NFL coaches make tough fourth-down and 2-point conversion decisions on every game day. Quantitative analysis can inform those decisions, both for those making calls on the sideline and fans evaluating their coach's decision-making.

So what do analytics tell us about these choices? Well, it's complicated. Is there a cheat sheet that could help show the correct decisions? No and yes.

There is not a simple answer because the permutations of game-management decisions in football are endless. That's why it's hard! In order to determine the correct decision on a fourth down, ESPN's model -- created by ESPN sports data scientist Brian Burke -- accounts for score, time remaining in the game, distance to sticks, yardline, number of timeouts each team has remaining, each team's chance to win entering the game and the relative strength of the offense and defense in question.

There are far too many possibilities to fit on a single chart to cover them all, but we can still provide a cheat sheet for the most likely scenarios. The following represents a guide to ESPN's decision analysis recommendations based on typical situations. Those are when teams are still in the point maximization phase of the game. Think of it this way: A normal game in the first half or even early in the third quarter, where teams are within two scores of each other.

Note that in any specific game, ESPN's recommendations might deviate from this chart even early because one team entered as a major underdog or there is a severe offense/defense mismatch between the two teams playing. Late in the game, the circumstances can cause recommendations that are significantly different, of course. (Note: This article originally ran Jan. 15, 2022. It has been updated with a new 2-point conversion chart.)

Jump to: 2-point conversion decisions

Fourth-down advice

Let's start with what to do on fourth downs. The chart below details the recommended decision (go, field goal attempt or punt) in a typical situation given a specific yard line and distance to first down:

The first thing you might notice when looking at this chart is that there is a lot more "go" area than expected. Indeed, ESPN's model is more aggressive on fourth downs than the average coach. In fact, our model recommends a go on fourth-and-1 in typical situations anywhere on the field. There are a few major reasons for the preference toward go:

1. The value of possession. Coaches have long been too conservative on fourth down, but particularly in the modern era when offenses are so explosive, possession significantly outweighs field position in terms of importance. A fourth-down conversion attempt might or might not fail, but a punt always turns the ball over to the other team.

2. There are two factors for why the model often prefers going for it to a field goal in more situations than most fans would expect:

• First, it recognizes opting for a field goal attempt rather than a guaranteed three points. Field goals don't always go in.

• Second, while touchdowns are worth seven points and field goals are worth three, both require kicking the ball to the opponent afterward. The possession and field position for the opponent is worth roughly one expected point in favor of the opponent. Once we consider the opposing kickoff, we can think of touchdowns being worth roughly six points and field goals worth roughly two to the game's margin. Thinking about scoring this way shows the relative value of a touchdown compared to a field goal is higher than you might think.

3. Close to the goal-line failures still result in putting opponents in bad starting field position.

How the model works

In comparing a punt vs. a fourth-down attempt, ESPN's model considers the win probability expected given a fourth-down success and fourth-down failure, and weighs those by the expected conversion rate of that fourth down. (The expected conversion rate is determined by league averages in similar circumstances and adjusted based on the strength of the offense and defense.) That produces an overall expected win probability given a fourth-down attempt, which can be compared to an expected win probability given a punt. The higher win probability is the recommendation.

Another way to look at these decisions is to look at what is called the "breakeven rate" of conversion. Given a particular situation and the win probabilities associated with it, the model can produce the minimum conversion rate to justify going for it. Here's an example of what that output looks like on an extreme error from former Saints coach Sean Payton in 2021:

Massive error by Sean Payton attempting a field goal from the Titans' 1-yard line in the fourth quarter, per ESPN's win probability model.

WP go: 14%
WP kick: 7%

Needed just a 21% chance of conversion to justify going for it. We estimated Saints' conversion probability at 60%.

— Seth Walder (@SethWalder) November 14, 2021

What about factors the model doesn't consider?

There are areas outside the purview of the model that a coach might take into account in his or her decision-making. These factors -- such as weather, injuries and matchup advantages or disadvantages -- are important and can shift a decision. However, it's important that if coaches want to deviate from base rates to make their decisions, they do so in both directions.

That means as often as we hear a coach using matchup factors to justify being more conservative than a model suggests, we ought to hear them using matchup factors to be more aggressive than a model suggests.

The aforementioned breakeven rate can be a guide here and can illustrate the clarity or strength of a recommendation. If the breakeven rate is within a couple of percentage points of the expected conversion rate in either direction, it's fair to grant some leeway to a coach considering additional factors. But if, say, a particular situation has a 40% breakeven rate and a team has a 60% expected conversion rate, it would hard to justify not going for it.

2-point conversion decisions

These decisions can also swing a game, so when should a coach go for two? It's actually not even clear that's the right question. The point expectancy for a PAT (93.7% since 2015) and 2-point conversion (48.1% in same span, but worth double) are so close that we should think of either option as an active choice.

But still, we'll answer the question: When should a coach go for two? We'll break down each score where there's frequently a question. Keep in mind three things:

1. It's really the combination of score and time remaining (including timeouts!) that determines whether or not a team should go for two. Note the time specifications within each score breakdown.

2. There are large swaths of score/time combinations in which a reasonable argument for either PAT or going for two can be made, and we will generally ignore those. Scores not included in the write-up below generally fit in this category, with their recommendations either close to the breakeven point or swinging narrowly between PAT and 2-point attempt.

3. Like with fourth downs, these are typical recommendations. Recommendations in a specific game might be different based on one team entering as, say, a heavy favorite or a mismatch between an offense and defense (that makes a conversion more or less likely).

In addition, because the breakeven point of a 2-point attempt is often right on a knife's edge with the expected conversion rate, small or specific changes in time can also swing a particular recommendation. As a result, the following should be taken as general descriptions of our model's preferences.

When to go for two: Score at time of decision immediately following touchdown

The chart above indicates the conversion probability required to justify going for 2 given score and time remaining in the game. The dotted line is at 48% -- a typical conversion rate on 2-point plays. When the red line is below that dotted line, it is advisable to go for 2.

Down 1 point: This usually comes up in the final minute or two of the game, when a team down seven points scores a touchdown, then considers going for 2 to try to nab the win in regulation. Outside of, say, 15-20 seconds left in the game, depending on timeouts, it is generally advisable to kick the PAT. The reason is that a successful two-point conversion encourages unbridled aggression from the opponent, therefore making it more likely to score. Once we get down to 15-20 seconds, either option is generally fine.

Down two points: You can either have a chance to be tied or definitely be losing, so which would you prefer? If someone says "don't chase points" in this scenario, be sure to never listen to his/her game management advice. Very early in a game, it's fine to kick a PAT in these spots, but going for two should not be criticized.

Down four points: It's better to go for two here, starting with roughly 8-9 minutes or less in the fourth quarter. Here's how you can think about it: Imagine you're down three points driving late in the fourth quarter, but you knew the result of overtime in advance. It would change how you played. If you knew you were going to win in OT, you could kick a field goal to win. But if you knew you were going to lose, you'd go for it on fourth downs and try to score a touchdown.

Going for two down four points is the equivalent to finding out the result of OT in advance. It's almost a 50/50, just like overtime. And it lets you know if you need to score a field goal or touchdown on the next drive.

Down five points: Either way is acceptable in the first half. Go for two in the second half to attempt to be down only a field goal.

Down eight points: Go for two starting roughly midway through the third quarter. I wrote an entire article on this one but the abridged version is this: If you go for two now and convert, you can kick a PAT on the next touchdown and take the lead. If you go for two now and fail, you can go for two again on the next touchdown and have a chance to tie. It's easier to convert once than to fail twice.

Down nine points: This actually is not so clear cut. Logically, it makes sense to go for two late, though the advantage is smaller than you might think. The idea is to find out now if you are down one score or two scores rather than finding out later, because it can affect your future decision-making. Our win probability model doesn't always see it this way, however. If you were asking me: I'd go for two, but the advantage gained is certainly small.

Down 10 points: This can go either way for much of the game -- for instance, a PAT allows you to take the lead with another field goal and touchdown -- but with roughly 8-9 minutes left in the game, going for two is strongly preferable because there are limited possessions left. At that point, the chance of being down eight -- which gives the possibility of tying through a touchdown and 2-point conversion -- is clearly preferable to being down nine.

Down 11 points: Go for two starting roughly around the beginning of the fourth quarter. This is the same situation as down four, with a touchdown added on top.

Down 12 points: Consider going for 2 very late in the game; it's essentially the down-9 scenario with a field goal added on top.

Down 13 points: Late in the game, it can be advisable to go for 2 in order to keep open the possibility of a tie via a field goal, touchdown and 2-point conversion.

Down 15 points: Go for two in the second half. This is the down-eight scenario with a touchdown added.

OK, so what about when to go for two when you're winning?

Up one point: In the second half, it is advisable to go for 2 in order to have a chance at being up a field goal.

Up four points: In the final few minutes of the game, it's usually better to go for 2 to create the possibility of a tie if your opponent scores a touchdown and misses the PAT.

Up five points: Go for two in the second half to be up a touchdown.

Up 12 points: It's best to try to go up two touchdowns later in the game.

Here are two more situations in which a coach might go for two:

Down one point: This generally comes up when a team scores late in the fourth quarter and considers going for two to win rather than the PAT to tie. Usually, it still is better to kick the PAT because if the team converts a 2-point play, that will encourage unbridled aggression from the opponent. It is acceptable to go for two when the opponent cannot realistically mount a FG drive on the ensuing possession, like when there are, say, less than 20 seconds remaining.

Up seven points: This is essentially the inverse of the down-nine scenario. And again, logically it makes sense to kick the PAT to not let an opponent know if it is down one score or two. There are times, however, when the model disagrees, so I'd have a hard time faulting a coach for either choice.

When to go for 2 in the new postseason overtime

This is quite clear cut.

If the first team possessing the ball scores a touchdown, it should kick the PAT. If we assume the opponent also scores (which is the only way this matters), we can also safely assume it will go for 2 (more on that in a minute). In that instance, the first team has roughly a 50/50 shot -- the chance the opponent converts their two point conversion -- to win the game.

Had the first team gone for 2 and failed, the opponent would be able to kick a PAT and win. Had the first team gone for 2 and succeeded, that would not guarantee a win, because the opponent could still go for 2 and also succeed, thus tying the game. Therefore, that is a worse proposition than simply defending a 2-point play.

The second team that is down a touchdown and scores almost certainly should go for 2. If it does not, it would be handing the ball back to the opponent in a true sudden-death situation - essentially the original OT rules after losing the coin flip. Almost any team would have a better chance of converting a 2-point play than doing that.