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    All points are not created equal

    by Ken Pomeroy on Monday, May 24, 2010

    Somewhere in the past week, this innocent blog post went viral. At least viral in the sphere of basketball blogs that still publish regularly in the offseason. The upshot is that coaches who bench players with foul trouble are only hurting themselves. It’s more geared towards the NBA, but the same principles discussed in the piece apply to any level of the game. My initial reaction was a desire to share a beer with Joe Morgan and decry the use of stats in sports analysis.

    But as the post picked up link after link after link, there was little dissent from the conclusion that a coach should be maximizing a foul-prone player’s minutes. The result of that thinking would be that a coach simply uses his player independently of his foul count.

    Consider me unconvinced. If a coach is trying to win, he should not be trying to maximize the player’s minutes (even after considering rest). And fortunately, I think every coach understands this. It’s not a product of tradition, it’s a product of trying to win games.

    The problem with the analysis is that it is based on a faulty premise. The object of basketball is not to score as many points as you can and limit your opponent to as few points as possible. You play to win the game. Those two concepts have plenty of overlap, but it’s not difficult to conceive scenarios where they oppose each other.

    The proof of showing that Bill Belichick’s fourth down call was defensible (or possibly even correct) was rooted in the idea that the Patriots chance of winning increased by going for it. Talk of baseball strategy is based on this fundamental as well. This is because winning matters, and all points are not worth the same when trying to achieve that goal. (To be fair, this follow-up post at least acknowledges win probability, but not enough for my liking.)

    It’s difficult to defend that all points are worth the same. Let’s consider the 2010 title game. With 18:23 to go in the first half, Butler’s Ronald Nored missed a three-point attempt. Butler, memorably, would lose the game by two points. If that attempt had gone in, would the Bulldogs have won the game?

    The correct answer is “I don’t know”. From Butler’s perspective, it would have been nice to have those three points. But then the rest of the game may have played out differently. Remember that Duke had a cushion in the waning minutes. If that cushion was reduced, they may not have milked every last second out of the shot clock on multiple possessions, trying harder to score points rather than limit possessions. Win probability calculations indicate that a Nored make in that spot would have increased Butler’s chances of winning by about 2.5%. Not insignificant, for sure, but not a game-deciding shot either.

    Now let’s consider Gordon Hayward’s three-point attempt with one-second left in the game. Same question here: If that attempt had gone in, would the Bulldogs have won the game?

    The correct answer is “yes”. A successful Nored or Hayward three would have both been “worth” three points in one sense, but in terms of contributing to a victory, Hayward’s points would have clearly been worth more.

    And this leads us to why coaches may appear to be overly conservative in saving their best players with foul trouble. You want your best lineup on the floor in the final possessions of a close game. When your best player picks up his second foul five minutes into the game, it’s not worth it to simply play him until he picks up his fifth. The coach doesn’t want to maximize the star’s minutes, he wants to maximize the impact the star can have on the outcome of the game.

    Of course, this is not as simple as saving the star for the last minutes of the game at all costs. In some games, points in the final minutes aren’t worth much, as the outcome is already decided. If you leave your star on the bench for too long, you may find the game becomes out of reach. But coaches don’t sit a star player with two fouls until there are five minutes left, either. They continually adjust their approach based on time and score. I’m guessing that most coaches have a good understanding of win probability, even if they would articulate it in much different ways than I would.

    Now, there’s plenty of room for studying how to maximize a player’s impact, or to predict how likely he is to foul out given additional minutes played. And I’m pretty sure that work has been done by people that aren’t in a position to share it publicly. I don’t profess to have the answers on that. But it’s safe to say that maximizing a star player’s minutes is not necessarily going to maximize a team’s chances of winning when the star picks up early fouls.

    I’m going to have a lot more to say about win probability soon, but one interesting finding is that a tie game at halftime barely changes a team’s initial win probability. If a favored team makes it to intermission tied, they haven’t given up anything in terms of their chance of winning the game. In that context, one might see why a coach would err on the side of saving a superstar rather than keeping him in the game to try to build a lead and thereby risk losing him for potentially more important moments later on.

    While I don’t doubt that some coaches at the college level have counter-productive biases in this area, I would be surprised if taken collectively, the 347 Division I coaches are significantly more conservative than is warranted. There are a bunch of ancillary factors not discussed here that influence how long to bench a star with foul trouble (most notably, whether he’s particularly foul-prone anyway), and coaches have a limited time to process that information and make a decision. This is a much more complex issue than the author of the original post made it out to be, but for now I’m taking the coaches’ side on this one.