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    Studying whether to foul when tied, Part 1

    by Ken Pomeroy on Sunday, July 13, 2014


    Late in the 1983 national championship game, heavily-favored Houston held the ball with a little over a minute remaining in a tie game. In the pre-shot clock era, Houston had the opportunity to hold for the last shot. N.C. State head coach Jim Valvano implemented what would be considered a controversial strategy today, ordering Dereck Whittenburg to foul Alvin Franklin with 1:05 remaining, instead of playing defense and hoping to get to overtime.

    Neither member of the CBS broadcast team, Gary Bender or Billy Packer, criticized the idea. Actually, the normally disagreeable Packer was fully supportive of the strategy. And he should have been. Franklin was a 63 percent shooter from the line, and—spoiler alert— I’ll show the math that supports that Valvano gave his team a better chance of winning by giving the foul, assuming Franklin truly had a 63 percent chance to make his free throws.

    Today, observers would not be so kind to the Valvano strategy. While popular opinion has seemingly turned the corner on championing the dubious philosophy of fouling while up three with a few seconds remaining, for whatever reason there are few observers who would endorse fouling when tied. Perhaps the introduction of the shot clock changed the thinking. Anyway, I suspect Packer himself might sing a different tune if he were still calling games.

    This is not an uncommon situation, by the way. Over the past five seasons, there have been 615 cases where a game was tied with a possession beginning with between 25 and 35 seconds remaining. It happened twice in the 2014 Elite Eight with both Arizona and Michigan on the defensive end of this scenario (and ultimately losing).

    In this situation it feels like overtime is a victory for the defense, and that’s may be how coaches, media, and fans view it. For that reason, there’s little discussion about an alternate strategy. If the goal is to get to overtime, then it would be foolish for the defense to foul. But if the goal is to win, then there are cases where the math justifies fouling.

    Especially for an underdog that would be expected to lose in overtime, there are times when the possibility of winning in regulation more than compensates for the chance of giving points to the opponent. Over the past five seasons, the defending team won 34.5 percent of the time when faced with the scenario described above. Given that the regulation win is largely a pipe dream for the defensive team, it shouldn’t be surprising that they are significant underdogs in this situation.

    Unlike the fouling-up-three situation, where there are plenty of cases of teams utilizing one of two possible strategies (either fouling or playing traditional defense), the fouling-when-tied idea is to my knowledge not used by anyone intentionally. So investigating this situation is not as simple as looking at history and comparing how two strategies have fared.

    What we can do is use history to figure out the win probabilities that would result after the fouling strategy was implemented. In the following calculations of expected winning percentage, I am assuming that a team has a 50 percent chance of winning a game that goes to overtime. I’ll eventually discuss the ramifications of changing that number.

    First, here’s the data on the defensive team winning with a tie score and the shot clock off:

    On defense (possession beginning with between 25-35 seconds left)
    Score     W   L  OT  W%
    ------------------------
    Tied     37 228 350 34.5
    
    

    Assuming the teams are of comparable ability, any alternative strategy one uses has to be successful more than 34.5 percent of the time for it to be justified.

    If the defense chooses to intentionally foul, they figure to get the ball back either tied, down one, or down two. It’s clearly best to give this foul early in the possession, so the assumption will be used here that the fouling team gets the ball back with between 20 and 25 seconds left. Here are the historical win chances for the fouling team in those cases.

    On offense (possession beginning with between 20-25 seconds left)
    Score     W   L  OT  W%
    ------------------------
    Tied    228  37 350 65.5*
    Down 1  132 234  58 38.0
    Down 2   40 310 123 21.5
    
    

    Through this information, one can start to see the appeal of fouling. If the opponent doesn’t make a free throw, the fouling team has flipped the script and made itself the last-possession bully. Even if the opponent makes one free throw, the fouling team has improved its chances slightly. It’s only the case of making two where the fouling team’s chances of winning are harmed.

    At this point, the alert reader realizes this analysis is missing a key factor that hurts the fouling math a bit - the offensive rebound. For both the tied and down-1 scenarios, we must investigate whether the offense or defense rebounds the missed free throw. I’ll get to that in the next installment, as well as some specific scenarios where this strategy could have been used.

    *I’ve simply reversed the chances of winning when tied with 25-35 seconds left. Over the past five seasons, the defensive team actually has a slightly better winning percentage (35.8) when tied and the possession begins with between 20 and 25 seconds than if the possession began with 25 to 35 seconds (34.5). This is probably due to the amount of noise in the data, and therefore I’ve applied to latter figure to both cases.