It’s 4th Down – Quick, I Need My Calculator!

With the bye week upon us, what a great time to consider the brain-numbing calculus of 4th down decision-making.  I know you’re all thinking, “yes, yes I love that stuff, and want more!  The late-night tete-a-tete in the comment string of John’s Utah game grades post just didn’t have enough Greek symbols and probability factors for me!”  With apologies to any quant jocks out there, and to the dawgpound posters who took the time to demonstrate their math skills, I offer no regression analysis, or deep-dive in to the details of the studies done by people much smarter than me.  Utilizing the data and paper below, you are certainly welcome to do so, but at least by taking just a cursory look at the science here and elsewhere in sports, I believe there is indeed merit to its application.  Think Sabermetrics, for example. 

What is important to keep in mind though is that the 4th down decision is a combination of both art and science.  We all know Sark isn’t on the sideline on each 4th down with a calculator and a slide rule, empirically calculating probabilities and outcomes.  Regardless, I wager that he has an informed view on situations where it does makes sense to go for it on 4th downs (science), and when combined with intent to establish the identity and mentality of his team (art), he arrives at decisions that strike us as either justifiably aggressive or boneheaded.

Statistics can certainly be manipulated and interpreted in ways to justify outcomes and conclusions that are erroneous, but there is strong evidence to support being more aggressive on 4th downs.  In fact, with credit here given to the folks at Cal, I reference a 2005 study done by David Romer of UC Berkeley that provides a reasonable foundation to justify going for it on 4th down more often than most coaches elect to do so.

If you decide to read this study, I suggest ample Tequila.  It didn’t help my comprehension, but I like Tequila.  The key take-away is that the decision process should be driven by the probability impact on achieving a positive outcome, i.e., winning the game (duh!).  A better way to say it is what is the change in the probability of winning if you succeed or fail on a 4th down attempt?  Still another way to think about it that I prefer is, what is the upside vs. the downside?  While still a valuable input, it’s not just about the probability-weighted point value differential of a FG vs. a TD.

Taking just the example from the Utah game, consider the possible outcomes of 4th and 1 at approximately the Utah 31 yard-line mid-way through the 1st quarter:

1.      Successful FG, score 10 - 0

2.      Failed FG, score 7 - 0

3.      Failed 4th down run or pass, score 7 – 0

4.      Successful 4th down run or pass, results in one of the following:

a.      Eventual FG, score 10 – 0

b.      Eventual missed FG or turnover, score 7 - 0

c.       Eventual TD, score 14 – 0

Under the successful 4th down scenarios, I ignored the possibility of an eventual turnover directly resulting in a TD for Utah because that could happen under any of the first three scenarios as well.  I also assumed that in the cases where the Huskies scored either a field goal or a touchdown (score either 10 – 0, or 14 – 0), Utah would take possession after a kick-off at their own 25 yard line, and after a failure (7 – 0), they would take possession at their own 30 yard line.

What you are left with is that there are three possible outcomes with respect to the score:  The Huskies will lead either by 7, 10, or 14.  The question is then what are the relative changes in the probability of winning the game given those three scoring scenarios at that point in the game.  The essence of Romer’s work implies that the increase in the probability of winning with a 10 point lead vs. a 7 point lead isn’t significant compared to the increase in probability of winning with a 14 point lead vs. a 7 point lead.  If you fail on 4th down, you haven’t given up that much in terms of your probability of success, so the downside is limited, and rather small.  If you are able to get the TD, however, your upside in terms of probability of winning is asymmetrically higher, i.e. the upside is much greater than the downside.  Therefore it is a rational choice to go for the 1st down in that given situation.

I am ashamed to say that I just couldn’t figure out how to input the appropriate variables in to the equations provided by the Author.  My conclusions regarding the relative change in probability factors stated above instead resulted from extrapolating some examples he provides, and by utilizing the graph from Figure 5 on the final page.  Perhaps some of those smart guys from Cal Golden Blogs can help out – it’s their alum that came up with this gibberish.  Nonetheless, my Confidence Interval is 97.5% (I made that up.  I just wanted to use a statistics term so you would think I know what I’m doing).

OK, you say, that’s a lot of gear-head driven stuff by some guy who is compelled to include the “Rules of Football” in an appendix.  If we’re going to think like that, we’ll just send Coach Holt over to the UW engineering department to drag out some PhD, leaving him whimpering near the bench in spittle-covered lab goggles to be available for 4th down calculations.  Maybe so, but this is one of many studies that arrive at the same conclusion.  Frankly, the concept resonates with me, and I tend to think that overall 4th down aggressiveness has become more common, both in the NFL, and in college.  I didn’t do any heavy lifting to prove it out, so it’s clearly anecdotal, but it seems that over the last 10 years or so offenses are much more wide open, scoring is higher, and there’s been an increased tendency to forgo the punt or long field goal when faced with 4th down in your opponent’s territory.

But hey, it’s football for Christ’s sake.  Sometimes you go with your gut, and I like the toughness and take-no-shit approach Sark is developing in our program.  There is little doubt that a meaningful part of his thinking on 4th downs is driven to establish that attitude in his team.  That’s part of the art, along with loads of other non-data driven variables, including knowing the strengths and weaknesses of both his players, and his opponents.  As for the science aspect, I have no earthly idea if he has ever read any of this stuff, but I hope he has because taken together with the more subjective inputs, it supports the decision to go for it more often than not.  It’s a tough balance to achieve, but I think he’s shown an ability to learn from his own mistakes in a way that maximizes the return for the risks he’s willing to take.  Overall, I am supportive of his aggressive approach on 4th downs.

So there you go – something to chew on the next time the Huskies decide to go for it on 4th down.  I hope you find this helpful in some way, but certainly fell free to ignore the blather all together, debate the pros and cons, or just pick apart my analysis.  I am too lazy to research several assumptions regarding historical trends, so I likely overlooked or mischaracterized plenty of salient points.  It’s the best a UW Poli Sci major with a University of Chicago MBA can manage (I know that’s a quant school, but I studied corporate finance, and frankly spent a lot of time discovering the pleasures of drinking establishments that stay open past 2:00AM).  If you find any glaring analytical errors, typos, or poor grammar, I announce here and now they were the fault of Nick Holt.  Regardless, try to be fair, rational, and most importantly open-minded.  We all have our biases, but try not to fit the data together just to support an existing belief.  Analyze, reason, and then decide.  Not the other way around.

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