Hello again, it’s been some time since my last post. On Monday night, I missed the Giants-Falcons game. I looked at the score and it was 20-12 with around 4 minutes remaining. I thought to myself, the Giants sure like their field goals, they have 4 of them in this game, with no touchdowns. Then my friend who was watching the game filled me in on what happened. The Giants were down 20-6, scored a TD, and went for 2 (not converting). My first thought was probably the same as for most people. What the hell? Is Pat Shurmur dumb? Did he have a brain cramp? Does he not realize that you can kick a PAT, then score another TD and kick another PAT, then go win it in OT? I’ve watched football for almost 20 years and that’s how it’s always been done. Then after my initial bewilderment, I thought to myself maybe Shurmur was doing what Jack Del Rio did two years ago when the Raiders were down 1 to the Saints after scoring a TD at the end of the game and went for 2 to win (and succeeded). My friend meanwhile was adamant that the call was wrong due to intangible factors such as momentum. He did concede in the end that he would have been ok going with a 2 point conversion if it came in the end. So I quickly forgot about my pathetic 1-6 Giants and got excited to test who is right and thus giving birth to blog post #6.
There has been a lot written about 2 point conversions being better value than extra points. So I won’t go into the general theory behind that. However, I will take a look at Monday night’s specific situation and show that Shurmur was 100% right, at least mathematically. I won’t argue anything about momentum or emotion. If there’s a way to measure that I haven’t discovered it. I will just look at the probability of winning based on using Shurmur’s strategy and the conventional strategy.
First of all, let’s discuss the assumptions:
- Two TDs will be scored in regulation and the Falcons will be stopped from scoring any more points. Without that, the Giants lose regardless of what Shurmur’s call was. I guess there are unusual scenarios like a TD and 3 FGs that could result in a win. Accounting for all scenarios, however, would make the analysis extremely complicated, if not impossible.
- I count ties as losses as I’m sure any head coach worth his salt does. So not winning means tying or losing.
To do the math there are really only three probabilities that need to be known. The probability of a successful PAT, the probability of a successful 2 point conversion, and the probability of winning in OT.
The probability of a successful PAT and 2 point conversion is covered in this (unfortunately slightly outdated) FiveThirtyEight article from November 15, 2016:
According to ESPN Stats & Information Group, there have been 1,045 two-point conversion attempts since 2001,1 with teams converting 501 of those tries. That’s a 47.9 percent conversion rate; given that a successful attempt yields 2 points, that means the expected value from an average 2-point try is 0.96 points.
Interestingly, that’s almost exactly what the expected value is from an extra point these days. Since the NFL moved extra-point kicks back to the 15-yard line last season, teams have a 94.4 percent success rate, which means that an extra point has an expected value of between 0.94 and 0.95 points.
Prob of PAT: 0.944
Prob of 2 point Conversion: 0.479
For OT, I went back the last two seasons since the change to a 10 minute OT. A bit of a small sample size but there have been 24 OT games and 22 of them ended with a winner. So 11/24 or ~0.458 of OT games end in a win for a team on average.
The following are the possible scenarios taking into account the assumptions:
First the conventional route:
That’s PAT, PAT, OT.
There are two possible winning scenarios here.
The probability of the win is calculated in each scenario by multiplying all of the events, e.g. 0.944*0.944*0.458333=0.408437
There’s also a far less likely scenario for winning. What if the first PAT is unsuccessful? The Giants still get a mulligan and can go for the 2 point conversion to tie it and then win it in OT.
So the probability of winning with this conventional strategy is 0.408437+0.0122943, which is about 42.07%.
Next, the Pat Shurmur strategy:
There are three possibilities here.
The 2 point conversion is good, then he goes for a PAT for the win and bypasses OT.
The second scenario is the least likely one. In this scenario, the 2 point conversion is good, but the PAT is missed, and then the Giants win the game in OT.
The third scenario is one where the 2 point conversion is unsuccessful, but a second 2 point conversion is successful, and the Giants win in OT.
The probability of winning in this situation, if you add up all of the scenarios is ~57.9%.
Finally, a scenario dedicated to my aforementioned friend that insisted that if they were to go for 2 they should have done so after their SECOND TD, not the first. His argument was about momentum, but here I’ll look at it from a mathematical perspective. I call this scenario the “reverse scenario” because it’s going for 1, then going for 2, rather than going for 2 then 1.
Here there are two possible scenarios:
The ideal scenario is kicking the PAT is successful and the 2 point conversion is successful.
The other possibility is one that was already looked at. the PAT is not good, the 2 point conversion is good, and the Giants win in OT.
The total probability of the reverse strategy is ~46.4%.
Looking at this more qualitatively, this doesn’t make logical sense even without looking at the numbers. In Pat Shurmur’s scenario, he gives you two shots at a 2 point conversion if one fails, in this scenario he gives you one shot. Another way of looking at it is that if you were to flip the events. In your ideal scenario, you kick the PAT and then get a 2 point conversion. Reversing these events is your ideal scenario of Pat Shurmur’s strategy. However, if your ideal scenario doesn’t work and you make a PAT but miss the 2 point conversion, you lose. On the flip side, if you go for the 2 pt conversion first and miss it, you’re not going for the PAT because in that situation you KNOW it won’t be enough, you’ll go for another 2 point conversion. You’re basically taking away the benefit of knowing how many points will be enough to stay alive in the game if you kick the PAT first.
Here are the final tallies of the probability of winning the game in the three strategies.
Pat Shurmur vs. Conventional Strategy +15.8%
Pat Shurmur vs. Reverse Strategy +11.4%
So mathematically, his strategy was sound.
To put into perspective how big the big 15.8% gap is compared to the conventional strategy, we can project win totals if a team plays 16 games where this situation manifests itself.
As a reminder, the conventional strategy gives a team a 0.42073 probability of winning. Projecting that to 16 games would result in ~6.73 wins, rounding that projection up leaves us with 7 wins. Pat Shurmur’s strategy gives a team a 0.578852 probability of winning. This projects to ~9.26 wins, rounding down to 9.
How big of a difference is 7 and 9 wins? I looked at the standings going back to 2002, the year the Houston Texans came into the league and realignment took place. I looked at the probability of a 7 win team making the playoffs and compared it to a 9 win team. For this exercise, I treated a 9-7 team as I would a 9-6-1 team to make things easier. The following is the result:
Putting the 15.8% winning percentage increase into perspective, if a team were to find themselves in this identical situation for all 16 games in their season, they’d have a 35% higher chance of making the playoffs.
Finally, there’s an argument my aforementioned friend made and one I read online was that these are league-wide averages and they’re not relevant to a poor Giants team.
There are two ways to try to see if this is correct. One way is to use Giants data. However, using only this season will create a sample size issue and using more than one season of Giants data is questionable in terms of relevance. For example, you can look 2 point conversions in 2018, but there have been only 5 so far. You can also include 2017 data to make the sample size larger, but 2017 was a completely different offense with no Barkley and Beckham only playing 4 games.
Therefore I took a look at what 2 point conversion percentage would be required for the two strategies to yield an identical win probability (the breakeven point). The math behind this is as follows:
Prob (Conventional) = Prob (Shurmur)
Prob (PAT Successful) * Prob (PAT Successful) * Prob (Overtime Win) + Prob (PAT Unsuccessful) * Prob (2 pt Conversion Successful) * Prob (Overtime Win) = Prob (2 pt Conversion Successful) * Prob (PAT Successful) + Prob (2 pt Conversion Successful) * Prob (PAT Unsuccessful) * Prob (Overtime Win) + Prob (2 pt Conversion Unsuccessful) * Prob (2 pt Conversion Successful) * Prob (Overtime Win)
I plugged in the numbers I previously calculated and made the probability of getting a successful 2 point conversion, X, for easier reading. The following is the quadratic equation that resulted:
0 = 0.458333X^2 – 1.402333X + 0.408437333
Since this equation is relatively complicated, I used solver in excel. For information on how to use solver please see Solver in Excel. Using goal seek is also possible but it’s a little less accurate. My result was ~32.6%. Thus if a team succeeds at 2 point conversions at a higher than 32.6%, Shurmur’s strategy is correct.
The most common complaint I heard was that the Giants are much poorer than average in the redzone so league-wide stats are not meaningful. Therefore, I took a look at redzone stats this season, the Giants are 42.86%, much higher than the 32.6% threshold. In fact, 32.6% is a higher percentage than any team’s redzone efficiency since the Kansas City Chiefs had a ghastly 27% efficiency back in 2012 (my how things have changed).
So, all in all, no matter what angle you look at this was the right move. It’s actually very promising for Giants fans to have their coach pay attention to analytics.
Data source:
Igor Zolotusky's Analysis 