The Situation
Miami has the ball and is leading Pittsburgh 31-28. It's 4th and goal on the Pittsburgh 9 yard line and 1:12 left to go in the game. The obvious play is to kick the field goal, which they do, and they now lead 34-28. However, on 4th down, with 3 seconds left, the Steelers complete a near miracle 5-lateral play to score a touchdown. However, Antonio Brown stepped out of bounds on his way to the end zone, ending the game and allowing Miami to escape with a win.
The fact that Miami won overlooks the 4th and 9 decision a minute before. Was it the right decision?
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| Antonio Brown steps out of bounds before finding paydirt |
The fact that Miami won overlooks the 4th and 9 decision a minute before. Was it the right decision?
The decision comes down to whether the Dolphins should kick the field goal, or run a play on 4th down.
The Factors
There are several factors which can help us decide the right course of action, some are more relevant than others depending on the decision made. We will look at all probabilities from the Dolphin's point of view.
- What is the probability of making the field goal?
- Given the field goal is made, what is the probability you will win the game?
- If the field goal is not made, what is the probability you will still win the game?
- What is the probability of scoring a touchdown?
- What is the probability of winning the game if you score a touchdown?
- What is the probability of winning the game if you don't score a touchdown?
All factors can be boiled down into one of the preceding factors. For example, how well your defense is playing or how well the opposing kickoff return unit is playing, all can be taken into account with the above factors.
The Calculations
To determine the best course of action, we need to calculate the total win probability for each action, then figure out which decision is more likely to win the game. With the game nearly over, the important metric is Win Probability (WP), not Expected Points (EP). Expected Points is something coaches should be looking to maximize early in the game as it's highly correlated with WP, but by the end of the game, EP and WP can diverge quite a bit.
Probability of Making a Field Goal
The first number we need is the probability of making a field goal. The line of scrimmage is at the 9 yard line, so the kick will be a 27 yard field goal attempt. The average kicker makes a 27 yard field goal 94% of the time. Kicker Caleb Sturgis, in his rookie season, has converted all 3 of his kicks between 20 and 29 yards so far. Sturgis' small sample size doesn't tell us much, but let's split the difference and say he converts at a 97% clip.
Win Probability when Making the Field Goal
Once the field goal is made, the Dolphins have to kick off to the Steelers who get one last gasp effort to win the game. The Steelers' hand is now forced, they need to go for a touchdown to win the game. Notice a tie at the end of regulation is extremely unlikely, only happening if the Steelers score a TD, but miss the extra point.
When making the field goal, the 4th down calculator at Advanced NFL Stats says the Dolphins will win the game 88% of the time. Where does this number come from? It looks at how often the opposing team will be able to win the game after receiving the kickoff.
The average kickoff will put the return team at their own 23 yard line. However, when looking at stats from earlier in the game, the Steelers have started at their own 20, 20, 17, and 22 yard lines. There were 2 kickoff returns unaccounted for. One was at the end of the first half, a shorter kick designed to minimize return yardage, and a kick returned to the 20, but moved back to the 10 yard line due to penalty.
The 20 yard line is a good place to estimate Pittsburgh's winning chances (and in fact was where they actually started with the ball in the last sequence. The Win Probability Calculator at Advanced NFL Stats has the chance of Pittsburgh winning at 9%, meaning the Dolphins win the game 91% of the time if they make the field goal, slightly different from the average number the 4th down calculator gives us for an average team.
One other key, which is relevant to all factors is the Steelers are out of timeouts and are fighting the clock at this point.
Win Probability when Missing the Field Goal
When missing the field goal, the Dolphins turn the ball over on the Pittsburgh 17 yard line. The Win Probability calculator figures Pittsburgh can win the game 10% of the time, meaning the Dolphins win the game 90% of the time even if they miss the field goal.
Total Win Probability when Attempting a Field Goal
To figure the total Win Probability for attempting a Field Goal, we need to add up each of the WP numbers, multiplied by the chance each one will occur:
Total WP = P(FG Made)(WP if FG made) + P(FG Miss)(WP if FG Missed)
Total WP = (.97)(.91) + (.03)(.90)
Total WP = 0.8827 + 0.027
Total WP = 0.9097 or about 91%
Surely this makes it an obvious move to kick the field goal, right? 91% chance of winning the game?
Probabilities when Going For It on 4th down
When going for it on 4th down, there's the potential of scoring a touchdown which effectively ices the game. However, even if the Dolphins don't score the touchdown, the Steelers are pinned back near their own goal line, making it difficult to drive for a winning tie or win.
The chance of scoring a touchdown on 4th and goal at the 9 yard line is actually 28% on a league wide average, according to the NFL calculator. The Dolphins themselves have converted at a 25% rate this year on 4th down. Most coaches in this situation do underestimate the chances of converting, so we can use the conservative number of 20% for the Dolphin's TD chances.
Win Probability when Scoring a Touchdown
If a touchdown is scored, it's now a 2 possession game for the Steelers, needing a touchdown and a field goal to tie the game. Though not impossible, we can set the chances of winning for the Dolphins in that situation at 99%
Win Probability when not Scoring a Touchdown
If the Dolphins fail to convert a touchdown, the Steelers will recover the ball near their own goal line, needing a TD to win, and a FG to tie and send it into overtime. This situation is actually better for the Dolphins, compared to missing a field goal, since the Steelers will be further back in their own zone.
Estimating the Steelers recover the ball at their own 9 yard line (assuming an incomplete pass), the WP calculator has the Steelers winning the game only 6% of the time. This includes the chance of kicking a tying a field goal and going into overtime, which is nominally a 50% chance of succeeding.
Total Win Probability when Going For It on 4th down.
We'll run the same calculation we did when figuring out WP for a field goal attempt.
Total WP = P(TD scored)(Win with TD) + P(TD missed)(Win with TD missed)
Total WP = (.20)(.99) + (.80)(.94)
Total WP = 0.198 + 0.752
Total WP = 0.95 or 95%
Conclusion
Going for it on 4th down means the Dolphins win the game 95% of the time. Attempting the field goal means the Dolphins win 91% of the time. Surprisingly, it's better to go for it on 4th down in this spot, even though kicking the field goal leads to a 91% of winning!
Why is this? The secret really comes to field position. On a made field goal, the Steelers will get much better field position than if a touchdown attempt fails. The extra 15 yards makes it much more likely the Steelers will score a touchdown on the ensuing drive (moving from 11% to 15%, over a 25% increase in TD probability).
The other key is the Steelers willingness to tie the game if the Dolphins fail to score. The Steelers still have to attempt and kick a field goal, never a gimme in Heinz Field conditions, so even if they don't have to get all the way to the end zone to score, it's far from certain they can tie up the game.
Changing the Dolphins' Chance of Scoring a TD
The analysis above was actually conservative, giving the Dolphins only a 20% chance of scoring a TD. What if we played with the numbers a little more. At what break even point should the Dolphins kick the FG instead of going for it on 4th down?
If we make the Dolphins' chances of scoring a TD on their 4th and goal situation, at what point will it make it better to kick the field goal instead?
To find this, let's set WP(FG) = WP(Go for It) and do some algebra, when we change the chance of scoring a touchdown
WP(FG) = WP(Go for It)
0.9097 = (x)(.99) + (1-x)(.94)
0.9097 = .99x + .94 -x(.94)
0.9097 = .94 + x(.05)
x(.05) = -0.0303
x = -.606 or -60%
This calculation means it is NEVER right for the Dolphins to kick the field goal!
Changing the Steelers' chance of driving for the winning TD
Maybe we're really underestimating the chances the Steelers can score a TD. After all, in the actual game, they were a couple of inches from winning the game. The problem with this analysis is adjusting ALL the numbers accordingly. Let's assume the Steelers will get to the end zone 20% of the time after an ensuing kickoff, 19% of the time if they recover at the 18 yard line, and 15% of the time if they're pinned back on their own 9 yard line. Now, the numbers look something like this:
Total WP(FG) = P(FG Made)(WP if FG made) + P(FG Miss)(WP if FG Missed)
Total WP = (.97)(.80) + (.03)(.19)
Total WP = 0.776 + 0.0057
Total WP = 0.7817 or about 78%
Makes sense the Dolphins' WP goes down if the Steelers offense is better. What about if they go for it? Let's assume once again a 20% chance of scoring a TD.
Total WP = P(TD scored)(Win with TD) + P(TD missed)(Win with TD missed)
Total WP = (.20)(.99) + (.80)(.85)
Total WP = 0.198 + 0.68
Total WP = 0.878 or 87.8%
It's still the right decision to go for it in this spot. In fact, if we give the Steelers a better offense, the separation between going for it and kicking in this spot is MORE pronounced.
Comments?
Does this surprise you? Do you disagree with the numbers? Enter your own numbers and see what you come up with?
One thing's for sure. The Steelers have problems with the sideline
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