Week 1, Patriots at Cardinals
4th-and-3, 4:10 remaining in 2nd quarter, Down by 10
The Cardinals went for it on a 4th-and-3 on the Patriots’ 3. The NYT 4th Down Bot approves.
If you disagree

The coach and I agree that going for it is the thing to do here, but you may be thinking it makes sense to attempt a field goal. That would be the right call if you think the Cardinals’ chances of converting on fourth down are less than 25 percent. But based on my analysis, I’d give the Cardinals a 42 percent chance to get a first down here.

Here's the full breakdown of my calculations:

Option Chance of converting
Chance of winning
Before play
After play Change
Go for it4th and 3, opp. 3 42% 40% 42% +2%
Field goal try20 yard kick (est.) 99% 40% 39% –1%
Punt 40% 30% –10%
My decision in context

Along with some circuitry to come up with a win probability for every game situation, all you need to figure out what you should do next is an estimate of how likely you are to make a field goal or convert a first down.

My estimates for these are based on the results of thousands of similar plays, but you may think you're smarter than I am. This chart shows you how changing those estimates would change my recommendation.

What to do on 4th-and-3 on opp. 3
Down by 10 with 4:10 remaining in the 2nd quarter
What coaches usually do
Go for it 51% of the time
Field goal try 49% of the time
Punt -
Based on about 1,045 fourth downs in similar situations since 2001.
What happened

Carson Palmer pass to the left to Larry Fitzgerald for 3 yards for a TOUCHDOWN. Carson Palmer pass to the left to Larry Fitzgerald for 3 yards for a TOUCHDOWN.

Where did these numbers come from?

To estimate a team’s chances of winning, I use a mathematical model that accounts for a whole lot of variables — including the difference in score, the time remaining in the game, and the number of timeouts each team has left. On top of that, I have models for the likelihood that a team makes a field goal and the likelihood that it will convert a first down.

By combining all of this information, I can come up with the best decision a team can make, according to math.

If you want even more details about the numbers behind my decisions, my full model is available on GitHub. Help make me better!