The Miami Dolphins once again faced a "close" 4th down decision nearing halftime of the New England @ Miami tilt in week 15. Down, 0-3, Miami decided to attempt a field goal, as color announcer Phil Simms said, "It looks like it's a whole yard short ... it's a good decision by the Dolphins [to go for the field goal]. Get on the scoreboard, Jim [Nantz], there nothing worse for a QB or coach to look up at that scoreboard and see that 0."
Was Simms right? Is it better to kick the field goal here?
The Situation
After the 3rd down pass to Michael Egnew falls short of the line to gain, the Dolphins face 4th down and a long yard (one closer to 2 yards than 0 yards) on the New England 24 yard line with 3:34 left in the first half. Out trots the FG team and Simms claims it's good to get the points on the board rather than to walk away with nothing. However, the game of football doesn't care if you score points, you need to out score the opponent, and in this situation, you should maximize the number of Expected Points you're going to get.
So how do we calculate whether it was the right decision to kick the field goal or not?
The Factors
We have to look at several factors to determine whether or not attempting a field goal is the right move here. Of course, we are simplifying some of these percentages, but if there is an obvious decision, that won't change with fine tuning of these numbers.
1) What is the chance kicker Caleb Sturgis will make the 42 yard field goal attempt?
2) What is the chance Miami will convert this 4th and 1 attempt?
3) If Miami makes the 4th and 1, what are the expected number of points they can expect from this drive?
4) When New England recovers the ball, either after a failed FG try, failed 4th down try, or after a kickoff following a Miami TD, what is their chances of scoring?
What is the chance kicker Caleb Sturgis will make the 42 yard field goal try?
Phil Simms says "take the points" here, but the actual chance of making the field goal is not 100%. Play-by-play announcer Jim Nantz then says, "Sturgis had a miss in each of the last 3 games." What is the actual chance for Sturgis to make this field goal? Looking at Sturgis' record in this, his rookie year, he has been 80% successful from 40-49 yards out. Looking broadly, the average in the NFL for a 40-44 yard kick is actually 76.2%, however given the game was being played in sunny Miami with no snow and little wind, the actual success rate is probably closer to Sturgis' 80% rather than the NFL average.
Still, Simms makes a big mistake of assuming 80% = 100% when he says to "take the points." It's another clear mistake in binary thinking, and a big mistake in evaluating an 80% success rate as 100%. To really determine if this was a mistake though, we have to evaluate the other factors and see if there was a better play to be made.
What is the chance Miami converts this 4th and 1?
Once again, using the 4th down calculator from Advanced NFL Stats, the average NFL team converts this 74% of the time. This number is close to the chance Sturgis will make the field goal, and since a touchdown is at least 6 points, it would seem to point to going for it on its own. However, consider even making the first down here won't always get a touchdown. However, making the first down will make it an easier field goal attempt in the future as well, plus take down the clock for New England's ensuing drive.
Which leads us to the next question:
If Miami converts the 4th and 1, what is the number of Expected Points (EP) they can expect from this drive?
Assuming they convert the 4th and 1, how many points will they get from this drive? We'll have to make some assumptions here, but if we make a conservative estimate, Miami runs the ball and converts the first down to the New England 23 yard line. Clearly, if Miami gets closer, then EP will be greater, so the estimate we come up with will understate Miami's true EP.
From the Win Probability calculator, the chance of a TD at the New England 23 is 44%, while the chance of a field goal is 36%. Assuming the Dolphins kick a PAT if they get a TD, the expected points in this situation (again, assuming they convert the previous 4th and 1) is:
EP = P(fail)(0) + P(TD)(7) + P(FG)(3)
EP = .44(7) + .36(3)
EP = 4.16
This of course, does not end the story. New England gets a chance to score as well, depending on A) their starting field position and B) the time left on the clock. New England does have 3 timeouts remaining, so the clock is not quite as much of a factor as it could otherwise be.
What is the Expected Points for New England when they get the ball back?
The EP for New England will depend on where and when they get the ball back. If Miami misses the FG attempt, we can assume NE will get the ball back on their own 32 yard line. With 3:30 left in the half, the Patriots are expected to score a TD 20% of the time and a FG 12% of the time. This leads to the expected points value of 7(.2) + 3(.12) = 1.76.
If the Patriots instead get the ball back on their on 20 yard line (e.g. after Miami Scores), that number gets down to 15% and 8% respectively, leading to an EP of 7(.15) + 3(.08) = 1.29.
If the Dolphins fail on the conversion, and the Patriots recover on the 24 yard line, the numbers don't change much. 16% and 9% respectively, leading to an EP of 7(.16) + 3(.09) = 1.39
What if Miami makes the 4th down conversion, but doesn't score? Since Miami is already on the New England 23, it's safe to say if they make the first down, but fail to score, they will likely be within the 20 yard line. A rough estimate will give New England an EP of 1.20 in this case.
The Calculations
Finally, we need to figure out which choice is better, trying a field goal, or going for it on 4th down?
Expected Points when Attempting a Field Goal
If it's a field goal attempt, the Expected Points formula can be found this way: Probability(make the field goal) * (3 points - the Expected Points from NE's ensuing drive) + Probability(miss the field goal)(0 - Expected points from NE's drive)
In a formula, it looks like this:
EP(FG try) = P(FG)(3 - EP(New England after a score)) + (1-P(FG))(0 - EP(New England after Missed FG))
EP(FG try) = (.80)(3 - 1.29) + (.20)(0 - 1.76)
EP(FG try) = 1.368 - 0.352
EP(FG try) = 1.016
The expected points for Miami trying a field goal is actually only 1.016 points. What about trying for the 1st down?
Expected Points when going for it on 4th down
Going for it on 4th down is a little more complicated, but again we are simplifying the math here. We need to determine the expected points when converting vs. failing. We need to look at the probability Miami makes the first down, then the expected points of that conversion. We will then need to take into account New England's EP depending on whether Miami scores or not. We will also need to account for the fact New England might stop Miami on 4th down and see what New England's EP are in that case.
In a formula, it looks like this:
EP(Go for it) = P(Make 1st down)(EP(make first down) - [P(MIA score)EP(NE after a score) + P(MIA no score)EP(NE after no score)]) + P(Miss 1st down)(0 - EP(NE after missed 4th down try))
That's a mouthful, but looking at each factor will show us where the numbers lie. Working it all out, we get:
EP(Go for it) = (.74)(4.16 - [(.80)(1.29) + (.20)(1.20)]) + (.26)(0-1.39)
EP(Go for it) = (.74)(4.16 - [1.032 + 0.24]) - 0.3614
EP(Go for it) = (.74)(2.888) - 0.3614
EP(Go for it) = 2.13712 - 0.3614
EP(Go for it) = 1.77572
The expected points if Miami goes for it is 1.78, over 75% more points than if they attempted to kick the field goal!
Conclusion
This situation is a little more difficult to calculate since we not only have to worry about Miami's chances of scoring, but also look at the negative side of not being successful. In this case, the difference between giving up the ball on the 24 yard line (on a missed 4th down) or on the 20 yard line (after a successful score) isn't that much. The difference in making the 4th down vs. making the field goal is much more than the difference in making the field goal or missing on 4th down. When you consider the chances of making a 4th and 1 are not that much worse than kicking a 42 yard field goal, it isn't a close decision.
So What Happened?
On this particular play, Sturgis didn't even get a chance to kick the field goal as bad snapper/holder communication caused a fumble in one of the more LOL moments of this season.
The bad result only highlights the poor thinking of Phil Simms and the Dolphins. Regularly evaluating 80% situations as 100% can lead to people getting fired in other jobs (e.g. finance). If people treated field goal attempts as ATTEMPTS, rather than gimmes, then we would see better decision making in the NFL.
In the game, Miami came from behind and wound up winning the game, but this was in spite of this decision, not because of it.
Disagree?
Once again, feel free to leave your comments about this analysis. Substitute your own numbers. Do you think New England has a better chance of scoring? Do you think Sturgis makes the field goal more than 80% of the time? Let us know!
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