i find this extremely interesting
Game Theory Bits Featuring Jim Harbaugh
Three things of interest happened over the weekend to the Everything Is Agricola portion of my brain:
1. Michigan had it first and ten from their one. Q: what's the difference in overall value between sneaking it for two yards and just flat-out taking a safety? I'm thinking it's not very large. Michigan did that and threw incomplete twice and then had to use their no-blocky punt formation. The result was EMU getting the ball around the Michigan 30.
I wonder if it makes more sense to just act like you're on the ten or something. It seems like giving away that down makes your life much tougher when the alternative is 1) rare and 2) maybe not that bad. You're giving up two points but you're probably gaining half of that back in field position. The difference between a punt from the five and a punt without any rush from the 35 (since punters usually drop back 15 yards) is big.
[UPDATE: I asked the Mathlete. He responded thusly:
1st and 10 at your own one has an expected value of -1.71. The offensive value is +.79 and the ensuing opponent possession is worth 2.50.
At 2nd and 8 the offense drops slightly to +.76 but so does the opponent to 2.27, improving the offense's expected value by 0.2 to -1.51.
A post-safety kick off from the 20 yields the opponent an average of 2.09 points but forfeiting the offense's expected points, giving up 2 points and getting back only a slight benefit in defensive EV.
The play is worth -2.38 points on 1st and 10 from the one and -2.58 on 2nd and 8 from the 3. The only time you can make a case for it is on fourth down when the offense has exhausted its value and it's the fourth quarter and the 2 points on the scoreboard won't be a major swing, i.e. between 4 and 6 points.
So it's a big deal. I'm following up to figure out whether pretending you're at the 30 and just running your offense is a better play than the usual strategy.]
2. Jim Harbaugh did something stupid. The scenario: San Francisco has just kicked a field goal to go up ten with 11 minutes left. A 15 yard penalty would put the ball on the Dallas 22 with a first down up seven. Harbaugh declines the penalty and San Francisco blows the game.
This does seem like a huge, stupid error. NFL kickers are near automatic from within 40, you might get a touchdown, and even if you don't you've bled another two minutes off a clock that's significantly in your favor.
The NFL win percentage folk say this is no big deal, though:
The 15-yard enforcement on the kickoff ensures a touchback. By taking the 3 points, the 49ers have a 10-point lead with the Cowboys having a 1st down at their own 20. This gave the 49ers a win probability (WP) of 0.90.
Accepting the penalty for a 1st down gives the 49ers the ball at the Dallas 22, up by 7. This is worth a WP of 0.91.
The percentage play would have been to take the points off the board and accept the 1st down, but just barely. In the grand scheme, this is a very small error. The common punt or FG attempt on 4th and short in most game situations is usually more costly, and most fans and analysts hardly take note of them.
I'm not sure I agree. For one, this situation seems like a stat more like save percentage than anything else. When 90% is the baseline success rate there's a big difference between 90% and 91%. If you look at it from a chance of losing perspective, forgoing the penalty increases your chance to lose by 11%. In hockey that's the difference between an AHL goalie and an NHL one.
3. Before that Jim Harbaugh did something even dumber. But even if we put that aside, Harbaugh went maximum puntasaur just to try the field goal. It was fourth and one on the 37! Doing anything other than going for it is the beyond stupid. It goes into the realm of irredeemable. According to the WP folks, that decision swung SF's chance of winning from 87% to 83%, a 31% increase.
The moral of the story, as always, is that if you find yourself at a poker table with a football coach other than Bill Belichick mortgage everything you have.
This stuff just must be not that important. Recruiting and strategizing and fundamentals and all that stuff has to be about 98% of the job or the odd guy who's heard of expected value would instantly shoot to the top of the league. What league? Any league.
Brady Hoke will disappoint sooner or later; the best we can hope for is that he won't do it as spectacularly as some coaches do. /shakes fist at 2005 Ohio State game