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Sep 15, 2009

The 4th Down Study - Part 1

If there's one topic where quantitative analysis can change the way football is played, it's 4th down decision-making. Many articles here have chronicled the conservative nature play-calling on 4th down in the modern NFL. In this post I'll explain, as clearly and simply as possible, why the evidence points to a more aggressive attack on 4th down.

Previous studies on 4th down decision-making include Carroll, Palmer, and Thorn's book Hidden Game of Football (1988, 1998) and Professor David Romer's Do Firms Maximize? (2005). The first serious study of the concepts used in these studies was by former NFL quarterback Virgil Carter, who co-authored an operations research paper examining the value of field position using data from the first 56 games of the 1969 season.

My own analysis published in this post largely repeats the methods used in previous studies. But I think I can add a good deal to the topic. First, this analysis is based on a much larger data set compared to previous research. Second, this analysis offers possible confirmation of previous results. Third, I think I can explain a complex, abstract subject such as this in a straightforward manner, which is essential if the 4th down revolution is going to make any headway. Frankly, it doesn't matter how strong the analysis is if it can't be communicated clearly and convincingly.

This is how the study goes: At each yard line, I'll calculate and compare the expected point value, based on recent historical averages, of each of the three 4th down options--punt, field goal, or go for it. The option with the highest value is the recommended choice.

I've divided the article into four parts. In this the first part, I review the concept of Expected Points for those who aren't familiar. I also review the concept of expected utility. Both ideas are critical for understanding the thrust of the study. The second part of the article will detail the kicking game. The third part will explore the value of 4th down conversion attempts. The final part of the article will put all the concepts together to ultimately produce a chart of recommended decisions for 4th downs at every combination of field position and distance to go.

'Expected Points'

Speaking of abstract subjects, this entire analysis rests upon the foundation of the Expected Points (EP) concept. Most readers here may already be familiar with EP, but I'm going to summarize it now before I move on to the meat of the study.

EP is the average potential points a team can expect given a certain situation. The most common example is the potential point value of a 1st down at each yard line on the field. EP is the average of all 'next' score values at any given yard line. It's not necessary the average points scored on the current possession because possession could be exchanged several times before the 'next' score. EP is positive when the offense will usually score next, and negative if the defense will usually score next.

Here is the EP graph for a 1st down at each field position. These EP values are based on data from 2,400 NFL games from the 2000-2008 seasons. I used only data from the 1st and 3rd quarters to exclude situations hurried by an expiring clock and by desperate teams or teams with large leads playing differently late in games.

I'll be referring to the graph several times, so be sure you understand how to read it. A 1st down on an opponent's 20 is worth 3.7 EP. But a 1st down on an offense's own 5 yd line (95 yards to the end zone) is worth -0.5 EP. The team on defense is actually more likely to eventually score next.

Note that a 1st down at an offense's own 27 yd line is worth 0.7 EP. This is critical to explain an important twist in the EP concept. Every score requires a subsequent kickoff, and this has value to the receiving team. So to understand the real value of a the score, we need to subtract the value of the kickoff. For example, field goals aren't really worth 3 points. In the long run, they're worth 3 - 0.7 = 2.3 EP. And touchdowns are really worth 6.3 EP.

This concept is especially apparent when considering safeties. After a safety, the scoring team gets the ball back, on average at its own 40, which is equivalent to 1.3 EP. A safety is therefore really worth 2 + 1.3 = 3.3 EP. These score values and the resulting EP values are used throughout the rest of this analysis.

Expected Utility

Before I go any further, I'm going to take a step back and explain the concept of 'expected utility' in general. Say I can choose one of two routes home from work each day. One route is through the side roads, and the other is via the highway. If I take the side roads my commute always takes 20 minutes.

But the highway is more dicey. Sometimes it's clogged with traffic and can take 25 minutes to get home, but most other times traffic is clear and it only takes 15 minutes to get home. The highway is backed up 40% of the time and clear 60% of the time. Which route should I normally choose?

My 'expected commute time' can be calculated using simple proportions. The side roads take 20 minutes 100% of the time, so that's easy--the expected time for that route is 20 minutes. But assuming each minute of my day is equally valuable to me, the highway's expected time would be:

(25 min * 0.40) + (15 min * 0.60) = 19 min

So over the long run, the freeway is the better option. Unfortunately, life isn't that simple. We don't have such clear-cut options and we don't know the probabilities and payoff values of our decisions. But in football, we do.

Continue reading part 2 of this article.


Jason said...

Unfortunately, even if a coach knows the odds, going for it on 4th down is high-risk/low-reward from a social standpoint -- i.e., what will fans/owners/players/media think if we make it (or punt) vs. what will they think if we miss it? If you make it or punt, nobody says anything. If you miss it, why did you go for it there, you idiot? While that shouldn't be the sole deciding factor for a coach, it can have an effect on his job security and will therefore almost certainly figure into his decision-making process.

I tend to think of editing the same way. Nobody notices and rewards good editing, but if I let a few sutble errors slip by in whats supposed to be a profesional text, I'm labeled as a poor editor.

(You probably looked at my first paragraph and didn't think there was anything special about it, but you looked at my second and probably figured I was an idiot. Obviously, there's no "risk" in editing properly, but it's the same general issue of perception. Nobody notices if you do the right thing but they all notice if you fail.)

James said...

I'm excited to see where this is going!

Kulko said...

Jason, of course you are probably nailing the reason why coaches behave as they do. But I think you are missing a few things here.

IF a more aggressive 4th Down Approach has a higher expected utility, it will lead to more wins, which help your job security a lot more then a nice perception.

Also if you read media articles of the last fw years, you will notice that the climate has definitely changed. Coaches get more ofen critized for being to timid, and aggressive failures have ample defenders in the press by now. SO I think even from a social risk/reward standpoint the times are changingand th caches should too.

Happy said...

Ultimately you can't argue with success. The coach may take some grief in the short run for an unconventional decision, but if their decisions have a firm basis in expectation value and increase the team's likliehood of winning the team will win more games.

That's when the coach gets to say "that's why I'm the coach and you're the fans." Not every coach has this level of confidence, but some do.

I'm curious if there are any teams with greater than 50% on 2-point conversions. Those teams should never kick an extra point in the first three quarters of a game.

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