There were many decisions to analyze from yesterday’s AFC Division Round matchup between the Texans and Chiefs. Houston raced out to a 24-0 lead and somehow still trailed at halftime, fueled in part by its own poor fourth down decisions (kicking a field goal on 4th-and-a-foot early, a fake punt later). Kansas City became just the third team to win a game by 20+ points after trailing by 20+ points earlier in the same game.

But there was an interesting decision late in the game that, while it wound up having no impact on the game, is still worthwhile to analyze. Here was the situation: Kansas City led, 48-31, with 8:10 left in the game. The Chiefs faced 4th-and-2 from the Houston 6-yard line, and had two choices:

• Attempt a field goal to take a 51-31 lead. This would gave Houston the ball at its own 25-yard line, down by 20 points, with 8:06 to go.
• Go for it, which would lead to one of three results:
  • Score a touchdown, effectively ending the game.
  • Convert the 4th down, and the drive still ends in a field goal attempt, albeit with probably two more minutes taken off the clock.
  • Fail on the 4th down conversion, which gives Houston the ball, down 17 with 8:00 remaining, at their own 6-yard line.

So what is the best decision here? Obviously the Chiefs chances of winning are extremely good no matter what they do. With 8 minutes left, the odds of Houston scoring 17, 20, or 21 points are all really low. Let’s think about it in a more competitive game situation.

Let’s just assume the Texans are going to score two touchdowns in the next five minutes. Because the analysis is really the same: we just slide the win probability significantly in all cases. So let’s think about the win probability of these options:

1) Kick the FG: Up by 6, with Houston having the ball on its own 25-yard line, with 3 minutes to go. A touchdown obviously beats you, which is the big concern here.

2) Go for it and score the TD: Up by 10, with Houston having the ball on its own 25-yard line, with 3 minutes to go. This game is still essentially over.

3) Go for it and convert, but drive still ends in a FG: Up by 6, with Houston having the ball on its own 25-yard line, with 1 minute to go. This is a much better situation than option 1, of course.

4) Go for it and fail: Up by 3, with Houston having the ball on its own 25-yard line, with 2:30 minutes to go (let’s assume the extra 19 yards of field position will cost 30 seconds). This is bad, but not that bad: while overtime is obviously much more likely, there’s a lower chance you lose in regulation, as Houston will be conservative once it gets into field goal range.

Now, how likely are the Chiefs to convert on 4th-and-2 from the 6? Using league average estimates, the average team has a roughly 47% chance of being made. I think we can safely assume the Chiefs were better than your average offense, so let’s just use a 50% chance here to make the math easier.

But given that converting nearly ends the game (and converting and scoring does end the game), it makes it really difficult to argue that kicking the field goal is the right choice. To do so, you’d have to argue that Houston’s chances of winning are twice as good if they are down by 3 than if they are down by 6. And I don’t know what sort of win probabilities you could assign to each situation to get there.

Unfortunately, there aren’t any good win probability models we can use to analyze this situation, so I think we are left using our intuition. But I will fall back on the old standby: if I was a Texans fan, I would have been relieved to see the Chiefs send out the kicker.