The 4th Down Study - Part 2

The is the second part of a four-part article on 4th down decisions. In the first part, I reviewed the concept of Expected Points and the concept of expected utility. This part of the article, details 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.


The EP value of the punt option is relatively straightforward. Based on recent historical data, we know the average net distance for punts from each yard line. The closer a team is to the end zone, the shorter a punt will tend to be due to touchbacks. Since we know the net distance of the punt, we know the expected subsequent field position for the opponent.

For example, a punt from a team's own 40 (60 yds from the end zone) nets around 37 yards, giving the opponent a 1st down at their own 23. This corresponds to 0.5 EP for the opponent, which is -0.5 EP for the punting team.

Field Goal Attempts

The EP value of a FG attempt is based on the probability of making the kick, which is dependent on kick distance. Just like taking the highway home from work, we can calculate the overall value of a FG attempt. Below is the graph of FG percentage by line of scrimmage.

A successful FG is worth 3 points minus the value of the ensuing kickoff for a total of 2.3 points. A missed FG is worth the EP value of a first down for the opponent at the spot of the kick (or the 20 yd line, whichever is larger).

For example, with the ball on the 20 yard line, the NFL average FG percentage is 82%. The spot of the kick would be the 27, which corresponds to 0.7 EP (that's -0.7 EP for the FG kicking team). Therefore the EP value of a field goal attempt from the 20 would be:

(0.82 * 2.3) + ((1-0.82) * -0.7) = 1.8 EP

Continue reading part 3 of this article.

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12 Responses to “The 4th Down Study - Part 2”

  1. Jeff Clarke says:

    This is a great post. I've seen so much academic research on this topic and all of it says that coaches should go more often. I have yet to read one study that mathematically defends the status quo.

    I realized something else yesterday listening to the announcers who were former coaches (particularly Gruden and Billick). There is an enormous amount of hindsight bias in the football community. On at least four different occasions I heard "The coach is making a mistake here. He shouldn't be doing this. [play works] Wow, what a great call. He obviously is a genius. He was so smart to make that call there"

    Just one example:

    Gruden said he'd kick the onside at the end of the game. Belichick kicks away and gets an extraordinarily lucky fumble. Gruden compliments Belichick on "knowing" the regular kick would work.

    ***side note I wrote a really long post on the Hawk n Dove page about that call.

    I wish announcers would be a little more upfront with the fact that the mathematically correct call doesn't work all the time and that the incorrect call sometimes gets lucky.

    I also think we should note that the most egregious 4th down mistakes always come in a situation where the team is likely to lose either way. Going for it might increase the win prob from 15% to 20% but the coach knows that there is still an 80% likelihood he is going to have a bunch of people second guessing his decision. Although its absurdly selfish, he'd rather avoid that than gain an extra 5% WP.

    If somebody in the mainstream media would just explain to casual fans the math involved in this, I think it would start to change. Then again, most Americans hate math and they'd rather avoid it in their free time.

  2. James says:

    By taking away 0.7 EP for a kickoff after a successful score, this assumes there is sufficient time left on the clock for a drive by the opposing team. Will you look at how little time needs to be left in a half for this to change the EP? For example, the Chargers only needed 40 seconds to score a field goal before the half last night against the Raiders (although that was largely a result of Sproles 59-yd kick off return).

    Also, Belichick and the Pats went for it on 4th down twice early in the game against the Bills. In the end they still won, but do you think that even an established coach like Belichick with a tendency for 4th down attempts would have taken some heat if the Pats lost?

  3. Brian Burke says:

    Jeff-You are so right about the hindsight bias.

    James-This type of analysis is for "normal" football situations, when neither team has a large lead and the clock is not a factor. We need to use a WP analysis for other situations. I'll address that issue in future posts.

    Belichick has so much credibility and reputation for being ahead of the game, he'd be the one guy who could pull it off.

  4. Ben says:

    I just was linked from TMQ so that is why I am commenting a week late.

    When you say "a punt from a team's own 40 (60 yds from the end zone) nets around 37 yards, giving the opponent a 1st down at their own 23. This corresponds to 0.5 EP for the opponent, which is -0.5 EP for the punting team," are you just using the straight average net punt yardage from a team's own 40? I don't know how drastically this would affect your values, but for a more rigorous calculation you would need to use the probability distribution of net punt yardage to calculate the EP of a punt from, say the team's own 40.

    For a simplisitic example, when punting from your own 40, if there were a 30% probability of a net of 45 yards and a 70% chance of a net of 30 yards, then your EP would be -(.3 * (EP from your own 15) + .7 * (EP from your own 30)) which would not equal the EP of the average (EP is not linear).

    Again, I don't know if you did this calculation behind the scenes, or if there simply isn't enough data to generate comprehensive distributions from every yard line (I would think there probably is, given the number of coaches who punt from inside opponents' territory).

  5. Brian Burke says:

    Ben, that's a valid criticism. I assumed linearity for simplicity's sake. Part of the goal is to be able to convince non-stat guys, so simplicity is important. Perhaps I can add the full distributions to the analysis in a future edition. Thanks.

  6. Anonymous says:

    i think your math calculation is wrong. should be 1.75 Ep

  7. Anonymous says:

    What most people don't know, but should is that football is like a coin that has two sides. Everyone knows the universal truth of the first side of the coin that says that a team that scores more points than the opponent always wins. What people don't know is how a team lost a game without factoring the score. The other side of the coin would say that the team with the most real turnovers always losses the game. Statisticians do not count all events that turn the ball over without first scoring atleast 6 points. If they did they would see that the team with the higher number always losses. Try this with any game and you will see that it works:

    Complete Turnovers: Interceptions, fumbles lost, missed fg's, punts, 4th down fails, kickoffs lost, safeties, and turnovers due to time (given if the team in possesion at the end of the half failed to score and has to kick to start the second half. Not counted if another turnover half or whole occurs at the same time. Also when the game ends and the team trailing fails to score before the time expiresn not counted against the team with the lead. also nullified if another turnover takes place.

    Half Turnovers: Failed extra point or 2pat, Successful field goal, 2point conversion allowed.

  8. PL says:

    You haven't taken into account blocked punts and fg's and the outcome of those, have you? What about penalties that result a 1st down?

  9. Brian Burke says:

    Yes, penalties are included. And to the extent blocks cause a missed FG, they are included. But the potential for a large return following a block is not included. This means that the case for going for it is very slightly stronger than described here, all other things being equal.

  10. Anonymous says:

    I only read part 1 so far... but I have an observation to make.

    This kind of strategy may very well win a team several games in a season. But, by the same token, it could lose you a game or two.

    So this strategy would work well for a coach in the long-run by improving his winning percentage. It may even help in the NFL because it would ultimately win you more games in a season.

    But in college, every single game matters. 1 loss could cost you a shot at the National Championship game. So teams can't afford risking a possible loss. Going for it on 4th would help sub-par college teams win games they wouldn't have won otherwise. But the "top-tier" in college football could cost themselves a shot at a national title because they can win against anybody anyway without the added risk.

    Just one example. This year, LSU's coach Les Miles may have cost LSU a win against Alabama. He clearly didn't have confidence in his team, and went for it and failed on 4th and 12 with a fake field goal. He kicked an onside kick in the 3rd quarter (and failed) after gaining momentum by scoring a touchdown, and only being down by 7 points. The fake field goal cost LSU 10 a point swing because Alabama went down and scored 7, and LSU failed to make 3. The onside kick led to no Alabama points. Alabama drove the ball all the way down to LSU's 5 yard line, but luckily for LSU, they created a fumble and recovered the ball preventing the touchdown. Those two calls could have easily been a 17 point swing. And I realize Alabama could have scored on those drives from deeper in their territory anyway, but both of those calls killed the momentum and emotion of the LSU team and made it easier for Alabama to sustain a drive.

  11. Anonymous says:

    Another thing I thought about. Not every drive results in points in the very next drive for the other team. Sometimes it takes a while for a team to score, but they have the field-position in their favor.

    For example. Team A goes for it on 4th and 3 at the 50 yard line and fails. Team B gains yards but fails to get into field goal range and punts. Now team A is pinned deep. Team A goes 3 and out and punts. This can go on for a few more drives until team B chips away enough to score points.

    Another point I'd like to make...

    Going for it on 4th down more often may make sense mathematically by looking at the stats for all teams in all games creating some kind of average. But games are individual match-ups.

    What if the team you are playing has a lock-down defense? What if your offense isn't moving the ball very well and the only thing keeping the game very close if the great play of your defense?

    If you play more risky in an individual game like that, it could cost you a win. So while going for it may make mathematical sense on an average basis, it doesn't apply for all match-ups, styles, or in the context of an individual game.

  12. Anonymous says:

    A useful graph might be receiving team net field position vs. line of scrimmage. Also, what happens if you have a punter and coverage team that is especially good at putting the receiving team close to their goal line? How much would that change calculations? Would a team that seldom punted lose proficiency in covering punt returns (by de-emphasizing it in practice or in personnel selection), thereby offsetting some of the advantage of going on 4th down more often?

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