## Should Mike Mularkey have gone for 2 against the Packers?

The Jacksonville Jaguars faced an uphill battle on Sunday: they were 15-point underdogs against the Packers in Lambeau Field. Trailing 14-6 in the final seconds of the first half, Blaine Gabbert threw a one-yard touchdown pass to tackle Guy Whimper. At that point, Mike Mularkey decided to go for two in an attempt to tie the game before the teams went into the locker room. The two-point conversion attempt failed, and Jacksonville ultimately lost, 24-15. So, did Mularkey make the right call?

In a lot of ways, this is similar to the decision Chan Gailey faced against the Titans in week seven. Essentially, Mularkey would need to calculate:

— (A) Jacksonville’s win probability in a 14-12 game
— (B) Jacksonville’s win probability in a 14-13 game; and
— (C) Jacksonville’s win probability in a 14-14 game

If we assume a 50% conversion rate on the 2-point attempt — more on this in a minute — then the question is a simple one. We just need to determine whether the difference between (A) and (B) is greater than or less than the difference between (B) and (C). Green Bay was set to receive the ball at the start of the second half, so according to Brian Burke, the values for (A), (B), and (C) are and 41%, 45%, and 48%.

I also looked at all games since 2000 where the team was set to kick to start the second half and was tied, trailing by 1, or trailing by 2 at halftime. In 275 tie games, the team kicking off to start the second half won 52% of the time. There were 70 instances where the team was trailing by 1, but they won just 39% of the time. And in 32 situations where a team was trailing by 2, the trailing team won 41% of the time. The sample sizes here are not large, and the set is of course biased; teams kicking off at halftime obviously had the ball in the first half, so if they trailed at halftime, that’s a signal that they were the inferior team.

So Burke’s model tells us that it’s a very close call; a small sample of results indicates a strong preference for being in a tie game. We can also look at Football Commentary, which theorizes that a team needs only a 36% chance to convert to make going for 2 the right call. So as you can see, the results are a somewhat over the map here.

My thoughts? It’s very close. It’s similar to the Gailey decision, but the uncertainty is magnified here with 30 minutes remaining instead of fifteen. There are a lot of ways for the game to unfold that make me think the difference between (A) and (B) is pretty close to the difference between (B) and (C). Still, my gut does tell me that — assuming a 50% conversion rate — it probably *is* better to go for two, but it’s certainly not obvious or a slam dunk. If I was a Packers fan, I would have preferred to see the Jaguars kick the extra point.

That said, understanding the resulting win probabilities is just one part of the equation. Let’s look at some of the others.

• What are the odds of converting the two-point attempt in that situation? For a league-average team, I think it’s right around 50/50. Consider the implications of that statement: the expected point values of going for 2 and kicking the extra point are essentially the same. Therefore, there really is no such thing as it “being too early” to go for two. When people say that it’s “too early” in the game to do something — go for it on 4th down, go for 2, kick an onside kick — they’re essentially saying “late in the game, even with a negative expected value, a high-variance strategy may be preferable to a low-variance strategy with a positive expected value.” But implicit in the “too early” idea is the fact that the high-variance strategy has a lower expected value. That’s not the case when it comes to going for two. Therefore, there really is no such thing as it being “too early” to go for two; there are probably some teams out there that would be justified in going for 2 after every score early in the game.1
• That’s just the league average, however. What were the Jaguars’ odds of converting the attempt? Certainly below league average, because Jacksonville sports a below-average offense at best. To the extent that a team is in a “now or later” situation where you know you’ll need to go for two, calculating a team’s individual likelihood of success is irrelevant, but that wasn’t really the case here. On the other hand, it’s a little discouraging for a coach to say that his team shouldn’t choose the best option because his team’s offense is so far below average. If you want to make the argument that Jacksonville should have kicked the extra point, in my opinion, the strongest reasoning would have been because they were unlikely to make it because they’re one of the worst teams in the league. So there’s that.
• However, being a bad team — and a severe underdog — is a reason to go for two. As a heavy underdog you always to take take advantage of high-variance strategies. Against the Packers, the option to increase your variance without decreasing your expected value should have been very attractive to Mularkey. This cuts against the fact that the Jaguars were unlikely to convert, although again, I’m not sure a coach wants to say ‘we went for two because we’re not very good.”
• Another option to consider for Jacksonville would have been to call a running play. From 2007 to 2011, teams converted on 33 of 50 running back runs on two-point attempts. I suspect that the success rate was so high because the defenses in those situations expected the pass, and as teams run more frequently in two-point tries, that rate will go down. It’s also a rate based on a pretty small sample size. Still, one could argue that the Jags were correct in going for it but should have ran the ball. On the other hand, the play call seemed pretty good to me, and I’d blame the missed conversion on execution, not playcall. It’s easy with 20/20 hindsight to say they should have tried a different method, but personally, I’m far from convinced that they would have been more likely to convert had they chose a running play.

There are two other key takeaways from this decision. One is the absurd notion that the Jaguars “hurt” themselves because when they trailed by 9 later in the game, it was a two-possession game. This is exactly the sort of “logic” that prevents teams from making the right call in other situations, such as whether to go for two when trailing by fifteen. Yes, Jacksonville was in a two-possession game when trailing by 9 late in the game, but that’s only because they missed the two-point conversion! If they had kicked the extra point and instead were trailing by 8, it still would have been a two-possession game because the Jaguars missed their two-point conversion attempt. There’s no reason to think that the Jaguars would have been more successful on their two-point conversion if they kicked the extra point to cut the lead to 14-13, the Packers scored a touchdown, the Jaguars scored a touchdown, and then Jacksonville went for two. In fact, knowing that Jacksonville was going to miss their first two-point conversion attempt of the game was useful information, and it is always better to learn that earlier rather than later. An 8-point game isn’t a one-possession game when you are going to miss your two-point conversion attempt, a fact that seems to get lost on many who want to extend the amount of time one feels that they’re “in the game.”

Lastly, Aaron Schatz has argued that those in our community need to stop arguing for aggressive, unconventional action when the difference in win probability is small and instead focus on the obvious, slam-drunk decisions. I think there’s a lot of merit to his argument. This was a move that I agreed with, but I only find going for it slightly preferable to kicking. This wasn’t the right horse to hitch to hitch to if you’re trying to convince folks that coaches need to be more aggressive. That’s because when the decision fails, the backlash is going to outweigh the small gain in win probability. If Mularkey had elected to kick the extra point, almost no one — stats guys included — would have batted an eyelash.

1. Obviously this doesn’t change the fact that going for 1 is the right call in many circumstances, but that’s based on win probability and not expected point values. Down 6 with 30 seconds left, a team that scores a touchdown should kick the extra point regardless of the expected value of going for two. []
• Danish

I need you guys to point out where I’m wrong here. The distribution of points scored on a series of two point attempts is binomially distributed. As is the case of extra point kicking, the difference being the probabillity parameter ie. the chance of scoring. If you assume a 100 percent conversion rate on extra points and a 50 rate on two pointers, you get the same variance! It seems counterintuitive – where am I wrong here?

• NateTG

> …you get the same variance! It seems counterintuitive – where am I wrong here?

http://en.wikipedia.org/wiki/Variance#Discrete_random_variable
Variance is the sum of the *squares* of the differences from the mean/expected value.
Let’s say going for 1 is 99/100, then the expected value is .99 the variance will be (.001*.001)*99/100 + (.99*.99)*1/100=.0098…
And going for 2 is 45/100 so the expected value is .9 and the variance is (1.1*1.1)*45/100+(.9*.9)*55/100=.99

So the variance on going for 2 is just about 100 times the variance of a PAT.

• Richie

Just like the Chan Gailey post, I think I would kick the PAT here. There’s still a lot of game to be played, and I like taking the sure point. They could be down 14-13, and the Packers kick two field goals in the 3rd quarter, so they are down 20-13. A TD+PAT ties the game.

The one caveat is that Jacksonville is not very good, so there’s a chance they will never be within scoring range again. So it might be wise to go for the tie there, and hope your defense can shut down GB the rest of the way. But again, there’s lots of game time left to hope that holds, and much more likely that the Packers’ offense wakes up.

• Jay