there's always next season
take the +EV, no matter how small
there's always next season
take the +EV, no matter how small
While it is true that we always want to make the most +EV choice, in the case of a football team, the EV in question is not yards gained or points scored, but games won. We can choose a play that does not maximize our yardage EV, but does maximize the chance of winning the game. (This is where the analogy of tournament poker comes in; we want to maximize chances of winning the tournament, not our chip EV.)
A completely obvious example of this is a late-game scenario. It's 4th and goal on the 1 with 5 seconds left in the game, and the team trails by 2 points. Our points EV is maximized by going for the touchdown, but clearly the right choice is to kick a field goal, since the goal of a football team is to win games, not score as many points as possible.
I would guess that pulling the goalie results in a lower expected value of the total net scoring differential.
Adapting the ideas of Jensen's Inequality
is not equal to the
What a hockey coach wants to maximize is the area of the distribution resulting in a TIE GAME OR BETTER. If pulling the goalie widens the distribution, pushing more area into the TIE GAME OR BETTER section, then he doesn't care that the widened distribution also makes it far more likely that the opposing team scores, and in fact will likely hurt the teams season Goals For/Goals Against differential. Obviously, it is maximizing the win-loss function that the coach cares about.
OP is right, A single game as an overwhelming favorite applies more to a tournament poker type idea than a cash game idea.
In cash game, yeah, do it. EV is EV, in the long term, it is a profitable play.
In a single game, there are a limited amount of plays. If you have an advantage, you'll want to lower variance and only take the highest EV plays. As an underdog, you'll want to take more chances of high risk high reward plays. This is basically what Urban Meyer was saying in that he didn't have to take chances because the way TN was playing, they had no chance of winning the game.
If you really care about learning the differences between tournament and cash poker, this is the difference between ICM play in tournament poker where more factors are taken into account than just the EV of the situation.
In the example OP gave though, it'd still be a snap-call in almost any situation, fwiw. The advantage of tripling up in chips as at least a slight favorite is more beneficial unless the other 8 players are complete drooling retards who decide to hand you chips without you ever putting them at risk.
"If you really care about learning the differences between tournament and cash poker, this is the difference between ICM play in tournament poker where more factors are taken into account than just the EV of the situation."
I'm not sure who this is directed at, but if it's me, that would be pretty funny.
In the end it comes down to we make it on 4th and 2 x% of the time vs. 1-x% that we don't make it x how many points they score on average from y field position vs. our defense, etc. Calculating EV here is different because if you have enough data there are so few unknowns. You can take into account a ton of factors and come up with a formula that's extremely complicated. I don't know. I've been drinking and can't really express my thoughts too clearly right now. I'm probably wrong. I definitely would say I sound wrong and not making much sense.
Anyway, I firmly believe that any team would benefit from having a game theory expert on staff.
The point in the OP's post is that it doesn't make sense for the player who has a huge edge over the table to risk all his chips unneccesarily. Say the blinds are 50/100 and you have 25k, there's no point in going all in vs 2 other players who you expect have hands like AQ and JJ, even though you're the player with the best chance of winning the hand, because better opportunities to take their chips will come later. This is not your best spot.
Central's decision to go for 2 vs MSU is analogous (to the decision of the bad poker players who rely more on luck). They figured they had a better chance to make the 2 point conversion than to win the game in OT. If it's MSU who scores a TD late, they kick to take it into OT, because they play the percentages.
My issue is the risk vs reward ratio and that you cant treat each decision in a football game as an all-in scenario. If you are a outmatched, significant underdog than maybe this holds true -- you must play a mistake free game, and not converting on a 4th down means you lose the game plain and simple, where as going for it late in the game may be necessary to pull off the upset.
I am going to pretend I am the coach of a Florida/Texas caliber team -- dominating in most aspects of the game with a good to average kicker. I am also going to pretend these percentages are rough but semi-reasonable estimates based on the above scenario.
Say you have a 4th and 1 at your opponents 25 yard line. The chances you get 3 pts with a 43 yard FG is somewhere in the 75% range, over the long run (hundreds of similar situations) you would average 2.25pts for this scenario (3 * 0.75)
On the other hand, the chances you convert the 4th and 1 are 90%. With a new set of downs inside the 25 you are going to get 7 points 60% of the time and 3 pts 30% of the time (1 - 0.4) * 0.75. If you consider the 4th down conversion and then the rest of the drive independent events, you multiple their separate probabilites to see what the chances are that both occur. In this case it would be 0.9 (0.6 * 7 + 0.3 * 3) * 7 = 3.88pts for this scenario. Over the long run in similar situations, going for it on 4th and 1 will net you +1.63pts/scenario compared to kicking the FG.
Now we can apply the same logic on the other end of the field, let's say a 4th and 1 on our 40 yard line.
If you punt you score 0 points, but your overmatched opponent now has a 20% of scoring 3 pts and 10% chance of scoring 7pts on the ensuing drive due to the long field (-1.3pts/punt).
If you go for it, you have a 90% chance of converting, 50% chance of getting 3 and 30% chance of getting 7pts on this drive. (+1.89pts/decision -- 0.9 * (0.5 * 3 + 0.3 * 7))
At the same time, now that your opponent now has a short field and is 2 times more likely to score.
10% chance of you not converting, 40% opponent chance of getting 3pts and 20% chance of getting 7pts (-0.26pts/decision -- 0.1 * (0.4 * 3 + 0.2 * 7)). This ends up being a net of +2.93pts/scenario because you went for it instead of punting. (1.89 - 0.26) + 1.3 = 2.93.
--All of these numbers are arbitrary and if I didn't have an exam tomorrow I would see if they are accurate.
--The scenario is over simplified because you don't take into account field position, turnovers or many other confounding factors
...but I think the basic premise holds, the better the team you are the more likely you are to benefit from aggressive coaching where as if you are the underdog I believe it becomes a WSOP situation. Uou probably don't want to push until late in the tournament where you can give yourself a chance at winning the whole thing. I am probably way off in a number of ways but oh well I hope it made some sense.
Your reasoning makes sense. However, as I recall, the the only reasonably good data we have about fourth down scenarios concerns whether to go for it or kick a field goal on 4th and two at the two yard line (similar reasoning may apply at some of other field positions also, but that is a bit more speculative). As I recall that the expected number of points favor going for it, rather than kicking. As your reasoning suggests, however, the object is not to score the maximum number of points but to WIN the game.
My memory may be incorrect, but I thought that the prior statistical analyes did also find that you are more likely to WIN the game by going for it.
In any case, unless you have objective data to support your decision--to kick or to go for it-- there is a real risk that you may--like an overconfident poker player--make unwise choices. Just reasoning about long-run effects is not enough, IMO. Of course, it's probably better that what most coaches do now.
I've seen 3 poker analogies recently on these boards. 2 have sucked. The other was meh ok and posted by Brian in the ND postgame thread.
The player should call in scenario 2 like 98% of the time. You need some pretty wacky structure/chip stacks/side bets to make that a fold. EVER.
I understand the concept you're trying to get across though. Sometimes the +cEV (chip EV) play is not always a +$EV play. This much is obvious.
However in football there really isn't an equivalent to tournament poker. It's a cash game without the rake. Every 4th down has a EV and you should always take the option that yields the most positive EV and there are four options to choose from. Go for it, punt, kick a FG. Each option has different factors that determine its EV.
If you find yourself in a 4th down situation on your own 30 and the most positive EV play is to go for it you better go for it.
I didn't even read the football portion of the analogy, so I won't comment on the overall usefulness of the comparison.
I will pose the argument that the player in scenario #1 should probably not call in all scenarios. In a scenario where he has more money on the table than the two guys that pushed in front of him, and depending on how much guys still to act behind him have in front of them, I think that most often he should be re-raising all-in for any remaining money he has with KK. Guys in position behind him might be getting a good enough price with 3 others all-in in front of them to take a shot with any pocket pair. With KK he may not be able to raise enough to price them out of the pot, but in a cash game you need to press this advantage and get as much money in the pot as you can when you have the most favorable odds to win it.
Scenario #1, the play is not to call, it is to re-raise.
Gregg Easterbrook ran a whole column discussing the no-punt strategy in the NFL about two years ago, and then used the Accuscore machine to "prove" that skipping punting does make you more likely to win. His reasoning did include EV and similar reasoning. Of course, he did it for the NFL, where the talent level is near equal, teams have a pro-style offense more likely to have a pounding RB/FB likely to convert, and other factors that are different from college.
I think that going for it on 4th-and-short consistently is almost always the right play (except for deep in your own zone, and when going for a FG makes more sense). Not are you more likely to convert than not, but it helps your third down play calling as well. If it's 3rd and long, you only need 6-8 yards to turn it into a convertible 4th, not 10, which opens up QB reads and other medium-yardage plays.
Incidentally, Easterbrook attributes conservative play calling to coaches who want to shift blame. If a 4th down play fails, the coach gets blamed for making a bad call, but if he punts and the team ends up losing, the singular play is always forgotten, and the players get more blame.
Would ND have turned out the same if we didn't go for it on 4th-and-3 when Forcier scored the TD?
are we assuming (in scenario 2) that he is at the final table of wsop? if so, chips stacks are not equal so we need chip counts to correctly analyze optimal play. assuming that he is a far superior card player than the other eight fish, then it would seem likely that at this point in tourney he would have a bigger stack than the two all-ins in front of him. we also should know what positions the players are in at the table. if the first fish went all-in with small stack from button to try to pick up blinds, then second fish from small blind could and should push all-in to isolate with a wide range of hands including med-pairs, Ax, two broadway cards, etc. you stated he has 50% chance to win, but he would be getting 2-to-1 odds (again depending on chip stacks) to call and a huge chip lead at final table if he scoops. essentially an insurmountable chip lead given his superior play.
side bets also need to be considered as far as how much side bets are relative to prize purse and what payout would be if he went busto on that hand. still, he isn't guarenteed to win wsop if he folds as later suckouts always exist.
also, own 30-yard line fourth down going for it, would be like shoving with a small chip stack to get lucky. i don't see why a coach would go for it on his own 30 unless late in game and down by points.
anyways...thanks for letting me spout, poker analogies are fun tho i do cringe at the cheesy "all-in" mantra for this year's team. to watered down...
This requires much further research and accuarcy, but the reason for going for it on your own 30 example is that in the research paper they contend in the great majority of circumstances it is more beneficial to go for it. I think a lot of people think we are just referring to the goalline or Brian's beef with punts from the 35yd line. The research calls for going for it in your own territory a lot, not to mention the guy in Arkansas that does not punt...ever.
i was bored at work, what can i say. :)
fun diary post though.
It's quite hard to assess in my own opinion. I am bewildered by the professional ideas here. I'll take note of all of them