This post is about game planning and play-selection

Suppose first that you wish to cross a river that is spanned by three bridges. (Assume that swimming, wading or boating across are impossible.) The first bridge is known to be safe and free of obstacles; if you try to cross there, you will succeed. The second bridge lies beneath a cliff from which large rocks sometimes fall. The third is inhabited by deadly cobras. Now suppose you wish to rank-order the three bridges with respect to their preferability as crossing-points. Your task here is quite straightforward. The first bridge is obviously best, since it is safest. To rank-order the other two bridges, you require information about their relative levels of danger. If you can study the frequency of rock-falls and the movements of the cobras for awhile, you might be able to calculate that the probability of your being crushed by a rock at the second bridge is 10% and of being struck by a cobra at the third bridge is 20%. Your reasoning here is strictly parametric because neither the rocks nor the cobras are trying to influence your actions, by, for example, concealing their typical patterns of behaviour because they know you are studying them. It is quite obvious what you should do here: cross at the safe bridge. . . .

[Now s]uppose that you are a fugitive of some sort, and waiting on the other side of the river with a gun is your pursuer. She will catch and shoot you, let us suppose, only if she waits at the bridge you try to cross; otherwise, you will escape. As you reason through your choice of bridge, it occurs to you that she is over there trying to anticipate your reasoning. It will seem that, surely, choosing the safe bridge straight away would be a mistake, since that is just where she will expect you, and your chances of death rise to certainty. So perhaps you should risk the rocks, since these odds are much better. But wait … if you can reach this conclusion, your pursuer, who is just as rational and well-informed as you are, can anticipate that you will reach it, and will be waiting for you if you evade the rocks. So perhaps you must take your chances with the cobras; that is what she must least expect. But, then, no … if she expects that you will expect that she will least expect this, then she will most expect it. This dilemma, you realize with dread, is general: you must do what your pursuer least expects; but whatever you most expect her to least expect is automatically what she will most expect. You appear to be trapped in indecision. All that might console you a bit here is that, on the other side of the river, your pursuer is trapped in exactly the same quandary, unable to decide which bridge to wait at because as soon as she imagines committing to one, she will notice that if she can find a best reason to pick a bridge, you can anticipate that same reason and then avoid her.

The above passage is from here. Can you explain in what way this informs play-calling and gameplanning? Here’s an (incomplete) hint.

  • steve

    Have you ever heard of Plato? Aristotle? Socrates?

  • greg

    Steve, gotta love the Princess Bride reference!

  • Tom


    Do what you do well. Have enough in the passing game to defeat any coverage. Preach physicality in the running game above multiplicity. And above all, don’t ask your players to do something they cannot do.

    Many coaches become pseudo-obsessed with “decided schematic advantages” that they forget to review what their players can and cannot do well.

  • Bill C.

    I’m telling you…this is the secret of the universe:

  • John B

    Ha, I read your “incomplete hint,” and the bit about choosing plays randomly reminded me of the time that I played my wife in Madden ’05. She had never played before and generally didn’t even know what play she was calling, letting the computer actually run the play. “Knowing football” gave me absolutely zero advantage because her play calling had no pattern. It was a much closer game than I care to admit.

  • Dave

    As I read the excerpt I thought of the article that is the hint.

    I get the point of the bridges example, but couldn’t one arrive to the conclusion to just randomly choose a bridge? If you know what the other person is probably thinking, and you know that they probably know what you are thinking, wouldn’t randomly choosing negate that? Or perhaps even better, wouldn’t illogically choosing a bridge work too?

  • Chris

    Dave, but then the other side might guess that you’d illogically pick the bridge that would pose the most risk to you, and she’d be standing there waiting for you….

    One takeaway (and not the only one) is that, play-calling is not easy, and a mixed strategy “kinked” in a direction of your strength but otherwise random might be the best, or at least the best starting point.

  • Dave

    “but then the other side might guess that you’d illogically pick the bridge that would pose the most risk to you, and she’d be standing there waiting for you….”

    But wouldn’t that be picking logically? It’s a continuation of the guessing game. Picking illogically to me would be like choosing the bridge with snakes because you like snakes and your pursuer doesn’t know that you like snakes. She might be on the other side but it would be because of luck and not because you were outsmarted.

  • Chris


    Yes, if that’s what you mean by illogical then that’s fine. You also could just choose randomly, and that was part of the answer.

  • Mr.Murder

    If you take the third bridge you can hear the woman shooting snakes and thus you know where she’s hiding.

    I’m trying to group plays in two categories.

    Situation(conversion, red zone, third down keys).
    Field placement.

    Then we can have a play call sheet that combines the two. On the armband we can color higlight the situation, and have that placed with the center placement for balance.

    Then we still have placement selections for wide field sides, and perhaps a restraint play or two built into those.

    We can run a lot more items in effeciency terms from placements to our sideline, so the restraint calls, different plays, should be there with greater frequency.

  • stan

    I’m not sure that your bridges provide a very good model for the decision-making involved in football playcalling. In football, both coaches have a lot of hidden information [e.g. my guard can’t pull this week because of a bad ankle, my QB lacks confidence to make a certain throw (or maybe the coach lacks it), we’ve figured out your tackle is tipping plays, our self-scout shows we developed a tendency (if you noticed, we’re going to cross you up), we have a major mismatch to exploit here and a disadvantage to cover for there, etc.

    More importantly, both offense and defense have dynamic decision-making. Players are coached to react and change on the move. This enormously complicates any attempt to quantify the odds of success or failure, even if you could calculate them for a given play vs. a given defensive call. In reality, coaches don’t really try to quantify relative odds in their playcalling. The large numbers of parameters, many without calculable metrics, make it effectively impossible.

    At best, you get some a feel or sense that some calls being riskier than others, and a sense that certain calls are better at exploiting the advantages your team has in a given situation. Unless you are confident you’re reading his mail, you can’t get too wrapped up in what specific call the other guy is making.

    When I have more time, I’ll pass on some advice I heard the other day that Norm Chow gave another college OC a few years ago when he was with the Titans.

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  • Breck

    John B, while what you are saying is true, you will not be playing your girlfriend if you are coaching a real football team. You will be going against coaches who know as much as you do if not more, and because of your football knowledge, you are more in tune with each other’s patterns and rhythms.