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    The 18th-most improbable win

    by Ken Pomeroy on Sunday, September 30, 2012


    One of the more famous comebacks last season was Western Kentucky’s triumph over Mississippi Valley State in the NCAA tournament. Sadly, it just missed the list published here last week. But since it was probably viewed in real-time by a few of you, I thought it would be a way to show why the win probability model seems like it may be a bit too certain of itself in some cases.

    After Cor-J Cox scored with 5:03 left, the Delta Devils led 53-37. At this point the Hilltoppers had just a smidge more than a 1% chance of winning*. Western Kentucky eventually won 59-58, becoming the only team last season to overcome a deficit of at least 15 points at the five-minute mark.

    Technically they were the only team to overcome at least a 13-point deficit with five minutes left. In fact, only three times all season did a team blow at least an 11-point lead with five minutes left. Here’s the data in monospaced, slab-serif form…

    Record with lead of x with 5:00 remaining (data from 2011-12 season)
     X    W-L
    >19 912-0
    19  110-0
    18  115-0
    17  116-0
    16  153-1
    15  164-0
    14  161-0
    13  202-0
    12  186-1
    11  220-1
    10  238-6
    
    

    Based on this, we might think that almost any double-digit lead is extremely safe with five minutes left. Indeed, these leads are probably safer than most observers give them credit for, but there are some cautions that need to be applied to interpreting this data.

    First, we need to consider that most of these cases involve the better team leading at this point. More specifically, of the 2,586 games where there was a double-digit lead at the five-minute mark, the trailing team was the pre-game favorite in just 56 of them. Four of the nine comebacks were from this select group of 56. The second-biggest favorite to face such a deficit, Temple against George Washington, was one of the successful comebacks. (The biggest favorite to face this deficit occurred in this game between UAB and Tennessee-Martin.)

    The lesson is that if you find yourself at the Bryant/Indiana game on November 9, and Bryant is winning by at least ten with five minutes to go, don’t leave. Because of what we know about Indiana’s skill level relative to Bryant’s, that lead is probably not very safe. Western Kentucky was just a modest favorite against the Delta Devils at tip time, so their victory was highly improbable, but not at unlikely as the bulk data would leave you to believe. (Hence the 1.01% chance.)

    But saying these leads are “safe” is not really the best description either, even though the leading team has a very high chance of winning. Yes, almost all of these leads result in victories, but not all of them finished without some nervous moments.

    Let’s violate the most sacred of coaching principles and talk in terms of moral victories. If the team facing a double-digit deficit with five minutes remaining is able to come back and tie the game at some point, I’m giving them a moral victory (and the loser, a moral defeat). Here’s how the previous table would look in that case.

    Record with lead of x with 5:00 remaining (data from 2011-12 season, moral defeats included)
     X    W-L
    >19 912-0
    19  110-0
    18  115-0
    17  116-0
    16  153-1
    15  163-1
    14  161-0
    13  202-0
    12  184-3
    11  217-4
    10  229-15
    
    

    There are 15 additional contests where a team erased a double-digit deficit in the last five minutes and still lost. Overall, teams that came back from a double-digit deficit with five minutes to go and eventually pulled even had a 6-15 record. That kind of puts a damper on the theory of momentum. Although, I’m guessing most of these cases involve teams that never had the ball with a chance to break the tie, so there’s probably no such thing as anti-momentum**, either. Indeed, the case of the 15-point comeback was this December 30th game, where Santa Clara went on a 20-5 run only to have Wagner win the game on the final possession. The experience was so traumatic for the Broncos that they wouldn’t win another game the rest of the season.

    The point here is that these kinds of things (and more extreme cases like the Pacific choke-job-turned-miracle-comeback against Idaho State) are baked into win probability. Thus, X chance of winning is not the same thing as X chance of winning easily. We haven’t even considered the cases where a team got within, say, three points.

    If your only exposure to college hoops last season was the Tuesday play-in game, you might think the concept of win-probability is useless. Western Kentucky didn’t just win, but they increased their chances of winning to better than 50% by the two-minute mark thanks to a 15-0 scoring blitz. Yet by relying on a larger set of data, it becomes clear that while they made it look fairly easy, the Hilltoppers’ comeback and victory was extremely unlikely. That is the knowledge gained from a win probability model.

    *When I state so-and-so has X chance of winning, it’s just according to my model. Somebody else’s model may differ. We can never truly know a team’s chance of winning at any given time. It is a mystical figure and this is just one man’s effort to estimate it objectively.

    **For a while, I though anti-momentum existed. If a team pulled off a big comeback in a game, they’d be less likely to win than in other cases.  But using last season’s data and the five-minute mark as a momentum-starting point, that doesn’t appear to be the case. More monospacedness…

    Performance in OT games where a lead was blown with five minutes remaining
     Lead     OT
    Blown   Games  Wins   Pct
       12      1     1  1.000
       11      2     1   .500
       10      6     5   .833
        9      4     3   .750
        8      9     4   .444
        7     12     6   .500
        6     20     8   .400
        5     37    14   .378
        4     44    22   .500
    Total    135    64   .474
    
    

    For instance, a team with a ten-point lead at the five-minute mark went 5-1 when they were taken to overtime. Based on the data overall, I’m guessing you could predict overtime outcomes by just going with the better team’s chances from the model, massaging for foul trouble, and ignoring momentum considerations.