Writers of Pro Football Prospectus 2008

12 Jul 2005

Football Commentary: Overtime Model

C'mon Feel the Math! Our good friend William Krasker is back, using his statistical model to ask the question: Does overtime -- and the presence of a third possible outcome, a tie -- change the optimal strategy for certain situations? The answer: Yes, and it matters more later in the season because teams know how a tie will affect their playoff chances. As an example, Krasker shows how a St. Louis decision to punt in overtime of Week 17 was the wrong decision, even though it would usually be the right decision. (The Rams had good luck and things worked out anyway.) By the way, there's a link to skip the math and I recommend using it.

Posted by: Aaron Schatz on 12 Jul 2005

48 comments, Last at 18 Jul 2005, 11:24pm by Miles

Comments

1
by Pat (not verified) :: Tue, 07/12/2005 - 12:45pm

The main problem I have with Krasker's analysis (that I mention almost each time :) ) is that I don't agree that coaches should necessarily choose the path most likely to win. They should choose the path least likely to lose quickly - that is, the path that extends the game as long as possible.

The reason for this is simply that you don't know how likely you are to get a yard on any individual down. His conclusion regarding the Rams/Jets game entirely hinges on an assumption that the likelihood for the Rams to get the first down is 0.54. If it was 0.48 (that's 6% less likely!!) then it would be better for them to punt rather than kick.

There's no way to say that he was 54% likely to get the first down rather than 48% likely. It's simply not true, because you haven't had enough data regarding your own team's ability to get a first down.

Personally, I'm always of the opinion that it's better to lengthen the game than risk a very short one on an uncertain assumption. Longer game = more possibilities.

2
by B (not verified) :: Tue, 07/12/2005 - 12:54pm

I think it's better to play to win instead of playing not to lose. Although, if we recall the time strategys, the stronger team should try to lengthen the number of possessions, where as the weaker team should try to shorten them.

3
by billvv (not verified) :: Tue, 07/12/2005 - 1:53pm

I think coaches come by an aversion to being responsible for a loss by being ripped by the media. Going for it on fourth down and failing is a failing. No thought is given to believing, wrongly, that your offense can do this. That you trust your defense more than your offense, who fail. An overtime loss is somehow easier to take than going for it, taking a win or a loss at your own hand, rather taking the safe tie and seeing what happens. I think it takes more guts than most coaches can muster and I think the second guessing is why.

4
by Pat (not verified) :: Tue, 07/12/2005 - 2:02pm

Although, if we recall the time strategys, the stronger team should try to lengthen the number of possessions, where as the weaker team should try to shorten them.

Yes, but this is an absolute statement. The question you should ask is "how often does the weaker team's coach actually believe it's the weaker team?" There are only a few instances I can think of where this is the case - Jeff Fisher and the Titans vs. the Colts this year, for instance.

5
by JasonK (not verified) :: Tue, 07/12/2005 - 2:08pm

I remember a Giants-Redskins game about 5 years ago where this came into play. The game was in OT (I think it was 10-10), and after a few possessions, it was clear that the Giants were playing for the tie. It was late in the season, and both teams were in playoff contention. The Giants had beaten the 'Skins earlier that year, so a tie favored them because they would have the first tiebreaker (record v. each other).

(You might remember this game as the day that Gus Frerotte decided it would be a good idea to celebrate a touchdown by smacking his forehead into the stadium wall.)

6
by Tim (not verified) :: Tue, 07/12/2005 - 2:13pm

"Longer game = more possibilities."

What leads you to believe that those future possibilities are more propitious for you than for your opponent? Anything can happen in a football game (which is the crux of "more possibilities"). It only takes one freak play in overtime for everything to end. When I have the probabilities on my side, I would rather strike while the iron is hot than hold off and see how things go. It may tip over and burn my house down.

7
by Starshatterer (not verified) :: Tue, 07/12/2005 - 2:25pm

How often does the weaker team’s coach actually believe it’s the weaker team?

It's rare that a team is actually and obviously weaker in all three categories (offense, defense, special teams). So Jack del Rio, taking Jacksonville into Indy, can say "Well, their offense may be better, but mine is good enough and my defense is better, so we'll play it straight." Even though Indy proved to be the better team by the end of the season, they split their games with Jacksonville, so that kind of calculus would be reasonable.

I think that strategy (the stronger team wants more overall possessions, the weaker team wants fewer) is too simplistic anyway.

How does it sound if we modify it to: the team with the better offense should want to increase the number of possessions when on offense, the team with the better defense should want to decrease the number when on offense. (All teams should want to increase the number of possessions when on defense, by forcing a punt or turnover while avoiding giving up a score.)

8
by Richie (not verified) :: Tue, 07/12/2005 - 2:48pm

“Longer game = more possibilities.�

What leads you to believe that those future possibilities are more propitious for you than for your opponent?

When I see these comments, it brings me back to my personal debate about what a team should do if it scores a touchdown at the very end of a game (with about a minute or less left to play), to pull within one point of the other team.

Kick it and go to OT, or go for two and try to win?

The first statement about lengthening the game, says we should kick the PAT and see what happens in overtime.

My hunch is that you should go for 2, because who knows if you'll ever have the ball within 3 yards of the end zone again.

9
by Pat (not verified) :: Tue, 07/12/2005 - 3:01pm

What leads you to believe that those future possibilities are more propitious for you than for your opponent?

Nothing. But I do know that the uncertainty in those future possibilities taken in aggregate is less than the uncertainty in one play.

That is, which is more certain - gaining 1 yard on 1 play, or gaining 3 yards on 3 plays?

The "you can lose on 1 play!" argument is a little silly, because for almost every chance you have to lose on 1 play, you also have a chance to win on that play. Those all cancel each other out.

What you should be concerned about are the fluctuations of normal plays. You'd rather bank your future on multiple plays rather than 1 play.

10
by Larry (not verified) :: Tue, 07/12/2005 - 3:32pm

Let me start by saying I love these pieces. They appeal to an analytical approach that is very satisfying and elegant to me. Keep 'em coming, Will. That said, let me pose a question:

Suppose I offer you a choice:
1) $20 right now
2) a 30% chance of $100 later

All our understanding of probability says to take choice (2). But, really, that's predicated on the idea that you will get to make this choice many, many times and in the long run, you'll do better with choice (2). This is good startegy in the regular season, you get lots of games, and the ultimate goal is maximize your chances of winning them.

But, what if you only get to make the choice ONCE, and never again. 30% doesn't really have meaning. The right choice is to bank the $20, I think, otherwise you'll get nothing. In playoff overtime, this is the situation, you have to win that game, right there. You don't get to build up an excess of right decisions that lead to more wins in the long term. I'm not sure that this is the precise way to put this statistically, but it might get at the gut aversion some people have to this kind of analysis.

11
by B (not verified) :: Tue, 07/12/2005 - 4:03pm

I don't think the "More possessions = Better chance for stronger team to win" strategy works well in OT. For one thing, if the teams get to OT, usually means they've been playing pretty much even throughout the game. Also, since OT is sudden death, it's better to maximize your current scoring chance than it is to concetrate on a future attempt, as long as the strategy doesn't give your opponent too much of an advantage.

12
by Pat (not verified) :: Tue, 07/12/2005 - 4:12pm

But, what if you only get to make the choice ONCE, and never again. 30% doesn’t really have meaning. The right choice is to bank the $20, I think, otherwise you’ll get nothing.

Actually, that supports the opposite argument from what you're saying.

The argument you're giving supports the "play not to lose" strategy. In the case quoted, for instance, if the Rams go for it on 4th down, if they miss, they've basically lost. If they punt, then the game continues. They have a risky action with high reward, and a non-risky action with low reward (reward for punting -> field position). Since you only get to make that action once - take the low-risk option.

13
by krugerindustrialsmoothing (not verified) :: Tue, 07/12/2005 - 4:13pm

Larry, I agree with you, I love these pieces, however your analysis is flawed I fear. In making a decision like that you must focus on expected outcomes if I recall correctly, and the best expected outcome is to wait for the $100 to roll around.

the limitation to this kind of analysis in football is that the odds change depending on the play each coach would decide to run and the ability of the players to carry out that play. So the 'odds' are not and cannot be known before the play is run.

14
by Parker (not verified) :: Tue, 07/12/2005 - 4:27pm

My issue with these types of articles has always been and continues to be the same. When you run numbers through this system and come up with decisions that are deemed 'correct' because they carry a 6% better chance of success than the incorrect decisions but use assumptive success rates as inputs and ignores any of the 'intangibles' that are part of these decisions (the D-line looks tired, my QB is playing with a broken toe, my RB looks like the second coming of Jim Brown, or James Wilder), I find it difficult to use this information as an indication that the coach made an incorrect call.

In fact, these articles have the opposite effect for me. I see them as evidence that these are very close calls that should be made by the man that has more infromation than the model will ever be able to collect, the coach.

That said, I do enjoy reading them and have a great respect for the amount of work that goes into them. It's good stuff.

15
by Dennis (not verified) :: Tue, 07/12/2005 - 5:47pm

Re: #8 "My hunch is that you should go for 2, because who knows if you’ll ever have the ball within 3 yards of the end zone again."

The chance of a successful 2 point conversion is 40%. The chance of winning in OT is 50%. Unless you have some reason to believe that you have a better chance of scoring the 2 pointer, the play is to kick and go to OT.

16
by Parker (not verified) :: Tue, 07/12/2005 - 6:21pm

#15 - Huh?

2-pt conversions = 40%. No matter who is attempting or who is defending?

OT Victory = 50%. On what possible basis would you make that claim?

17
by RichC (not verified) :: Tue, 07/12/2005 - 6:27pm

That's actually my main problem with the Krasker model -- it (as far as I can tell) uses league-wide averages. But if every team performed to league-wide averages, they'd all be 8-8.

So while in the abstract I like the probabilistic approach, I think you need to assign probabilities based on the specific teams playing rather than using league-wide averages. Unfortunately, I doubt there's a large enough sample size to do that meaningfully.

18
by Larry (not verified) :: Tue, 07/12/2005 - 6:36pm

Pat said:

Actually, that supports the opposite argument from what you’re saying.

The argument you’re giving supports the “play not to lose� strategy. In the case quoted, for instance, if the Rams go for it on 4th down, if they miss, they’ve basically lost. If they punt, then the game continues. They have a risky action with high reward, and a non-risky action with low reward (reward for punting -> field position). Since you only get to make that action once - take the low-risk option.

I don't think I implied they should go for it in that situation. I think you summarize the argument I'm considering very well. (I'm not really convinced one way or the other at this point, it's just a line of thinking that makes me pause)

krugerindustrialsmoothing said:

In making a decision like that you must focus on expected outcomes if I recall correctly, and the best expected outcome is to wait for the $100 to roll around.

My point is that if you only get to make the choice once, then you don't get to wait for the $100 to roll around. It won't, there's no second time. The expected outcome has no meaning in the one time only case. It only means something if you perform the test many times. So, it isn't clear to me what the right choice is.

To summarize, playing the percentages is a good way to win more playoff games. But, I think, as fans, we don't want our team to win more playoff games, we want them to win ALL playoff games (in a given year, anyway). Whether coaches or owners feel the same way is another question entirely, but I'm guessing players and fans are pretty sure which way they lean.

19
by Reinhard (not verified) :: Tue, 07/12/2005 - 7:20pm

Larry, that is a good example you have chosen. However, the "later on" for (2) is actually unnecesary for teh analysis. In the long run you will get more money always picking (2) in expected returns. But what if the long run doesnt matter... i.e. what if there is only one chance? Then I will pick (1) although expected return is lower... on the other hand, if I have to get $25 to win, then I'll pick (2) again.
Point being, even with a very simple model, the decision making can get complicated real fast with situational factors in football.

20
by Paul (not verified) :: Tue, 07/12/2005 - 7:30pm

These comments are very similar to those under the Allais paradox (click on my name or just google it) from decision and game theory.

Subjects are asked to choose between the following 2 gambles, i.e. which one they would like to participate in if they could:

Gamble A: A 100% chance of receiving $1 million.
Gamble B: A 10% chance of receiving $5 million, an 89% chance of receiving $1 million, and a 1% chance of receiving nothing.

After they have made their choice, they are presented with another 2 gambles and asked to choose between them:

Gamble C: An 11% chance of receiving $1 million, and an 89% chance of receiving nothing.
Gamble D: A 10% chance of receiving $5 million, and a 90% chance of receiving nothing.

At the first stage, neither answer is correct, it is just a matter of your risk acceptance. At the second stage (assuming that no money was delivered after the first choice), if you would choose A, then you should choose C to be consistent mathematically. If you choose B, then you should choose D.

This means, first off, that the $20 or 30% chance of $100 has no right answer in a general sense. On an individual basis, it absolutely does have a right answer, based on the individual and their risk acceptance/aversion AT THAT MOMENT. What choices a coach makes at the start of the season could be very different with the season on the line. That's because the difference between 2-1 and 1-2 are small compared to 10-6 and in the playoffs and 9-7 and out.
Also, the owner's risk aversion/acceptance may be different than the coaches, particularly if the coach's job is on the line or a stadium deal is on the line.

21
by Mike Tice (not verified) :: Tue, 07/12/2005 - 8:19pm

My brain just exploded.

22
by the K (not verified) :: Tue, 07/12/2005 - 8:43pm

This is why I love Mike Tice as a head coach. Probabilities and statistics, you be damned. Let's play some football!

Kidding aside, the "50% chance to win in OT" above can actually be explained simply, and in simple terms, makes sense. If the game goes to overtime, you can win, or lose. If the teams played equally enough to end up in OT, 50% would be accurate. But in a regular season game, there's the possibility of a tie....

This is a fun discussion but it's relatively pointless. Primarily because no head coach in the NFL will take such a chance as go for fourth and a foot in OT at their own 35. They'll be chastised if the team gets stopped and puts the opposing team, if not already in FG range, very close to it.

23
by Pat (not verified) :: Tue, 07/12/2005 - 9:39pm

On an individual basis, it absolutely does have a right answer, based on the individual and their risk acceptance/aversion AT THAT MOMENT.

And on how accurate they believe their risk assessment to be. (The "I feel lucky" factor).

That's part of what I was trying to say. Football coaches shouldn't maximize winning percentage, because you can't calculate winning percentage accurately enough to actually be able to believe . Football coaches should minimize risk, because you can assess the risk of a given situation. And going for it on 4th and 1 on your own 35 in OT should set off even Mike Martz's risk-o-meter. If Martz had gone for it, and said "Yah, I went for it because I felt lucky", he'd be up for Idiot Coach of the Year in my opinion.

24
by Pat (not verified) :: Tue, 07/12/2005 - 9:49pm

In fact, now that I think about it, Krasker's analysis is very wrong in this case (no offense to the guy, I've always thought the model was a very cool idea).

Why? Because Martz was absolutely, positively, in a position where he could not risk anything.

As an example, to continue the gambling bit here, imagine if you've got person A and person B. Person A has $500. Person B has $100. Both A and B are presented with an option: wager $100 to have a 20% chance of winning $1000. Person B should definitely go for it - he's got plenty of money to afford that kind of a risk. Person A, however, probably shouldn't - he can't afford to lose $100, even for such a decent payoff.

In exactly the same way, Martz was offered almost exactly the same choices. But the Rams could not afford to lose, or even tie - they'd miss the playoffs. They had to win. Therefore, it's better for him to take the low risk option, and kick it away. Reverse the situation (the Jets were already locked into the #5 seed), and the Jets definitely should've went for it (if it gives them a better chance of winning), because they could easily afford the risk.

25
by Adam (not verified) :: Wed, 07/13/2005 - 1:59am

Re: 22
Actually Dom Capers went for it on a QB Sneak to win a game either last year or two years ago instead of kicking the PAT.

26
by Jim A (not verified) :: Wed, 07/13/2005 - 2:23am

That’s actually my main problem with the Krasker model – it (as far as I can tell) uses league-wide averages. But if every team performed to league-wide averages, they’d all be 8-8.

Not true. Try flipping a coin for each game in an NFL season. Unless you're really arguing that every game would be a tie.

I think you need to assign probabilities based on the specific teams playing rather than using league-wide averages. Unfortunately, I doubt there’s a large enough sample size to do that meaningfully.

That's all the more reason to use league averages. In truth, the small sample size at the team level probably means that only a few outliers in a particular situation can be determined to be statistically different from the mean with any reasonable degree of confidence. And it might be worthwhile to compute these out just in case. But if they aren't significantly different, what else do you go by? The guesstimate of the coach?

This gets back to the issue of how accurately the coaches can judge the probability of success. I think the section on overconfidence in the Massey-Thaler Loser's Curse NFL Draft paper is very relevant here. The paper cites numerous studies from psychology that show that people generally overestimate their ability to judge things accurately by failing to properly account for uncertainties, and such overconfidence increases with more information. Every coach believes his team is above average, which is statistically impossible, and he probably also believes he can better his previous performances by calling the right play or employing the right personnel.

27
by Scott de B. (not verified) :: Wed, 07/13/2005 - 10:24am

"the limitation to this kind of analysis in football is that the odds change depending on the play each coach would decide to run and the ability of the players to carry out that play. So the ‘odds’ are not and cannot be known before the play is run. "

But this uncertainty can be incorporated into the odds. It increases the error bar, so to speak. But if you have to choose one value for the probability (and that is what, in effect, you are doing no matter what choice you make), it makes most sense to choose the mid-point.

Now, in extreme cases, this breaks down. There is a classic fallacy - if there are two possible outcomes, and you don't know the probabilities for each, you should assume that they are 50% for each, since that minimizes your maximum possible error. But then that leads to conclusions like there is a 50% chance that aliens will invade tomorrow, which can lead to irrational decision-making.

I agree that individual circumstances should be taken into account. Maybe your team has a better than 40% chance to make a 2-pt conversion, maybe it has a worse chance. But I don't think I ever see coaches actually incorporate that kind of reasoning into their decision-making process (e.g., I have never heard a coach say I took the PAT because I figured we only had a 30% chance at 2 points) except on the 'gut feeling' level.

So maybe Krasker's estimation of probability on St. Louis going for it was off the mark. But I don't think Martz punted because he did the calculations differently and came up with a different result -- he just did it instinctively. I think working with a model like this could help coaches make more mindful decisions, which would be a good thing.

And there are multiple iterations, although the details of each are different. If every time a coach faced a decision like this he could increase his team's chances of winning by 0.5%, over the course of a season or career that would add up to a significant difference in wins and losses.

28
by Dennis (not verified) :: Wed, 07/13/2005 - 11:46am

Re: #16

2-pt conversions = 40%. No matter who is attempting or who is defending?

That's why I said "Unless you have some reason to believe that you have a better chance of scoring the 2 pointer".

"OT Victory = 50%. On what possible basis would you make that claim?

From http://www.footballoutsiders.com/ramblings.php?p=87&cat=1:

"Going into this season, there had been 342 overtime games in NFL history. Of those games, 177 times (51.8%) the team that won the toss won the game, 149 times (43.6%) the team that lost the toss won the game, and 16 games (4.7%) ended tied."

So if you want to get picky about it, you have a 47.7% chance of winning if you go to OT (higher if you win the toss, lower if you lose it) and a 4.7% chance of a tie.

Again, unless you have a good reason to think you have a better than normal chance of converting the 2, or a reason to think you have a lower than normal chance of winning in OT, you should kick the PAT.

29
by Pat (not verified) :: Wed, 07/13/2005 - 12:38pm

That’s all the more reason to use league averages.

Which means that you have to use the spread from the league averages as well. That is, you have to have some way of estimating how accurate your description (league average = every team) is.

Take the 2 point conversion, for instance. Most people say 40% or so. But a proper way to do it would be to take all the 2 point conversions that have occurred, calculate the success chance, but then also figure out how much that number varies if you remove one team from the data set. That'll give you an estimate of the error in that 40%.

The problem with a small data set is that fluctuations can give you very different answers. The problem with large data sets is that all of your data might not be identical - and so you'll have biases inherent inside the set.

As an extreme example, assume Team A has a 20% chance of making a 2 point conversion. Assume Team B has a 60% chance of making a 2 point conversion. They both attempt 10 times - team A succeeds 2 times, team B succeeds 6 times, and the league total is 8/20, or 40% - which is 20% off the actual success rate for either team. If you then calculate for only Team A, you get 20%, for team B, you get 60%, and so you could say "well, the league average 2-point conversion success rate is 40%+/-20%", and that would give you a much better basis for evaluating conclusions like this.

30
by Parker (not verified) :: Wed, 07/13/2005 - 12:49pm

RE #28

I wish I had access to a database of NFL information and the know how to use it. If I did I would run some numbers and see if my thoughts on this carry any water at all. Unfortunately, I don't, so I'll just throw this out and see what happens.

The odds you mention are based on one rather non-football related factor, a coin flip. So based on a coin flip (which is inherently 50/50), you end up with outcomes close to 50/50. I would be interested in seeing what the win % in overtime is for various situations. For example, home vs away. Is there a historic advantage in OT games for the home team? (Again, I wish I could answer this rather than just asking.) How about the team that scored last? Is there some sort of 'momentum' effect? What I mean by that is, if your team just came back from a 10 point 4th quarter deficit, are you more likely to win in OT because you are currently playing better than the other team? Does time of possession of number of plays run on offense have any correlation?

My point is that there dozens and dozens of factors that may have an influence. We have picked one, the coin flip (or to be more accurate, the first possession) and declared that it is a near 50/50 probability and use that number for analysis, which I think is so limiting that it renders the analysis almost pointless.

If it could be shown to me (and I wish I could do it myself) that the most obvious factors (home vs away, previous record disparity, 4th quarter 'momentum') still produce a 50/50 split (or thereabouts), I would be much more inclined to accept that the statement 'Your chances of winning in OT are 50/50' is indeed true.

Respectfully,
Parker

31
by Richie (not verified) :: Wed, 07/13/2005 - 2:07pm

Again, unless you have a good reason to think you have a better than normal chance of converting the 2, or a reason to think you have a lower than normal chance of winning in OT, you should kick the PAT.

But if you tie the game and go to OT, your chance of winning suddenly drops to 43% just by losing the coin toss. So, yeah, there are definitely other factors involved. Being the visiting team might be a better time to go for 2. If the opponent has outscored you 24-6 in the fourth quarter, then going for 2 is probably a good idea. If the score is 7-6, and the game is playing played in bad weather, or your offense has not been effective for the whole game, going for 2 would be good.

I don't think it would always be good to go for 2, you would need to evaluate the circumstances, but I think it might be a better idea in most cases.

32
by Richie (not verified) :: Wed, 07/13/2005 - 2:10pm

Oh, and a quick Google found this info from Pasquerelli's site last season:

"Through the first 10 weeks of this season, teams have converted 21 of 41 two-point tries following touchdowns. The 51.2 percent success rate tops the previous best, 50.9 percent in 1994, and is far superior to the cumulative rate, 43.5 percent, for the 1994-2003 seasons."

So, single-season success rates have been as high as 50.9. And since the cumulative for 10 seaosons was 43.5, there may have been a couple of seasons under 40%. Quite a swing.

33
by brasilbear (not verified) :: Wed, 07/13/2005 - 4:11pm

And the Bears under...Wanny I believe in 97 or 98 tried for two against the Packers and ended up losing by one when they failed. Can anyone check how often coaches have gone for two and the win?

34
by Bright Blue Shorts (not verified) :: Wed, 07/13/2005 - 5:59pm

3 comments ... sort of related to the topic ...

1) in any sport, the longer a game lasts the higher the odds of the best team winning. Which probably explains someone's possessions comment. Doesn't always work out that way, but that's why they're odds, not guarantees.

2) I was recently reading a comment about Lombardi and the Ice Bowl. Trailing Dallas by 3 pts they could have kicked a FG and taken the game into OT. But Lombardi elected to go with the sneak and they scored the TD. Brave decision - well rewarded.

3) There was a week 17 game last season, possibly the Rams, that went into OT. One of the teams had nothing to play for in the game, as they'd already qualified for the playoffs. They took it into OT and played an extra 10 mins of football. The following Saturday they had to play their wild-card game. All in all, I think they would have been better off gambling at the end of regular time, and avoiding injuries / wear&tear.

BBS :-)

35
by B (not verified) :: Wed, 07/13/2005 - 6:26pm

BBS: That was the Rams. The other team was the Jets. Who had to play another OT game in wildcard weekend, and then went on and played a third OT game in a row, finally losing on a missed field-goal.

36
by Starshatterer (not verified) :: Wed, 07/13/2005 - 8:06pm

B, BBS (#34-35 )--

TMQ wrote (article linked) that he thought the Jets should go for broke to win in regulation, rather than play for the tie and overtime, since their playoff seeding was already locked with the Bills' loss to the Steelers.

O' course, the Jets and Rams both won their wild-card games, and the Jets came within shouting distance of winning in the divisional round. Maybe the football gods were pleased by their doggedness, if not their judgement.

37
by David Keller (not verified) :: Wed, 07/13/2005 - 8:11pm

Overtime takes place in football games in which the two teams involved in the game are tied after four quarters. A third team not involved in the game is never, except in rare instances, invited to participate in the overtime.

38
by Richie (not verified) :: Wed, 07/13/2005 - 9:14pm

Go away Keller.

39
by Vern (not verified) :: Thu, 07/14/2005 - 1:38pm

Re: 18, 19, etc. about probabilities and the long term.

I think it is best to use Kraskers result as the base model, very similar to the play tables used in bl-ckjack, developed at MIT. It is well known, however, that in the short term strategy should deviate from the model.

The Travel Channel had a great show demonstrating this. Over a weekend, one player played the "correct" model, another played "bad bets". Get this, the player making the bad long shot bets was revealed as the mathematician, and he came out ahead. His argument was, you might as well play to have fun, because with such a short duration, the probabilities are meaningless and luck really dominates.

In football, since it's not random luck is less a factor. Instead, specific local factors, such as tiredness of your team, surprise effect of a certain play call, tendency analysis of your opponent, would far surpass the base strategy based on probability in determining the chances of any given outcome.

In fact, use of local factors is what card counters do. By tracking local factors (the distribution of high or low cards) they adjust from the base strategy by changing bets - and beat the odds. The base strategy is still useful, however, because it helps you decide how much you have to overcome - how favorable the local factors have to be. For example, it could gived you a sense of how much surprise you'd need to have for a given play call, to overcome the base odds.

40
by David Keller (not verified) :: Thu, 07/14/2005 - 4:17pm

Oddly enough, the act of going away is not possible. What needs to happen is that the middle linebacker needs to fight off a block from the fullback, and tackle the halfback.

41
by Reinhard (not verified) :: Sun, 07/17/2005 - 6:31pm

Good point Vern.

Personally, I think that the loser can't afford to NOT risk it. The odds are already stacked against him doing nothing. A high-risk bet, with better expected return, has a chance of helping even the odds, and a chance of screwing you over. So what is being weighed between low and high risk is what gives you better (or worse) odds: being behind or playing aggressive

42
by Parker (not verified) :: Mon, 07/18/2005 - 12:51pm

I honestly think that in some way the decision of the coach is tied to how the coach feels the decision wil be viewed by others.

In some cases, his job may be on the line. So, doing something that is a) risky and b) different than conventional wisdom could end up not only costing you a victory or a play-off spot, but could also mean your job.

You can come up with a formula that says going for it on your own 31 is a good strategic move, but can you sell it? Can you sell it the local sports radio guy? Can you sell it to the season ticket holder? Can you sell it to you own team?

I can imagine a scenario in which Martz thinks to himself, 'I've seen a model that says that it's a good idea to go for it here. I believe that model. But good lord, I'll look like an IDIOT if we don't make it'.

I have long had the theory that a good offensive team would benefit from more 4th down attempts and would certainly benefit from going into a set of downs knowing they have 4 plays to pick up 10 yards instead of 3. Of course, I have nothing to back up that theory. I would love to see it in action but I am sure that it won't happen. I imagine a coach that did that and lost two games would be immediately fired.

Then again, Mike Tice is still at the helm of a professional franchise, so anything is possible.

43
by Starshatterer (not verified) :: Mon, 07/18/2005 - 1:07pm

You can come up with a formula that says going for it on your own 31 is a good strategic move, but can you sell it?
Win. Winning closes the sale on coaching decisions.

If your decisions consistently have favorable odds, you should win. If you keep losing anyway, adjust your models while you spend the next few seasons as a consultant.

44
by Richie (not verified) :: Mon, 07/18/2005 - 2:27pm

#42 - I don't understand the pounding of Mike Tice. On one hand you are basically saying that it would be nice seeing coaches make decisions based on what they feel is the best chance of winning, regardless of what fans and media think.

On the other hand, I see Mike Tice as a coach who tends to make some unusual coaching choices. Sometimes they fail and he looks like an idiot. Other times they succeed and everybody forgets about it.

I like coaches like Tice and Martz who think outside the box. Whether they do it out of brilliance or stupidity is irrelevant to me - it makes for interesting football.

Barry Switzer is famous for failing on 4th and short from his own 30 on consecutive plays (due to penalty). I love the balls of making that decision twice in a row.

45
by Starshatterer (not verified) :: Mon, 07/18/2005 - 2:39pm

Richie (#44 )--
I don’t understand the pounding of Mike Tice.
The knock on Mike Tice is, his teams have been loaded with talent, but underachieved.

Granted, only part of that shortfall has been even arguably Tice's game-day decisions. But the head coach is also supposed to be responsible for motivating his star wideout, and instructing his defense in tackling.

Tice has probably earned some punding.

46
by Richie (not verified) :: Mon, 07/18/2005 - 5:07pm

But haven't the Vikings had bad defenses during Tice's entire tenure?

47
by Starshatterer (not verified) :: Mon, 07/18/2005 - 6:13pm

The knock on Tice's defense has been, not so talented but still managed to underachieve.

It's often said that you can't teach brains, or speed, and it's true. But tackling can be taught, and the Vikings (linebackers especially) tackled very poorly for professional players. That almost certainly cost them games last year, and that's a coaching problem.

48
by Miles (not verified) :: Mon, 07/18/2005 - 11:24pm

Re: #10/19 -- the money theoretical examples. Just thought I should point out that the value of money has a very real time component to it, which can be calculated. $1 today is not equal to $1 100 years ago, and neither will be equal to $1 in the year 2100.