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Just tried to post a large post that had some links to papers, sites, youtube for EPA papers on Regression Models (typically Linear Regression) and explanations. Can’t post them because these forums eat posts with embeds. If you’re interested, just search stuff. If not, skip the top part and move to the lower parts. Or ignore entirely if you’re not interested (which is likely!).

There are both Inference and Prediction approaches (decision-point navigation inside of an actual football game, gambling, and personnel valuation and decision-making on the latter). Paramaterization on the latter has pretty tight consensus (from what I’ve seen), so the models don’t diverge much.

The seminal work is Brian Burke’s stuff in the early 2000s and since then (developed EPA modeling and ESPN’s QBR). He has multiple papers you can look up (I think his last one is 2017?).

Then data-scraping NFL.com from 2009 onward became available. That is when FBO’s work began to my knowledge.

Keith Goldner developed a stochastic model for an NFL football drive sometime in the last 5-10 years (you should be able to locate the paper with a little digging).

Numberfire has had a lot of good work as well.

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The work explains why yardage as a metric of success has very little explanatory and predictive power and why high variable play is typically bad for success (Mike Martz and Bruce Arians offenses have an inherent high degree of volatility…put Kurt Warner at the helm and you have perhaps the greatest offense all time…put any number of several others and you’re struggling to win football…sub Winston for Brady and you go from Super Bowl to losing football). 2nd and 15 is many times worse for a football team’s drive prospects than 2nd and 5 is good for that team’s prospects. Yards are not equal. The EPA value of those two situations diverge powerfully. So the production of two Running Backs who yield the exact same Yards on the exact same number of Carries might be wildly divergent in terms of EPA. Because of efficiency. Compare the two spread of carries; same TDs, but the different yards, efficiency, explosives, and 1st downs.

2 (converted 3rd and 1) – W
3 (TD) – W
4 – W
2 – L
7 – W
12 – W
6 – L (3rd and 7)
0 – L
3 – (converted 3rd and 2) – W
2 – L
5 – W
11 – W
2 – L
3 – (converted 3rd and 1) – W
7 – W

15 Carries, 68 Yards, 1 TD, 5 First Downs, 2 Explosives, 67 % Efficiency

-3 – L
0 – L
14 – W
23 – W
3 – (converted 3rd and 1) – W
7 – L (3rd and 12)
-4 – L
1 – L
3 – L
31 (TD) – W
0 – L
4 – W
-2 – L
8 – W
-1 – L

15 Carries, 83 Yards, 1 TD, 3 First Downs, 3 Explosives, 40 % Efficiency

Who had the better game by EPA valuation and FBO’s DVOA valuation? Its no contest. Despite having 15 less yards (averaging 1 less YPC) and 1 less Explosive Run, the 1st RB clearly had a better game.

* The 2nd RB had 3 Stuffed Runs (A tackle at or before the Line of Scrimmage) and 4 carries for losses (2 of them major), which significantly negatively impact the gamestate and carries significant Drive EPA implications for their teams. Meanwhile the 1st RB had 0 carries for losses and only 1 Stuffed Run.

* The 2nd RB was 27 % less Efficient which carries with it, again, significant gamestate and Drive EPA implications. Another 1st Down Converted by the 1st RB is also folded into this.

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Another good example is WR play and why (a) Mike is better than most NFL fans realize and (b) hidden yardage and hidden positive qualities of a Bruce Arians offense (with downfield physical threats like Mike particularly).

EPA parameterizes every possible outcome of a play. Its one of the other (again, hidden) reasons why throwing the football is “always” better than running it (outside of a few scenarios like RZT and 3rd and 2 or less).

Illegal Contact
Defensive Holding
Defensive Pass Interference
Hit in a Defenseless Receiver/Leading with the Crown

These are all ENORMOUSLY gamestate affecting penalties on the defense that can occur downfield in the Passing Game (and they’ve been amplified the last 7 years and then again a few years ago).

Mike was # 4 DYAR and # 6 DYAR this season despite being down in Receptions and Yards but up in TDs and a hair in Catch Rate. Plenty of guys below him had way more Catches, Yards, sometimes more TDs. Why? Because 9 DPIs for 171 Yards. Those 9 Penalties are CALAMATOUS for a defense. That is a ton of hidden EPA. Arians offense and Mike in particular produces these penalties at a rate that other offenses don’t produce and other receivers don’t produce.

2019 same thing for Mike. # 6 DYAR and # 14 DVOA because 8/139 DPI (but well down in Catch Rate and TDs).

In the last 2 years, no player is even in the same universe as Mike in DPI.

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3rd and 2. (a) Why is it still a Passing Down but (b) why should it 100 % be considered a Running Down (which Arians doesn’t consider it one unfortunately. Designed Runs vs Passes for the best DVOA offenses in the NFL, excluding us (and Baltimore because different game).

KC – 12 Runs vs 6 Passes
GB – 4 Runs vs 10 Passes
NO – 7 Runs vs 9 Passes
Sea – 7 Runs vs 11 Passes
Buf – 6 Runs vs 12 Passes
Ind – 8 Runs vs 10 Passes
Min – 6 Runs vs 6 Passes
LAR – 12 Runs vs 13 Passes

62 Runs vs 79 Passes

Those offenses are running the football 43.26 % of the time on 3rd and 2 and they’re converting at near parity; a hair under 2/3 for both Run and Pass.

It makes sense. You should still be Passing on 3rd and 2 because the Conversion Rate is nearly at parity and the EPA for any individual Pass is much higher than the Run. Only on 3rd and 1 and deep inside RZ Tight does the EPA of the run reach parity (and in some cases exceed, I believe) Passing, and this is because of the disproportionate conversion rate for the Running Game + the less likelihood of a negative play (eg Sack specifically, but Sack/Fumble also).

Now us:

TB – 5 Runs vs 15 Passes

So we’re running the ball only 25 % of the time on 3rd and 2. HOWEVER, we’re simultaneously (i) converting the Run at a higher clip than the NFL (80 %) and not converting the Pass at the NFL’s clip (we’re 56 %).

I would say that the model for the rest of those great offenses in the NFL is better than ours. Hitting a 3rd and 2 Explosive along with the boon of a Defensive Backfield Penalty along with the risk of getting Sacked or an Offensive Holding or OPI Penalty is a significant gamble. My guess is (just sort of eyeballing it with my knowledge of “EPA exchange rate”, if you’re 67 % – 80 % Efficient on the ground, you would need to convert 50 % of the time with something like a 30 yard average per play for the EPA difference from starting gamestate to post-outcome gamestate to be better for “the Shot.”

I don’t have Tom’s exact data for those 3rd and 2 (and it would require me trolling through a lot of stuff to get it). But on the year he’s 42.9 % Adjusted Completion % on Deep Throws w/ 34.25 Effective Yards Per. But this is every down and distance rather than 3rd and 2 so I don’t know how many of those 8 Completions were explosives and I don’t know how many of those 15 Attempts were Deep.

What I do know, however, is that KC’s defense is about as easy as it possibly can get to run the ball against on 3rd and 2 or less. If they weren’t the worse in the league, they’re 30+. And they’re a high variance defense because of their propensity to blitz, propensity to roll coverage and/or play trap coverage, and their willingness to play Man.

So lets say we’re 3rd and 1/2 x 3 in that game. If we’re going to go for it on 4th down for sure…then yeah, protect with 6 or 7 and take a Shot. But if we either protect with 5 (leaving ourselves vulnerable to a big negative play that would either (a) turn the ball over or prevent us from going for it on 4th or take us out of FG range) or aren’t going for it on 4th down? I don’t see how “taking a Shot” remotely has good returns in this game…particularly given (i) how precious every single Drive is going to be in this game, (ii) how terrible their RZ Defense is, and (iii) how Efficient we’ve been on the ground in 3rd and Short this year + how horrific they are on 3rd and Short.