why the Patriot’s decision to let the Giants score a touch down makes sense

I was shocked to see the Patriots allow the Giants to score a touchdown (TD) in the Superbowl with 57 seconds left. Here is why it makes sense.

From my earlier post on going for two points after a touchdown, we can model this situation as a one possession game. That is, the Patriots would get the ball back and finish the game with it. As I recall, the Patriots had no time outs. The key issue was how much time would they have? It’s easier to score with 57 seconds left than with 15.

First, let’s consider that the Patriots allow the Giants to score a touchdown. Now they have 57 seconds left on the clock. Historical data suggests that there was a 19% chance of scoring a touchdown. Yes, the Patriots had Tom Brady, but time was a factor. Allowing the Giants to score a TD would give the Patriots a 19% chance of winning.

Now, let’s see if not allowing the Giants to score would have improved the Patriots’ chances. Let’s go back to the Giants’ touchdown scoring drive. Before they took the lead, there were three outcomes:

1. Giants score a touchdown. If the Patriots didn’t make it so easy, let’s say that there would be 15 seconds left on the clock. Let’s conservatively give this a 50% chance. Regardless if the Giants went for two, the Patriots would need a touchdown.
2. Eli Manning would throw a interception. He did this in 4.4% of his passes, but surely he was considering more conservative passes here. Let’s say there was a 3% interception chance. The Patriots would win outright.
3. Giants score a field goal. They would have a 47% chance of a field goal attempt. Wayne Winston’s Mathletics suggests a 99% success rate. The Patriots would need a field goal to win.

Let’s say that that the above options would have left 15 seconds left on the clock. Let’s look at the outcomes from the perspective of the Patriots.

1. Giants score a TD. Let’s say that the odds that the Patriots would score a touchdown decreased from 0.19 to 0.10 with less time on the clock. Again, I think this is generous, even with Tom Brady.
2. Giants interception. Patriots win with virtual certainty.
3. Giants go for a FG. The Patriots could get into field goal range with a probability 0f, say, 0.2. A distant field goal would succeed with a probability of 0.5.

Putting this all together, the odds that the Patriots would win in the second option are:
0.5(0.1)+0.03+0.47[(0.01)+0.99(0.2)(0.5)] = 0.13

(the first component is from a Giants TD, the second component is from a Giants interception/fumble and the third component is from a Giants FG attempt and then miss + success)

Not allowing the Giants to score a TD would give the Patriots a 13% chance of winning.

[2/6 update at 2pm] Three things:
1. I was told that the Patriots had one time out left. I don’t think that would drastically affect anything here.
2. The Giants could have run out the clock while scoring if the Patriots did not allow them to score. That, of course, would have given the Patriots an even smaller chance of winning (down from 13%). Again, that would not have changed the Patriots’ strategy.
3. It looks like Coach Coughlin of the Giants knew that Coach Belichick of the Patriots would allow the Giants to score so easily and then told his players not to score so quickly. This was a quick decision conveyed to all players on the fly. This type of game strategy suggests that sports analytics matter.

I think the Patriots were right. What about you?