I’m always interested in creative ways to maximize your team’s chances of winning. A few weeks ago, I wrote that when trailing by 14 or 15 points, teams should go for two if they score a touchdown. A different scenario came up during the Ravens-Cowboys game, as Baltimore was up 24-23 with just under five minutes to go when Ray Rice went in for a one-yard score. At that point, some clamored that Baltimore should have gone for two and essentially put the game away. A conversion would have given the Ravens a 9-point lead, while a miss would still leave Baltimore a touchdown. On the surface, it might sound like a risk-free proposition, where even if the gamble fails, you’re still in good shape.

But I don’t think I’d advocate for the bold decision in that situation. In essence, you’re deciding whether your offense is more likely to convert when going for two than your defense is likely to prevent your opponent’s attempt. The decision depends on the likelihood of success: If the league-average rate was 75%, then you’d want to go for two, but if the average rate was 25%, you’d rather force your opponent to have to convert.

In reality, the conversion rate hovers around 50% in the NFL. From 2007 to 2011, teams went for two on 269 plays and converted on 130 of them (48.3%). We can break that down further:

• On 21 quarterback runs, the conversion was successful 13 times (62%). That is made consists of a 6-for-11 rate on runs up the middle and a 7-for-10 rate on other quarterback runs (which may include some scrambles on designed pass plays).
• On 50 running back runs, teams converted 33 times (66%). That includes being 21-of-32 on runs to the outside and a 12-for-18 rate on runs up the middle (which includes two Danny Woodhead runs from shotgun).
• There were also three trick plays with wide receivers throwing passes (Cedrick Wilson, Josh Cribbs and Anquan Boldin) with two of them being successful.
• On the other 195 pass plays, four times the quarterback was sacked (2%), twice the pass was complete but short of the end zone (1%), and 107 times the pass was incomplete (55%). That leaves 82 successful passes (42%) on two-point conversion pass attempts.

It’s tempting to say that teams should simply run the ball more frequently in these situations, but I think we need to be careful and not let the data speak too loudly. The fact that teams passed on 74% of these plays is itself an indication that passing is the higher-percentage play. When a backup running back has a higher yards per carry average than the starter, it doesn’t mean that the starter is the worse player. I think running is a nice surprise move in these situations, but if teams ran more frequently, the success rate would surely drop (of course, the success rate on passes would then increase, which might make it wise just as a matter of course for teams to try to run more frequently in these admittedly rare situations).

In any event, I don’t think teams should get overconfident about their ability to convert when going for two. However, it’s worth noting that usually it is losing teams — and perhaps that means bad teams — that are going for two. Indeed, on only 108 of the 269 conversion attempts (40%) was the team winning before attempting to go for two. In those 108 cases, teams converted 60 times (56%). For what it’s worth, 31 of the 71 rushing plays (44%) came in these situations, and teams were 41-of-77 (53%) when passing with the lead.

So there does seem to be something to the idea that “bad” teams are dragging down the league average rate, although we’re dealing with small sample sizes. It’s the easy way out, but my gut tells me the actual rate really is right around 50/50.

In that case, does going for 2 up by 1 (before the touchdown) make sense? I don’t think so, unless your offense is much better than your defense (or your opponent’s offense is much better than its defense). In some ways, we should be indifferent about whether we go for two or if our opponent is forced to; it’s like caring about whether you get to call the coin toss or your opponent does.

Say you are up by 1 point and score a touchdown with two minutes to go. Let’s stipulate that the opponent has a 28% chance (to use what will be round numbers in a minute) of going down and scoring to tie it up. If you kick the extra point to go up 8, you have a 93% chance of winning — a 72% chance you stop your opponent plus a 14% chance that even if they score, you stop them on the 2-point conversion, plus another 7% chance that even if they force overtime, you win.

Now, if you go for two and convert, let’s say you have a 100% chance of winning. So converting gives you an extra 7% chance of winning. If you go for two and miss, you still have an 86% chance of winning — the 72% chance your opponent does not score plus the 14% chance you win in overtime. So choosing to go for two and missing only lowers your odds 7% — again, teams should be relatively indifferent about whether it is them or their opponent who ultimately goes for two, assuming the roughly 50% success rate.

But the above analysis is ignoring something, which to me, makes the decision easy. With a minute to go, and a good offense and bad defense, maybe you go for two. But that’s not the situation Baltimore was in — the clock read 4:41 when Rice scored his touchdown. Here is the part that is counter-intuitive but true assuming a 50% conversion rate: the difference between being up by 7 or being up by 8 is *larger* than the difference between being up by 8 or being up by 9.

That’s because going for 2 and converting doesn’t end the game; your win probability doesn’t shoot up to 100%. Down 9, the opponent will play more aggressively, knowing they need two scores. Assume you go for 1 and extend the lead to 8. If your opponent faces a 4th and short on their next drive, they may still punt, because it’s (in their minds) a one-possession game. They won’t punt if down by 9. They are more likely to take their time trying to score (which is beneficial to you, the leading team), which means the odds are very low that they win in regulation. Trailing by 9, they know they need two scores, and will play more aggressively to win the game. To me, I don’t see any reason to incentive bold moves by my opponent, and the more time remaining, the worse the decision to try to “ice the game” by going up 9 looks.

The Ravens game provides a good example. Suppose Baltimore had gone for two and missed. Well, the Cowboys went down and scored, and would have kicked off to the Ravens. Instead — in this case, it is irrelevant that Baltimore kicked the XP and Dallas missed the 2-point conversion, we can assume Baltimore went for two and made it — the Cowboys went for the onside kick and got the ball back. That’s not a move you make in a tie game, but one an aggressive team trailing has to do. Going for 2 early doesn’t bring your win probabiliy up to 100%, and this effect is magnified the more time remaining in the game.