Week 3, Cardinals at Bills
4th-and-8, 11:45 remaining in 1st quarter, Tied
The Cardinals punted on a 4th-and-8 on the Bills’ 36. The NYT 4th Down bot was thinking the same thing, although attempting a field goal would have been fine, too.
If you disagree

I lean slightly towards punting, but I don’t have strong feelings here – my numbers tell me that either punting or attempting a field goal could be the best play. Specifically, attempting a field goal would be the right call if you think your chances of making the kick are greater than 70 percent. (Based on my analysis of over 13,000 field goal attempts since 2001, I give the average kicker a 61 percent chance to make a kick from this distance in a outdoor stadium.)

Here's the full breakdown of my calculations:

Option Chance of converting
Chance of winning
Before play
After play Change
Punt 66% 67% +1%
Field goal try53 yard kick (est.) 61% 66% 66% -
Go for it4th and 8, opp. 36 34% 66% 66% -
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-8 on opp. 36
Tied with 11:45 remaining in the 1st quarter
Behind my field goal number
What coaches usually do
Field goal try 69% of the time
Punt 28% of the time
Go for it 3% of the time
Based on about 1,385 fourth downs in similar situations since 2001.
What happened

Drew Butler punts for 25 yards to Buf11. Drew Butler punts for 25 yards to Buf11.

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!