How to tell when a college basketball game is out of reach.
By Bill James|Posted The Slate (a while ago, but a good one!)
Question: How do you know when the contest is not officially “over,” but the outcome is no longer in doubt?
Answer: How would I know? I was a Huckabee guy.
With apologies to the Sage of St. Louis, there comes a time when it ain’t over, but … it’s over. There comes a time in a relationship when a woman will still answer your phone calls, but you’re wasting your money buying flowers; you know what I’m saying? There comes a moment during a job interview when you’re still talking, but you might as well take off your shoes. There is a time in an illness when you’re not dead yet, but you might as well stop taking that nasty medicine.
There is a line there somewhere, and how do you know when the line is crossed that separates hope from fantasy? If we’re talking politics, romance, job interviews, or medicine, I don’t know. When it comes to college basketball, I’ve got a theory.
This thing has a 40-year history, actually. I’ve been attending basketball games at Allen Field House in Lawrence, Kan. (home of the Jayhawks), since 1967. The Jayhawks usually win by 15 or 20 points, and sometime in about 1968 I started wondering whether there wasn’t some way to decide when the game was no longer in doubt. I began to experiment with heuristic inventions to try to find the moment at which the line was crossed. A heuristic could be loosely defined as a mathematical rule that works even though no licensed mathematician would be caught dead associating with it.
Let’s see … what about: The game is over when the number of points you are ahead (or behind) is more than one-tenth the number of seconds left in the game? *
Nah, that doesn’t work. If you’re 30 points behind, the game is over much more than five minutes out (300 seconds); if you’re two points behind, the game is not over when there are 20 seconds left. The rule doesn’t work on either end.
Eventually I found a rule that did work at that time, but at that time there was no 3-point shot in basketball. When they added the 3-point line, I had to recalibrate my system.
OK, I’ve stalled as long as I can. You ready?
- Take the number of points one team is ahead.
- Subtract three.
- Add a half-point if the team that is ahead has the ball, and subtract a half-point if the other team has the ball. (Numbers less than zero become zero.)
- Square that.
- If the result is greater than the number of seconds left in the game, the lead is safe.
If you’ve got a 10-point lead and the ball with 10 minutes left, is that a safe lead?
An 11-point lead with nine minutes to play—we’ll let you keep the ball. That’s an 8.5-point safety margin with 540 seconds to play; it’s 13 percent safe (72.25 divided by 540).
A 12-point lead with eight minutes to play … that’s a 9.5 point margin. It’s 19 percent safe (90.25 divided by 480).
A 13-point lead with seven minutes to play … 26 percent safe.
A 16-point lead with four minutes to play … 76 percent safe, assuming the team with the lead also has the ball. It’s really unusual for a team to come from 16 back with four to play and win, but it does happen. I would guess it happens twice a year somewhere in the world of college basketball.
A 17-point lead with three minutes to play … bingo. That’s a safe lead. Seventeen points with three minutes to play is a safe lead whether you have the ball or not, actually; a 17-point lead with the ball is safe at 3:30; a 17-point lead without the ball is safe at 3:02.
Once a lead is safe, it’s permanently safe, even if the score tightens up. You’re down 17 with three to play; you can make a little run, maybe cut it to 8 with 1:41 to play. The lead, if it was once safe, remains safe. The theory of a safe lead is that to overcome it requires a series of events so improbable as to be essentially impossible. If the “dead” team pulls back over the safety line, that just means that they got some part of the impossible sequence—not that they have a meaningful chance to run the whole thing.
Why calculate when the lead is safe? The real answer is “because I like to.” I like to feel that I understand little things about sports. I like to feel that I can see the difference between a safe lead and a live contest for the same reason that I like to feel that I can recognize a zone defense and recognize a pick-and-roll.
Blog post by: RobbieStats (Statsheet.com) on this very topic
Before I started using this on StatSheet I wanted to test (Bill James’s Formula) out. For the close to 10,000 games I have in the StatSheet database that contain game flow data (ie, scores throughout the game), I wasn’t able to find one that failed the Bill James test. None of the games had a different outcome than the one computed by Bill’s formula. In the aforementioned article, there was at least one game his editor was able to find that broke the Bill James test. It was none other than the magical comeback by UNC when the Heels were down by 8 with 17 seconds to go against Duke in 1974.There may be other cases, but it is clear his formula works most of the time. But that might also suggest that his formula is too conservative. This is where I plan on evaluating and possibly changing the formula if I can find other indicators that determine a game is over sooner. Bill just went by the score, but I have access to both team and player stats (seasonal and game-by-game) which may help predict even better. More to come on that!For now, if a game is “statistically over” sooner than the end of the game (some games are so close they aren’t over early), you’ll see it highlighted. Here is an example: http://statsheet.com/mcb/games/2008/04/05/kansas-84-north-carolina-66– See more at: http://statsheet.com/blog/when-is-a-basketball-game-statistically-over#sthash.KNPGLVvB.dpuf