The coach’s decision to attempt a field goal is the right call if you think the Chiefs’ chances of converting on fourth down are less than 29 percent. But based on my analysis, I’d give the Chiefs 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%  62%  64%  +2%  
Field goal try20 yard kick (est.)  99%  62%  62%    
Punt  62%  52%  –10% 
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 attempting a field goal, I estimate the Chiefs’ chances of winning would be about 64 percent instead of 62 percent.
Field goal try  73% of the time 
Go for it  27% of the time 
Punt   
Cairo Santos 22 yard field goal attempt is GOOD.
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!