QB ANY/As Through Week 15: Brock Purdy Is Having A Mathematically Improbable Season

Let’s start with the terminolgy.  Statisticians, as a whole, will always tend to avoid saying the chance of something is 0% or 100%.  When it come to chance, very few things are impossible.  You flying is impossible.  That isn’t chance, that’s the laws of physics.

Saying that, when a statistician says something is highly improbable, to a non mathematician this can almost be read as that is impossible, or at least so unlikely there is no cause for concern.  A plane crash is a good example.  Yes it is possible the plane you get on will crash, but it is so unlikely that it is no cause for concern.

And that brings us to the mathematically improbably season Brock Purdy is having, at least when it comes to one popular way of measuing QB production and efficiency, ANY/As.

Why Adjusted Net Yards Per Pass Attempt – ANY/A?

This measure is considered to be one of the best for correlating to wins. The average ANY/A will vary from one season to another but is generally around 5.35 ANY/A. This can be calcluated on an individual passer level and on a team level.

Did Someone Order A BP Lite?

Jake Browning is performing like Brock Purdy Lite in limited sampling.  Along with the 7.45 ANY/As value, he has a passer rating of 107.

Hmmm, guy gets his chance because of injury late in the season.  Rallies team into the playoffs.  Comes back next year and is off the chart.  Maybe draft Jake Browning next year for fantasy if he keeps this up.

And just a quick tip of the cap to Joe Flacco who at 38 came off the couch and put up a 5.55 ANY/As since his return.  That is almost dead on league average and actually slightly above historical average ANY/As score.  No camp.  Limited preparation.  Probably doesn’t know half his teammates’ full names.  Just wisdom, guile and an old cannon with a few shots left in it.

The Improbabillity of Brock Purdy’s ANY/As Statistics

The chart above takes the ANY/As statistics for all QBs and comparess them to each other using Normalization and Standardization.  Purdy scores a perfect 1.00 Normalized, and is 2.88 Standard Deviation units above the norm.

I included Passer Rating & QBR scores as well, and they were also normalized and standardized for comparison sake.  Purdy scored 1.00 (Norm) & +2.61 SD units in Passer Rating, & 0.97 (Norm) & +1.96 SD Units in QBR.

Purdy’s ANY/As value is 1.63 poins higher than Tagovailoa(7.92) in second place.  That is the same span between Tagovailoa in 2nd and Derek Carr(6.28) in 13th (7.92 – 6.28 = 1.64).

The Chances of Purdy’s ANY/As Value

Look at the graph below.  It is the normal probability chart, aka the Bell Curve.  I put a red X at +2.88 Standard Deviation Units to indicate where Purdy’s ANY/As value would appear.

I could go into a very long winded and detailed explanation of exactly what all this means, but I can try to sum it up quickly in a few sentenses:

• 99.7% of all data will fall within 3 standard deviation units from the mean.
• 99% of all data will fall within 2.6 SD units from the mean.
• Purdy ANY/As is +2.88 SD units

So if the league had 100 QBs that put up the stats to qualify(and this list has 42), less than one QB would fall into the range Purdy is currently inhabiting.  If it had 1000 QBs, 3 or 4 would put up stats close to Purdy’s.

Furthermore, the average ANY/As value historically is 5.35, and in 2023 the average of the top 42 QBs is 5.62.  If anything, Purdy is being compared to an above average group of QBs as far as the ANY/As stat is concerned.

ANY/As Change Since Week 11

I first ran ANY/As in Week 11.  Here is a chart that combines that list with this list.  Notes:

• Purdy’s 2.88 SD Units above the norm increases to 2.96 SD units if this group of 42 scores are used.  The slightly different lists, produce slightly different avg & stdev, and therefore the small movement in the final numbers.
• Jake Browning & Joe Flacco had no stats in Week 11, so they were kept off this list.
• Some QBs who appear on the Week 11 list do not appear on this list simply since they have little to no stats.
• Clayton Tune was elimated due to his almost unbelievable -2.46 score as it impacted the avg and sd values for the week 11 group when compared to a group without a complete muppet.
• The AVG ANY/As for week 11 for this group of 42 QBs was 5.51.  The AVG ANY/As for the group through week 15 was 5.61.
• Note how Normalization limits the range to 0.00 – 1.00, while Standardization is going to be -3 to +3 in almost all cases.  This means it is much easier to see how much better Purdy is performing by looking at the Standardization column compared to the Normalization column.

Purdy through week 11 was at 9.05  ANY/As and an SD of +2.36 units.  So he was bordering on the 99th pct.  If you were a betting person math would tell you he cannot keep up such production vs his peers.  If he does either he is Super QB, or the other 31, or in this case 41 QBs are a collective pile of Ryan Leafs in comparison.  Last time I checked Patrick Mahomes & Josh Allen were still breathing so the latter option is not a great one to argue.

So what has happened since week 11?  Purdy’s ANY/As has increased by 0.49 points to 9.55 & he has added another +0.52 SD units.  This may not sound like much, but to a statistician it is tremendously impressive.

Increasing SD once you get out to near and over 2.6 is much like trying to go faster in a plane or a car once it reaches a critical speed.  Past that point to increase even a small amount requires a great deal more horsepower or thrust per mph to be gained. The percentile different between +2.6 SD and 3.0SD is in the thousandths. Its’ the slow creep up from 99.00% to 99.99%.

Look at the top 10 QBs for ANY/As in Week 11.  Below is the same chart sorted for week 11.

• The only other QB from the top 10 in week 11 to go up in ANY/As besides Purdy is Jared Goff who went up 0.02 points.  Purdy went up 0.49 points while starting at 9.05 compared to Goff’s 6.87
• The next highest ranked QB to show an increase in ANY/As is Baker Mayfield in 13th(now 9th in week 11).  Mayfield increased his ANY/As by 0.30 points, about 60% of the increase Purdy showed.  Mayfield had a week 11 score of 6.24 to build on, much lower than Purdy’s 9.05
• The greatest increase from week 11 to week 15 was Matthew Stafford with a gain of 1.01 points.
• Outside of Joshua Dobbs(-0.68), the biggest decrease was Justin Herbert -0.66
• Other Big Winners:  Jordan Love +0.52, Aiden O’Connell +0.97 & Tommy DeVito +0.67.  It should be noted that even with large increase both O’Connell and DeVito scores are below average so gains are much easier.
• Other big losers: Justin Field -0.53 & Kyler Murray -0.51, who both started low enough where such large decreases shouldn’t be too likely in normal scenarios…

The MVP Case – Purdy vs Other QBs

Unfortunately we can’t compare McCaffrey and Hill to the Purdy using ANY/As so let’s leave those two outside this comparison.

That leaves 5 quarterbacks with odds for MVP outside Purdy: Lamar Jackson, Dak Prescott, Jalen Hurts, Josh Allen, Patrick Mahomes.  I am going to add Tua Tagovailoa because statistically he belongs in that group.

• Tagovailoa has the best case against Purdy in ANY/As and Passer Rating, but trails significantly in QBR(and I don’t like QBR but some do so let’s leave it at that).
• Prescott is closest for QBR to Purdy but is still significantly behind. He is also behind Tua for ANY/As and Passer Rating which can’t really help your MVP case.
• Jackson, Allen, & Hurts all add an element that Purdy does not with the power running game.  As a scrambler, Purdy is decent to good, but he is not a power runner like the other 3 who could handle a big running load week after week and do short yardage stuff consistantly.  But none of the three are close to Purdy in any of the 3 QB measuring stats.
• Mahomes is simply not having a great season when he has one legitimate target in Kelce and one emerging one in Rice.  If you gave every QB the same set of WRs & TEs then Mahomes is probably without question the best.  But these are statistical ratings based on what QBs have produced this season and his ratings in these 3 metrics simply are nowhere close to Purdy’s.
• Look at the Standardized colums.  This what give you a sense of how much better Purdy’s stats are than his peers.  A great example of this is between Purdy’s and Prescotts’ QBR scores.  Purdy scores 76 and Dak 72.7 in QBR.  the 3.3 point sin different is worth 0.01 in Normalization but 0.24 in Standardization.  Thus is it easier to see Purdy has been much better in Standardization than Normalization.  Remember statistically Purdy’s stats are in the 99.something percentage with scores of +2.88 and +2.61 SD units.
• In Passer Rating Purdy 119 Tua 106.  Normalized Purdy 1.00 Tua 0.94.  You look at that and say, bah only a few hundredths.  Now look at Standardized.  Purdy is 1.07 SD units above Tua.  That is a massive amount when you are talking about the high end of the range.

Really the only QBs that can legitimately beat Purdy for MVP based on these ratings would be a QB who brings things outside passing to the team/game.  Tagovailoa is a passer like Purdy, he does not bring that element.  Mahomes is out for 2023.  That just leaves Prescott, Jackson, Allen & Hurts.  If one of these 4 can lead their team to a #1 seed and dominate in weeks 16 – 18, that would be the only other viable QB candidate outside Purdy, assuming Purdy doesn’t completely crater int he next 3 weeks.

Three More Weeks Of Magic

Regardless of whether you believe Purdy is a system QB, or benefits from the players around him, or is the product of Shanahan, you have to give the guy his due.  You cannot be this much statistically better than your peers without having some ability you bring to the table.

As we can see from the week 11 to week 15 changes, statistics says he will fall back in the final 3 weeks, but he has been defying the odds all season.  If he can maintain his current dominance against his peers in ANY/As, it will be perhaps the best weapon to use in his MVP candidacy race.  Not only is he the best, but he is the best by a massively wide margin.

I may be the only person in the country that is rooting for him to reach +3.0 SD units in ANY/As in comparison to his peers.  It would be the statistical equivalent of seeing a shooting star and perhaps the slam dunk argument for his MVP case.