One of my favorite Web sites is AdvancedNFLStats.com.
It has live, up-to-the-second win probabilities as games go on. For example, the Chargers' probability of beating the Steelers dropped greatly after Willie Parker's touchdown before the half.
Now, Brian Burke, who operates the site, has added a win probability calculator, where you can see the chances of winning given certain circumstances—the score differential, the time left in the game, the field position, and the down and distance (though it doesn't include timeouts). Check it out here.
Using this tool, I determined whether teams should kick the extra point or go for the two-point conversion during various late-game situations.
Let's take a circumstance under which there may be a question of what to do after scoring.
You're down by eight before a touchdown, with seven minutes left in the fourth quarter. Do you kick the extra point or go for two?
If you make the extra point (which we'll say is good every time), you're down one, with seven minutes left, and the opponent gets the ball on their own 20 (assuming a touchback).
In that case, your win probability is 42 percent.
If you make the two-point conversion, you're tied, with the circumstances above.
Your win probability is now 47 percent. That's if you make the two-point conversion.
Given that about 45 percent of all tries are good, we have to see what would happen with the other 55 percent.
Your win probability if you miss the conversion is now 37 percent. Thus, we can say that
WP(attempting the two) = (0.45 * 0.47) + (0.55 * 0.37) = 0.2115 + 0.2035 = 41.5 percent.
So, you have a 42 percent chance of winning after making the extra point, and a 41.5 percent chance of winning if you attempt a two-point conversion.
The probabilities are almost the same, so in this case, attempting the extra point or two-point try is dependent on how your defense has performed in the game.
Could you stop them and get one more possession? Kick the extra point.
Is your defense horrendous and you have no chance of getting back the ball? Go for two.
Now let's see what happens if we change the time left from seven minutes to five.
In this case, you have only a 32 percent chance of winning if you kick the extra point. Your win probability is 55 percent is you make the two, but only 29 percent if you miss.
Your chance of winning if you attempt the two-point conversion would be 40.7 percent, which is significantly higher than the 32 percent chance if you make the extra point.
The graph below shows the chance of winning after kicking the extra point or going for all 30-second increments from two minutes left to eight minutes left.
The break-even point would be seven minutes left, where the win probability is virtually the same if you go for two or make the extra point. With less than seven minutes on the clock, going for two should be the choice over kicking the extra point.
Note, however, that because the calculator does not include timeouts, you should add 30 seconds (the amount of time saved with a TO) to the time left in the game. So if a team has three timeouts and there's five minutes left, you should look at the 6:30 mark, which still says to go for two.