I lean slightly towards punting, but I don’t have strong feelings here – my numbers tell me that either punting or going for it could be the best play. Specifically, going for it would be the right call if you think the Chiefs’ chances of converting on fourth down are greater than 34 percent. (Based on my analysis, I’d give the Chiefs a 34 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  

Punt  84%  85%  +1%  
Go for it4th and 8, opp. 38  34%  84%  85%  +1%  
Field goal try55 yard kick (est.)  30%  84%  84%   
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.
Field goal try  64% of the time 
Punt  32% of the time 
Go for it  5% of the time 
Dustin Colquitt punts for 27 yards to SD11. Dustin Colquitt punts for 27 yards to SD11.
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!