The coach’s decision to punt is the right call if you think the Texans’ chances of converting on fourth down are less than 26 percent. But based on my analysis, I’d give the Texans a 41 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 6, opp. 45  41%  12%  13%  +1%  
Punt  12%  12%    
Field goal try62 yard kick (est.)  3%  12%  8%  –4% 
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.
If the coach had gone for it instead of punting, I estimate the Texans’ chances of winning would be about 13 percent instead of 12 percent.
Punt  85% of the time 
Go for it  15% of the time 
Field goal try   
Shane Lechler punts for 31 yards to Buf14. Shane Lechler punts for 31 yards to Buf14.
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!