to 2013.
2. Starting with QBs that had 200+ dropbacks, I randomly split all of their dropbacks into Set A and Set B.
3. I calculated the correlation (r) between Set A and Set B for that group of QBs.
4. I performed 25 iterations of Step 3 so that r converged.
5. I repeated Steps 2-4 for QBs with 300+, 400+, 500+ dropbacks, and so on.
6. For each group, I calculated the number of dropbacks at which the explained variance, R2, would mathematically equal 0.5.2  This value represented the group’s mandatory minimum.
7. I calculated the average across groups by weighting each group’s mandatory minimum by its sample size.

### Results

Minimum SplitnAverage SplitrR2 = .50
Wtd Average154
1001925320.47113
1501636050.50150
2001297190.56160
2501147840.59172
300998620.67148
350869440.69154
400771,0110.70169
450721,0510.71188
500631,1340.72191

In this table, “Minimum Split” is the smallest split size a QB needed to be included in a given group, n is the the number of QBs that were included, “Average Split” is the average split size for that group, r is the group’s split-half correlation, and “R2 = 0.50″ is their estimated mandatory minimum to qualify for ANY/A comparisons. So for instance, there were 63 QBs who had at least two sets of 500 dropbacks for the same team, and those 63 QBs actually averaged 1,134 dropbacks in each split. Their split-half correlation was 0.72, which implies that their mandatory minimum should be 191 attempts.

So, as was the case with PR, I found that the mandatory minimum for ANY/A rankings should be far lower than 224 dropbacks in today’s NFL. The “Wtd Average” column shows we can reliably compare ANY/As for QBs with 154 or more dropbacks.

Although no QB since 2002 got robbed of an ANY/A title under this lower threshold,3 it still would have given us a different picture of the yearly rankings:

• 73 additional QB seasons would have qualified.
• 19 “non-qualifying” QB seasons would have ranked in the Top 20.
• 8 of those 19 would have ranked in the Top 10.
• 2 of those 8 would have ranked in the Top 5.
• The highest finish among “non-qualifiers” would have been Vinny Testaverde ranking 4th in 2003 with a 6.80 ANY/A on 204 dropbacks.

One final quirk worth mentioning is that the Top 3 “non-qualifying” ANY/A seasons came from different QBs all of whom have ties to the Eagles:

1. Vince Young posted 7.34 ANY/A on 169 dropbacks for the 2010 Titans.
2. Jeff Garcia’s late-season playoff push for the Eagles in 2006 produced 7.11 ANY/A on 194 dropbacks.
3. Michael Vick got a Philadelphia football version of the Wally Pipp treatment last season despite producing 6.93 ANY/A on 156 dropbacks while healthy.

### DT: IR :: TL : DR

I used reliability analysis to determine the mandatory minimum number of dropbacks that a group of QBs should need in order for us to compare, rank, or analyze their ANY/As. The magic number turns out to be 154, not the NFL-mandated 224. If we use this statistically derived threshold instead of a seemingly arbitrary one, 73 additional QB seasons would have qualified over the past 12 years.

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1. UPDATE: I still haven’t heard back from the league or its official statistician, the Elias Sports Bureau.

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

3. Do QBs even pay attention to that title?

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