Should Hoke have gone for two?

[EDIT: There's been much contention about this. I post this in the comments, but it's worth posting here as well: If someone has a model to calculate win probability (other than the Advanced NFL Stats one, because it doesn't really work here), I'd love to see the analysis of win probably for the following (with 7:53 left on the clock and kicking the ball off):

WP(extra point) vs. WP(2-pt make)*.4 + WP(2-pt miss)*.6

I think this is the crux of my argument. My assumption is that WP(extra point) is higher.]

In the wake of Michigan's loss to Iowa, game theorists are criticizing Brady Hoke's decision to kick the extra point rather than go for two on Michigan's fourth-quarter scoring drive. Though I know it goes against traditional game theory to kick the extra point, I can't shake the feeling that it was the correct decision.

Hear me out. Michigan scored to make the game 15-24 with 7:53 remaining on the clock. Game theory states that Michigan should go for the two-point conversion because, if they miss, it will inform the coaches whether or not they need one or two scores with the remaining time, and can adjust their playcalling accordingly. But there's one play that this theory doesn't take into account: a successful, expected onside kick.

First, let's examine the path to victory that Michigan would have to follow for all of the possible scenarios (with the exception of missing the extra point because, well, if you do that twice in a game, shame on you):

Go for 1	Go for 2 make	Go for 2 miss
Defensive stop	Defensive stop	Defensive stop
Touchdown drive	Touchdown drive	Touchdown drive
2-point conversion	Extra point	Extra point
Overtime	Overtime	Expected onside kick recovery
		Field goal drive

Michigan, obviously, elected to kick the extra point. With that decision, the team was essentially playing for a coin flip (2-point conversions are successful about 40% of the time). Kicking off with 7:53 remaining, Michigan needed a defensive stop as well as a successful touchdown drive and two-point conversion. As the game played out, Michigan had ample time for that. Not only did the defense force a stop after 2:41, but they were able to fit in two more drives and a second defensive stop (offensive drives consisted of: 1:13 off the clock preceding a punt, and 2:15 off the clock ebfore stalling at the 3 yard line; the second defensive stop took 1:44). Had they been able to punch the ball into the endzone, they would've had a 40% chance of tying the game and sending it into overtime. From there, it's anyone's game.

If Michigan makes the two-point conversion, the same scenario unfolds as above, but instead of needing a two-point conversion after the possible tying touchdown they only need an extra point. There is ample time for this situation, and it is the best-case scenario.

The problem lies in missing the two-point conversion early in the quarter. If Michigan had gone for the two-point conversion and missed, it's a two-possession game (9 points) with 7:53 to go. In that instance, not only does Michigan have to force a defensive stop (which they do), but also receive the ball, march down for a score, successfully complete an onside kick (about which more later), and drive for another score. Not only does the successful completion of an onside kick present problems, but time then becomes a major factor.

Hypothetically, let's say that Michigan scores with 7:53 left in the game and misses its two-point conversion attempt. They're down nine, kicking off, and need two scores. If the defense produces the identical defensive stop, they will receive the ball on their own four yard line with 5:12 remaining. Michigan's fastest scoring drive of the day was its final one, which covered 57 yards and took 2:49 (0.337 yards/second). If Michigan continued that pace, a drive of 96 yards would take them 4:44. If we're generous and shave off a minute from that time, Michigan is left with 1:28 and probably zero timeouts. In that time, they have to successfully recover an onside kick and move the ball about 35-40 yards to have a makeable field goal for the win.

While this is doable, onside kicks present a huge gamble. According to Advanced NFL Stats (caveats about these being NFL numbers apply, but only barely),

Onside kicks in the NFL are successful 26% of the time. It’s true, but it’s also very misleading. Onside kick success rates are very dependent on whether the receiving team is expecting one...

When teams are expecting it, when WP is about 0.15 and below, the success rate is about 20%. But when teams aren’t expecting it, the success rate averages 60%.

In this situation, Iowa would be expecting an onside kick, making the success rate somewhere at or near 20%. With a true freshman kicker who has never attempted a collegiate onside kick? Michigan's chances would be low.

The point is that going for two points earlier in the quarter, while it would pay off significantly if you convert (40%) basically puts the game out of reach if you fail (60%). Not only does clock management become a significant issue if you miss the two-point conversion early, but Hoke would also be asking his team to play nearly perfect football for close to 8 minutes. With Michigan's current team, that's asking too much.

This is why I feel like the "information" angle of game theory here is short-sighted. Would Michigan's coaches know whether or not they needed two scores? Sure, but getting two scores in that time-frame while playing errorless football is the equivalent of putting the game out of reach. By kicking the extra point, Michigan creates a potentially one-score game and forces Iowa to play errorless football (a fumble or interception changes the game significantly). Most importantly, it removes the variance of a successful, expect onside kick.

As it played out, if Michigan was able to score, that gives them a 40% chance of taking the game to overtime. But that same 40% chance of making the two-point conversion earlier in the quarter significantly increases the win variance and Michigan's ability to convert what is needed for an eventual victory. So while kicking the extra point may not make the game a guaranteed one-score game, it does indicate that you're playing for one more scoring drive. Because with the time remaining, playing for two is nearly impossible.

To beat OSU: Break tendency; play the underdog

Michigan's deep in it going into their final game of the season against Ohio State on Saturday. Rich Rodriguez has long said that he doesn't care about time of possession, and that's pretty obvious from the stats this season (Michigan is 119th in the country in time of possession at 26:22 a game). If Michigan wants to have any chance going up against Ohio State on Saturday, it's going to have to break this tendency and try and grind out the game, slowing it down to a crawl.

A great post a few months ago from Brian at MGoBlog went a ways to explaining it. I suggest you read the entire thing to get the whole scope of it, but the gist is this:

And it's the same for the favorite and reducing their variance: sometimes it's worth reducing expectation to get it, but only in certain situations and when you're a considerable favorite. In Bo's time, Michigan was a considerable favorite much more often and the game lent itself to low-variance moves: a 40-yard punt is much more valuable in an era when ten points is a potentially game-winning number. Anyway, to the assertion above: modern offenses have more variance to them because they score more. Don't lose sight of expectation here: Missouri had a lot of variance in their scores but that was because they averaged 42 points a game. Michigan had far less but they were averaging 20. Offenses that do this quickly are actually more predictable because they get in more trials. Moving fast without sacrificing expectation is advantageous to the better team, which is why Oklahoma was in zero even halfway close games against the Big 12 rabble. (Texas is not rabble, obviously.) Defenses reduce variance by, you know, having safeties that can tackle. The very best defenses are low variance because all of the outcomes have the same result for the opposition: shame and humiliation. In that situation, punting your ass off makes sense, because you're a big favorite, you're not giving the opponent much of an opportunity and you're reducing variance in a way that helps your overall chances of winning. The main problem with Michigan's defense over the last few years has been their suckiness, which by the way increases variance as your defense falls to a point where opponents can drive the field on them regularly.

So what does that mean for Michigan on Saturday? It means they need to chew up as much time off the clock when they have the ball and pray for Terrelle Pryor to arm punt his way to a loss. The other problem here is that it presumes Michigan will be able to stop the OSU offense, um, once or twice or three times, which at this point, seems unlikely.

Having Brandon Minor this week is going to go a long way to make this happen. Without Minor, Michigan's run game (and subsequently, it's most consistent way to run time off the clock) takes a serious hit and depends a lot on Carlos Brown--a player who has made his mark this year on the big play. Vincent Smith, last week, looked like he might have the ability to cut through holes and pick up 4 or 5 yards at a time. If Michigan can get this kind of consistent play from Smith and Minor is out (for the record, it being Minor's last game, I assume he'll play, injured or not), it will go a long way to this end.

When the ball is in Forcier's hand, Michigan is going to need to limit sacks, penalties, and dropped passes. I'd be surprised to see Michigan take more than one shot downfield if they realistically want to win this game--it seems counter intuitive, but the faster Michigan scores, the more chances it gives Pryor and his offense to score. If Ohio State is blowing up Michigan's bubble screens and breaking into the backfield on rushes, Michigan will lose. There's no doubt about it. Also, Michigan is going to need to slow the pace of their offense down. Not that they should huddle up after every play, but taking most of the time off the play clock before snapping the ball would be advantageous.

On the other side of the ball, the key for Michigan is limiting the big play. Ohio State has lived off of the big play this year and has struggled when they haven't gotten it. Misdirection plays are going to be key, like they usually are for OSU, and the safeties' ability to stay home on these will be critical. If Michigan can force Pryor to march down the field, they further take time off the clock and increase the chances that Pryor will throw a pick. It's an uphill battle and Michigan needs to treat it as such if they want to have any chance in this game.