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.
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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
September 19th, 2011 at 3:58 PM ^
Just this past weekend:
I am pretty sure I saw Fickell punt in Miami territory late in that game. Based on the later clock management perhaps he was just throwing in the towel.
Same with the sainted coach from East Lansing -- I couldn't believe it when I saw them punting from mid-field down 15 with under 5 minutes to play...It was like he KNEW the ND returner was gonna muff that punt (Shenanigans!!) or was just plain stupid.
September 19th, 2011 at 4:11 PM ^
Fickell's actions (or lack there of) in this game with Miami would be enough to not keep him around past this year if I was an Ohio fan. It looked like he was clueless there at the end not using any timeouts when there was at least a chance his team could come back. Inexcusable.
Granted, as a Michigan fan, I rather enjoyed the show. I was pleased to see Ohio actually getting punished for the 5-game suspensions.
September 19th, 2011 at 4:00 PM ^
Did the right thing vs EMU. I held my breath at 4th and 7 from EMU's 37's. But he left his offense on the field so Denard could miss Hemingway by 4 yards and get picked off.
But it was still the right call. Maybe he didn't learn everything from Carr.
September 19th, 2011 at 4:07 PM ^
I honestly don't see that many stylistic similarities between Hoke and Carr outside of beginning public comments with "Well..." and saying "tremendous" a lot.
Both game theory and how they hire/work with with coordinators appear to be VERY different.
September 19th, 2011 at 4:26 PM ^
I probaly saw 3 Ball State games when he was there, and maybe 3 SD State games. I'll defer to someone who had.
September 19th, 2011 at 4:13 PM ^
Let's see what he does when he has a punter that has greater than a 1% chance to get the ball between the goal line and the 10 yard line.
September 19th, 2011 at 4:03 PM ^
While we're talking NFL on the front page, can we get a chart for Stafford's throws yesterday?
September 19th, 2011 at 4:06 PM ^
Interesting point on the first and ten from the one. I agree that the 1st down plow between the guards is a worthless and wasted down. I would much rather prefer Denard do a qb keeper from the shot gun, as I can not recall a time when that has ever lost yardage and he usually can find a way to at least get 3-5 yards with it.
September 19th, 2011 at 4:13 PM ^
or how about a Brady to Welker flare for 99.5 yards & a TD like last Monday night in Miami?
GO BLUE!
September 19th, 2011 at 4:13 PM ^
the pats had 1st and 10 from the own one in each of their last two games. both times they threw it. last week that resulted in a 99 yd touchdown and this week a ~14 yarder. it's probably an even easier play than normal because the defense is expecting you to run and loading up the box.
September 19th, 2011 at 4:24 PM ^
It helps when you don't telegraph your intentions by lining up in the goal line formation.
September 19th, 2011 at 7:41 PM ^
1st and 10 that close - to me that's the perfect time for the goal line formation except you pass out of it. With that formation the defense is expecting run.
September 19th, 2011 at 4:14 PM ^
Michigan lined up in the shotgun, Denard kept it on the zone read, and he almost took it to the house.
September 19th, 2011 at 4:19 PM ^
Well, you're also giving up a possession in addition to points. It's like the only have so many possession, no matter whether you score quickly or slowly, because it goes back to the other guy thing - this is the only case where the other team scores, AND they get the ball back. And frankly, in pretty decent field position, because free kicks are not kickoffs (yes, it's still a lot better, but still not a bad place for an offense to start). So you're are making that 3 or 7 you're giving up maybe 5 or 9. Maybe back when Purdue gave it up in the snowstorm they thought it was worth the field position, but not in general.
Now, if you want to argue that playing risk free so you don't give up a TD on your goalline is maybe not worth it if they're likely to score one from your 30 anyway (because while you at least have a chance to stop them in the later, you're taking away a good portion of your chance to move it out), I could see that argument.
So I guess safety=bad; not running it into the middle on first down=definite maybe.
Edit: #3- Don't you mean it decreased SF's chance to win?
September 19th, 2011 at 4:34 PM ^
Brian is talking about the fact that we were looking at surrendering a possession in either scenario. In this particular case, you were probably looking that trading 2 points for 30 yards of field position. The other factor is that there is a possibility that you do get a first down. If you get the first down and move about 5 more yards in your next set of downs, you also get to use an actual punt formation, which probably cuts the return by 10-15 yards. So, in the three scenarios, you are (a) 3 and out and you are no better off or worse (b) surrender 2 points and take your opponent about 30 yards out of FG range or (c) get a drive started and at worst put your opponent about 30 yards out of FG range. In B and C, if you can hold them to 3 and out or just prevent them from moving 30 yards, then you have successfully taken a FG off the board, making the risk of 2 points worthwhile.
September 19th, 2011 at 4:46 PM ^
I said it's reasonable to want to take a chance at some reward by running a play on first down, over just running a low risk low reward play that dooms you to a punt. But it's whether the safety is a better way to avoid this than running up the middle.
Not all punts from the endzone result in automatic FG range. Maybe in the case of our coverage, but that's not the norm. If you hold them to 3 and out in either case, you're probably removing the 3 points either time. And then you're making them go through the descision Harbaugh is rightfully getting killed for whether they go for it and give up great field position, or punt it trying to pin the team back again.
In the case of the safety you're giving back possession just like you do when you have to punt, but it's the only play you're giving back possession after turning your offensive drive into a scoring drive for the other team. Even if you pick six it, you get the ball back after. You'd really have to show that the average drive of another team won't just get them back into FG range, judging from the difficulty as the field shortens. Because ideally you're talking giving up 2 instead of 3 (though I don't know how many teams would have taken a safety to prevent a FG against us last year), but depending on how many yards they can probably be expected to get, you may very well be talking giving up 5 instead of 3.
September 19th, 2011 at 6:34 PM ^
"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."
I was going off of this. I assumed that this was an extension of his first thought, but I can see where those were seperate but parallel thoughts.
September 19th, 2011 at 4:11 PM ^
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.
Brian, it's not that it's not important, it's that it's not important when EVERYONE except one person is on the same side. It's essentially a wash, and what allowed Oakland with Billy Beane to win a bunch of games and what allows Belichick to continually win. They exploit the inefficiency to win games on the margin. Until enough other coaches do though, it's a wash and doesn't matter.
TL;DR - the stuff doesn't matter and is a bonus, until not paying attention to EV matters and teams are disadvantaged for not caring about reality and favoring conventional wisdom.
September 19th, 2011 at 4:12 PM ^
I must have blocked it out of my memory.
September 19th, 2011 at 4:21 PM ^
Fourth and 4 punt from around the 35 with 3ish minutes left while leading by something under a FG.
September 19th, 2011 at 8:33 PM ^
It was 21-19. I think there were more like 4-5 minutes left, though.
September 19th, 2011 at 11:25 PM ^
4:18 left on the clock when OSU got the ball and then proceeded to march down the field like our defense didn't even exist.
September 19th, 2011 at 11:44 PM ^
Given that shitty prevent shell we were running it may as well have not existed. Good thing it let them score with only like 25 seconds left in a time before Denard.
September 19th, 2011 at 4:19 PM ^
Hasn't it been proven that football coaches are an extremely conservative lot? They think it's better to lose by playing conservatively than to lose taking chances?
I equate it to this: If you're counting cards, you can obtain a slight advantage over the house. (all card counting caveats apply). When your baseline win % is 49.5% and you can increase that slightly to 55% when the count is high, that's obviously way better than you would normally expect, the difference between a NCAA Goalie and a NHL one.
Now there's also guidelines about how much to bet given what count, but that's where the risk is, as they're guidelines. If you're aggressive, you can push more money in and if you lose, you lose spectacularly ala NE vs. Indy a few years ago. If you're conservative, maybe you only double your bet. If you win you still win, just not optimally, whereas if you lose, you've lost little and it's instantly forgettable, lost in the shuffle.
The point is that until the general population is wise to those facts, it's much wiser to lose conservatively than spectacularly.
Edit: BTW, I thought the worst call of the game was when Eastern kicked their short field goal instead of going for it on 4th and Goal. You're Eastern Michigan playing Denard Robinson. You have to go for the TD if you're that close. At the end of the day, will it matter if EMU loses 31-0 or 31-3?
September 19th, 2011 at 6:36 PM ^
If you remember, Eastern had just stopped Michigan, I believe twice, and they themselves had been stuffed at 4th and 1 at the goal line. Getting 3 points to go up 3 to 0 is a good call. Now if EMU had instead looked into their crystal ball and seen that Al Borges was going to shelve MANBALL-Power the rest of the game and score 4 TDs on 5 possesions, then yes, they should have acted like it was the end of the game.
The thing that always blew my mind about my probability and statistics classes was the situation in coin flipping. While it's very improbable that you can get a Heads result 20 times in a row ( and thus always betting Heads is NOT a sustainable tactic), the probability that you get Heads after 19 Heads in a row is still 50/50
Running Denard has a great likelihood of getting lots of yards. But it's also got a chance to get him hurt, which then drops his chance of getting yards next time to zero. But if you never run Denard and get zero then it's just as good as if Denard is hurt, so why not take the chance at him getting hurt?
This is the same issues you have playing poker, or really any other game theory setup. You have to play with the situation handed to you. If it were as easy as always picking the 100% chance at success, then Bill Belichek would have to start putting Super Bowl rings on his toes by now. Even if you always make the smart choice, it doesn't mean you will succeed on any individual instance, but in the long run you should be more successful than everyone else.
This is great if you are playing baseball and have 300 opportunities to win a game. It's a little different when you have 12 opportunities.
Now let's move on to something more valuable to prove like our present Turnover margin isn't sustainable because everything regresses to the norm rather than it's all a result of "Toughness". How do we know we're tough? We can Hear It!
September 19th, 2011 at 4:16 PM ^
re the first harbaugh example - you definitely are right. to insist otherwise is to deny context. you can only move the expected win percentage 10 in the right direction. 1 of those 10 points is huge.
September 19th, 2011 at 4:17 PM ^
I know this is complete circumstantial because there no way any coach would tell a player to do this but regarding the Vincent Smith TD in the Notre Game:
Wouldn't the +EV play be to fall down on the one yard line instead of scoring? Especially with our D the way it is. If he falls down, then say Denard falls down at the 1 on first down. I don't remember ND's TO situation but we have at least ran through all of them or burn some clock. We would then have 2 downs to punch it in from the one and at worst overtime with a FG the size of an extra point. I just remember at the time wishing that we hadn't score that TD so quickly.
I know, purely a hypothetical since no college or NFL coach would ever risk that, and would likely not want to coach a player to not go 100%.
September 19th, 2011 at 4:24 PM ^
IIRC, Brian Westbrook of the Eagles took a knee on the 1 or 2 yard line instead of scoring a couple years ago to ice a game. It was an example of great decision making.
September 19th, 2011 at 4:28 PM ^
Or losing at that point?
September 19th, 2011 at 4:31 PM ^
Leading.
http://nbcsports.msnbc.com/id/22301082/
Jon Runyan was the one that told him before the play to take a knee. Wooo Michigan smarts!
September 19th, 2011 at 4:37 PM ^
It' a great play, because it takes the chance of losing from .0001 or something small with them needed to score twice with an onside, to .000000000000000000000000001, or the one time in history that guy (think it was an Eagles-Giants game) actually fumbled the snap to down it and run out the clock.
But in his example we were still LOSING the game. And while, it may work out to run it like he suggested, and has some good strategy to it, I'm just not sure how that works when you're actually playing the game to think all that through. And then you damn well better score. Because if you don't, as a player and or coach, you'll forever be known as the guy who had a clear path to the game-winning TD, but decided to get cute and take knee to run clock and watch his team get stuff/fumble it away/miss the FG.
September 19th, 2011 at 4:49 PM ^
I think you always take a score when down points, short of maybe trading time for downs when you've already consigned yourself to a very makeable field goal when you'll take the lead with the FG and you have a super awesome kicker. I can't think of a time when scoring will LOWER your win expectancy.
September 19th, 2011 at 6:39 PM ^
If you are down by a score with 2 minutes left, I would think it would be wiser to run the clock and score than give it back to the other team with plenty of time to move down the field and score, especially if they only need a field goal.
September 20th, 2011 at 1:13 AM ^
Sure, but if you have a %100 chance of scoring, you should still take it, regardless of the time. 7 points now is probably better than a possibility of 7 points in the future. Besides, say VIncent Smith intentionally goes down - do you waste two downs to use NDs timeouts and burn clock to < 30 seconds? Who knows what happens then.
There's probably some combination of time and yards in which scoring right away is worse than downing the ball, even though you're not winning. But my gut sense is that those times would be limited and rather difficult to figure out in the few seconds you're running with the ball. So "score when you can" is probably a good rule, unless you're winning. Then you can down it.
September 19th, 2011 at 4:26 PM ^
But how do you tell a player when you're that far out (the screen wasn't a 5 yard play) to fall down at the one, IF you get open, and towards the endzone (where he was almost tackled twice on the play) and to be thinking about that, vs. thinking about dodging guys and trying to get into the endzone. It's a game of emotions, and fast reactions.
Then just statistically you'd have to take into account what's more likely...getting stoned on 3 straight plays vs. someone going for a TD in just a minute (remember, a FG wasn't doing anything for them).
The better example I see in the NFL time and time again is when the other team has the ball, and if they get a first down they can just run out the clock, why you don't let them score and make them make that tough mental decision (with guys who are worried about how many TDs they get because it might hit a contract bonus) so you can get the ball back, and maybe have to score, onside, and score, but at least gives you a chance with a possession rather than watching them just take a knee and run out the clock. It's seen as "giving up", when it really is just giving yourself a chance to win.
September 19th, 2011 at 4:33 PM ^
It was Jon Runyan who told Westbrook in the huddle not to score a TD if he had the opporunity. (Link) Michigan genius.
September 19th, 2011 at 4:50 PM ^
Lloyd actually did that against Illinois in 1998. We were down 28-27 and Illinois had the ball. UM let Illinois score a TD so that we got the ball back down 8. We wtill wound up losing, but not until we nearly scored a TD that would have made it 35-33 with a chance for a game-tying 2-point conversion.
An interesting comparison is the 2005 Rose Bowl, in which we led 37-35 with Texas driving late. Once Texas got into FG range, we could have let them run it in, and get the ball back with a chance to win. But the question there is, at what point on the field do you let them score? If the opponent is at the 25-yard-line, it's still a 42-yard FG which is no gimme for a college kicker--but just 5 more yards makes than an easy 37-yarder and if you elect to continue playing defense, you are taking precious time away from your own offense.
September 20th, 2011 at 10:45 AM ^
Because you never know what might happen. A really close NFL FG is about the surest thing in sports, but a snap/hold can go wrong, you could fumble it centering, all sorts of things. And in the Rose Bowl case, it wasn't even close to NFL XP sureness. Now, they might have used their timeouts more wisely in that situation, but they certainly shouldn't have let them score...because they were just an extra knuckle away from blocking it and winning the game.
September 19th, 2011 at 8:35 PM ^
Given how stout ND's run defense is, I would not have been in favor of that. Take the TD where you can get it.
September 19th, 2011 at 4:24 PM ^
it's that they pay off in the long run, and for most coaches, there is no long run. It doesn't matter if your strategy is better, becaue if it's different and you lose, then it's your fault, therefore being different is wrong, therefore they need to replace you with a coach that will make conservative decisions. If your strategy is better and you win, then you're just one mistake away from losing, in which case it's your fault, and see above.
So a coach like Belichick can make the higher-percentage decision because a) he is the Honey Badger of coaches and b) he isn't getting fired no matter what. Harbaugh can't do that (even if he were inclined to) because he has about two years to turn the 49ers around before people will be calling for him to be replaced with Generic NFL Coach Possibility X.
September 19th, 2011 at 4:27 PM ^
but the problem with a bunch of short-term -EV decisions is that, even if you're not getting criticized for any individual one, over time you're costing your team football games in a way that will inevitably get you fired unless you recruit like Jim Tressel (see: Wannstedt, Dave).
September 19th, 2011 at 4:32 PM ^
There is "over time" unless you've already won 3 Super Bowls, and can do that stuff without consequence. Over time it will even out, but if it doesn't work, it has the appearance of a more spectacular fail, and you don't last long enough to get to see the percentages work your way. If you're to the point where your back is to the wall anyway, you might as well do it, but if you still have a chance to establish yourself you're going to need them to succeed, and right away. I think we're all familiar with how some bad luck can turn perception around quickly and then it's really hard to dig out of the hole around here.
September 19th, 2011 at 4:46 PM ^
my point is just that consistently making -EV decisions is going to get you fired eventually anyway, because you'll win fewer football games.
September 19th, 2011 at 4:24 PM ^
Fire... Harbaugh?
FIRE HARBAUGH!!!!!!!!1!!!!1!!!!!!!!!!
September 19th, 2011 at 4:26 PM ^
This extremely hurt me cause Im a niners fan. :( Sucked that our 1 and 2 WR didn't play. He may have had more confidence on throwing the ball more instead of being SO damn conservative like the previous 7 OC's. I know he's a HC, but it was all his philosphy! Bad! He's a rook though... he'll learn!
September 19th, 2011 at 4:30 PM ^
If you're trying to win the game, yeah, the stats guys are right. But if you're trying to keep your job, then it makes sense to play conservatively. If you lose you are less likely to be criticized if you are too conservative than if you are unorthodox and aggressive. Doesn't that explain the conservatism of football coaches? They are playing the "I want to keep my job" game.
September 19th, 2011 at 4:50 PM ^
IIRC, this is the Romer paper's conclusion.
September 19th, 2011 at 4:48 PM ^
This argument only holds when you include the assumption that both teams are roughly average in a number of areas. the .9 vs..91 moves a lot if the 9ers have a K with better than average long field goal ability, an offense prone to turnover or a defense likely to give up big chunks of yards, etc.
I'm not knowledgeable enough of SF football to speculate. you know who might be? their head coach. Just like the "right" play in Blackjack changes on some hands if you know the deck is face card heavy or your expected value in a poker hand changes when your buddy signals that he already folded with 1 of the aces your opponent needs, you can't assume that league average historical performance is the best input to this equation.
September 19th, 2011 at 4:56 PM ^
I agree with you to a point. During the OSU-Miami game the 'Canes had a 4th and 1 around the OSU 40 up 17-6 in the fourth, and I thought they should punt. But that was an extreme outlier based on BAUSERBOMBs.
In an NFL game where yardage is kind of close to parity I don't think the percentages swing enough to make the 55 yard FG attempt even close to reasonable. You can make an argument for the penalty being a feel call, but not fourth and one from the 37.
September 19th, 2011 at 8:40 PM ^
At that point in the game Harbaugh may have thought Kitna was in for the rest of the game. Not 100% sure but the sideline reporter definitely reported it late in the 3rd, just not sure if Romo had returned or not. That could effect your decision at that point.
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