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Monday, October 22, 2012

The "End of the Game" Illusion

So, Eli Manning threw for a touchdown with just over a minute left to win yesterday's game for the Giants. Today, on talk radio, the experts were saying, "Manning played poorly early, but he is always good when it really counts, at the end of the game."

Yes, think about how much it would have changed the game if Manning had thrown that touchdown one minute into the game instead of with one minute left (ceteris paribus, of course). Then, instead of the Giants beating the Redskins 27-23, the Redskins would have lost to the Giants 23-27.

Because you know what? Touchdowns, field goals, safeties: they don't count for different numbers of points when scored at different times during the game. All you need to do is to have more points than your opponent: it doesn't matter at all when you get them.

Now, we all love a great story, and snatching victory from the hands of defeat is a classic story line. But the first minute "really counts" every bit as much as the last. If you score 48 points in the first half while shutting out the other team, while in the second they score 47 while shutting you out, you've won! The other team gets exactly zero consideration for scoring more "when it really counts."

I suspect this is a sort of cognitive bias humans suffer from that will appear in other guises, and thus is worth exploring further.

21 comments:

  1. A team taking the lead in the last minute is statistically much more likely to go on and win the game than a team taking the lead in the first minute.

    so scoring in the last minute is "scoring when it really counts" in that respect.

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    1. "A team taking the lead in the last minute is statistically much more likely to go on and win the game than a team taking the lead in the first minute."

      Absolutely. But if the Giants had scored that TD in the first minute, they would have been up by 11 with 1:40 left, and statistically really, really likely to win!

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    2. Only because you added a "(ceteris paribus, of course)" in you oost.
      Of course other things are not really equal if the other teams has 59 mins rather than 59 secs to reply to a score.



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    3. I thought about this a bit. Of course, ceterises ain't paribus. Here is one thing unequal to think about, however: if you pile up points early, there is a tendency for the other team to get discouraged and "quit." Even if they don't do that, it tends to make them change their game plan from the one they wanted to play, which you have to like. So, at least several of the factors that aren't equal weigh strongly towards saying "*Early* point are more important"!

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    4. at least several of the factors that aren't equal weigh strongly towards saying "*Early* point are more important"!

      This agrees with research Football Outsiders did many years ago. The conclusion:

      People want to believe that the teams that can win the close ones are championship teams. But as counter-intuitive as it sounds, championship teams are generally defined by their ability to easily win games over inferior teams.

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  2. The nature of play changes towards the end of the game because time constraints start to really limit you.

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    1. "The nature of play changes towards the end of the game because time constraints start to really limit you."

      Yes, it does. Best to be up by a few touchdowns when that time constraint starts to hit.

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    2. It's always better to be ahead. My point is that while a touchdown counts for as many points regardless of when in the game it occurs, the difficulty of scoring a touchdown depends in part on how much time is left on the clock.

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    3. I agree with that last point.

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  3. Gene, I agree that the people who use this phrase say it in a sloppy fashion, but I think you are as wrong on this as the debt stuff. You are nitpicking the man-on-the-street for what is basically a correct intuition.

    Another way of putting it: If you were the coach of an NBA or NFL team, and implemented all of the "duh" strategies you talk about on this blog, I think you would get crushed. I'm not saying *I* would beat you, I'm saying the coaches whom you think are systematically morons would crush you.

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    1. "implemented all of the "duh" strategies you talk about on this blog..."

      What "strategies" have I talked about implementing?!

      "I'm saying the coaches whom you think are systematically morons..."

      What coaches have I said are "systematically morons"?!

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    2. And, by the way, although I have recommended no strategies here and not called any coaches morons (these were a bunch of "analysts" on the radio I was talking about in this post), you do know that pro coaching wisdon *has* been shown to be systematically biased several times recently, and that coaches have learned from this and won as a result, right? I'm thinking specifially of Moneyball, and also the tendency to "go for it" far too little on fourth down.

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    3. Ah, I recall, in basketball, I did talk about sitting out someone with fouls for less time. But I certainly didn't talk about any strategy here, except "be up by a lot before the last minute," which is a strategy I think EVERY football coach would agree with!

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    4. And as far as my "getting crushed":

      "NBA statheads have reasoned for years that it doesn’t matter when a player plays as long as he maximizes his court time. In Tobias Moskowitz and Jon Wertheim’s 2011 book Scorecasting, the writers note that coaches are too risk-averse when it comes to foul trouble. After reaching five fouls, Moskowitz and Wertheim explain, players only receive a disqualifying sixth foul 21 percent of the time, and that even then, it’s usually not too long before the final buzzer. Their book also disproves the myth that teams perform worse when foul-troubled players are on the court. The assumption that these players might cost their teams by being more tentative in potentially foul-drawing situations turns out to be incorrect. Another study points out that it’s actually success in the third quarter that correlates to the most wins."

      (http://www.slate.com/blogs/browbeat/2012/06/21/foul_trouble_in_nba_finals_are_the_heat_and_the_thunder_coaches_acting_rationally_by_pulling_durant_and_other_players_.html)

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  4. Hmmm... I'm more than a little out of my league hanging out here, but it seems to me that there is a difference in delivering when there is still a chance for future success vs. delivering when there is probably only one chance. Yes, the point values are the same - but the pressure isn't.

    I'm not sure if you are a golfer but I relate it to the difference between hitting a big, powerful drive dead straight when you are on the range vs. doing it in front of an audience. The club and ball don't know the difference, it is just a shot like thousands of others, but you know the difference.

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    1. "but it seems to me that there is a difference in delivering when there is still a chance for future success vs. delivering when there is probably only one chance. Yes, the point values are the same - but the pressure isn't."

      Sure, the latter is harder. So, isn't it better to be up by enough strokes that you don't have to hit that pressure birdie, rather than being the guy who always needs to scramble to come back?

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  5. I fail to see what being so literal about this particular phrase is supposed to accomplish.

    Yes, it would be nice to score the touchdown in the first minute rather than the last, but that's irrelevant. The fact is that they didn't score it; they were down, they needed to score and had very little time to do it. Manning led the scoring drive when they needed it more than at any other point in the game given the circumstances. So if there is a high pressure situation (aka "when it counts") and Manning has to make something happen, he can be counted on to do it.

    And your counter to blackadder's point is insufficient, because a lack of time in game play does not necessarily mean there exists a time constraint. If you're up by "a few touchdowns" late, the other team has little or no time constraint because they are aware that the chances that they can make up the required number of points in the time remaining is very slim if not zero.

    There is no disagreement as to whether you would be better off with a big lead at the end of the game; you're always better off with no pressure. But it has nothing to do with the point of the phrase, either.

    And Moskowitz and Wertheim are hardly the final word on the subject of foul trouble:

    "Philip Maymin of NYU-Poly, along with co-authors Allan Maymin and Eugene Shen, used play-by-play provided by basketballgeek.com to study how having a starter in foul trouble affected a team’s chances of winning the game during the 2006-07 NBA season...

    "Their finding...is that teams play worse when they leave starters in foul trouble on the floor, especially during the third quarter. Why? The obvious explanation is that players in foul trouble play differently, avoiding the necessary plays–especially on defense–that carry the risk of drawing another foul. From this perspective, the issue is less about maximizing the total number of minutes the player is on the floor and more about maximizing the effectiveness of those minutes."

    http://www.basketballprospectus.com/unfiltered/?p=615

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    1. "The fact is that they didn't score it; they were down, they needed to score and had very little time to do it. Manning led the scoring drive when they needed it more than at any other point in the game given the circumstances."

      Right, because, as these guys said, Manning played badly earlier on. Why does his playing badly early on not really count, while making up for it later does? I'd put it this way: Manning has trouble *focusing* until the game is on the line. If he could fix that *problem*, the Giants wouldn't need to come from behind so often!

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  6. Off the top of my head:

    ==> You used one dubious study to "prove" the whole sports world was wrong about replacement NFL refs

    ==> You have criticized an NBA coach leaving in a star player at the end of the game (Kobe?).

    ==> You have criticized NBA teams' strategy wrt 3 pointers

    ==> You have said the "hot hands" thing is dumb

    ==> I am pretty sure you criticized going for 2-point conversion (or maybe not punting on 4th down) strategy of an NFL coach after an important game, but I might be confusing you with someone else.

    In the context of me firing off a snarky blog comment at you, I stand behind my remarks.

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    1. "==> You used one dubious study to "prove" the whole sports world was wrong about replacement NFL refs"

      There was a "strategy" involved in this?

      "==> You have criticized an NBA coach leaving in a star player at the end of the game (Kobe?)."

      No, it was letting him take so many of their end-of-game shots. I am far from alone in this critique: one sports writer has extensively documented how low a percentage Kobe shoots in clutch situations.

      "==> You have criticized NBA teams' strategy wrt 3 pointers"

      Can't recall.

      "==> You have said the "hot hands" thing is dumb"

      I said the "disproof" that there are hot hands doesn't disprove what it says it disproves. In this I agree with most coaches and players!

      "==> I am pretty sure you criticized going for 2-point conversion (or maybe not punting on 4th down) strategy of an NFL coach after an important game, but I might be confusing you with someone else."

      Don't recall. But critiquing one call on one play is just what gripey sports fans do: listen to sports radio! It's not a general critique that widespread coaching wisdom is wrong.

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    2. Oops you're right about the hot hands, sorry. I can't remember what your position was, I just remember thinking you weren't doing the Bayesian inferences right or something.

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