What’s The Chance?
My good ol’ friend Dr. F., that I mentioned in a previous post, loves football. When his team is playing, he will always watch until the very end, which at times I find questionable. When it’s a close game, and the weather outside is not conducive to a game of catch, I don’t mind as much. But if his team is down by 3 touchdowns with :30 left, he’s glued to the tv, waiting until the game is official. He’s confided in me that his mind is trying to figure out how his team can win the game. It goes something like “if the quarterback fumbles the snap, and the defense recovers. We can get a quick score on a missed tackle, then get the onside kick…” I guess when you grow up and witness a tragic sporting event, it scars you for life.
At these times, when the last seconds of a meaningless (and already lost) game bore me to tears, I wish I had some logical argument to say, “with your team losing by X points with Y time left, there is Z% chance of winning.” Having this kind of knowledge would be great when watching any sporting event. For example, if the Knicks are up by 12 to start the fourth at home, wouldn’t it be great to say that they have a 94% chance of winning the game? To do something like that you would probably have to look at all the games played where the home team was winning by 12 points in the fourth quarter, and see what percentage of teams won the game. In fact maybe you could do that for every single game & map out the winning chance for any score & time?
Well someone did, and I can stay in line with my theme this week of “talking about the APBR_analysis group”. In their files section there is a chart called “game_state_matrix.pdf” (uploaded by Dean Oliver – who else?). Actually, it’s not one charts, but two. The top chart is when the home team is winning, and the bottom one for the road team. Along the left side is the lead, and along the top is the time left in the game. If you remember your coordinates properly the first number at (Q1, 0) is .57. That means at the end of the first quarter (Q1) if the home team is leading by 0 points, the chance of winning the game is 57%.
What’s interesting to me is the road team’s chances. If the road team is winning by 1 at the end of a half, they’ll only win 45% of the time. Let’s say right before the half, the road team is winning by one. By holding for the last shot, and hitting a 3 pointer, their chance of winning goes up to 56% (Q2, 4). We know that the home team wins 64% of the time. Having a one or two point lead at the half doesn’t give the road team good odds to win (not more than 50%). But by the third quarter the road team has the advantage. Having as little as a 5 point lead going into the final 12 minutes gives them a 68% chance of winning.
There are more interesting applications of this. Let’s say we’re the coach of a team, and we’re up by 1 point with a minute left. Does it make sense to try for a 3 pointer with an X% shooter or a 2 pointer with a Y% shooter? Two more points will increase your chances of winning from 64% to 82% at home and 64% to 79% on the road. However a 4 point lead will increase your chance all the way up to 97%/96% (home/road). That’s a 15% increase of winning, so if you have a good three point shooter that you can get open, it’s a good idea for that player to try and knock down that shot.
Now I’ll have to find if someone has created one of these charts for football. This way I can increase my chances of getting in a game of catch between the 1pm & 4pm football games with Dr. F.