Bill James shares his method to determine when a college basketball game is out of reach.

Previously published Slate articles made new.
March 18 2009 7:03 AM

The Lead Is Safe

How to tell when a college basketball game is out of reach.

Also in Slate, Josh Levin runs through the Teams We Hate in this year’s bracket, and Chris Wilson explains a system that will help you win your NCAA pool.

There are five minutes to go and your team has a 15-point lead. You start to flip the channel but then have a moment of doubt—is there a chance that the other guys could come back and win? From now on, you'll never have to wonder. Last year, Bill James, a lifelong Kansas Jayhawks fan, shared his personal formula to determine when a lead in a college hoops game is safe. If you're thinking about switching to another game during March Madness, just keep this page open and plug the current score into the Bill James Lead Calculator. The piece is reprinted below.

Tyler Hansbrough #50 of the North Carolina Tar Heels. Click image to expand.
Tyler Hansbrough

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 don't have a calculator handy, use the tool below to do the calculations for you.)

If you've got a 10-point lead and the ball with 10 minutes left, is that a safe lead?

Of course not; teams come back from a 10-point deficit all the time. A 10-point lead, plus the ball, gives you a 7.5-point safety margin. It's safe for 56.25 seconds—56, rounded down. With 600 seconds to play, a 10-point lead (with the ball) is 9 percent safe. That doesn't mean a team with a 10-point lead and the ball with 10 minutes to go has only a 9 percent chance of winning. Rather, it means they're 9 percent of the way to having a completely insurmountable advantage.

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.

But if that answer doesn't work for you ... you pay a price in sports for anything you believe that is not true. The fact is that everybody around a college basketball game—the coaches, the announcers, even the referees at a lower level—calculates when the game is really over. They calculate it with intuition and guesswork. When the lead is judged to be safe, the coaches empty the bench. When the lead is judged to be safe, the announcers start re-ranking the top 25 and talking about the upcoming games or the next-round matchups. When the lead is safe, the Jayhawk fans start doing the slow, spooky Rock Chalk chant. I love that.

If a coach misjudges the moment at which the lead is safe, he can empty the bench too early and get himself into trouble. I've never actually seen a coach lose a game that way, but I certainly have seen coaches misjudge when the lead is safe, empty the bench too early, and get hit by a haymaker. More commonly, because coaches are afraid that that might happen, they continue to compete after the game is beyond any reasonable possibility of a reversal. That has consequences, too. You can get a player hurt playing for nothing. You can miss the opportunity to get a little bit of rest for players who are tired at the end of the season but have a game on Saturday. You can miss the opportunity to get that 12th man his 20 seconds in an NCAA tournament game—and if there's no value in that, then why do they do it?

And I think we've all seen games in which the announcers misjudged the moment when the lead was safe and started talking about the consequences of an outcome that was never to be. Probably announcers don't enjoy doing that.

I have never personally seen a game in which a team lost after having a safe lead. In February 1994, LSU led Kentucky by 31 with 15:30 left to play, only to see Kentucky rally for a 99-95 victory. That was impressive, but a 31-point lead without the ball is safe for 12:36. The lead was 81 percent safe. And then this year, LSU blew a 15-point lead to Villanova with 2:59 to go—which, again, is close but no kewpie doll. With 179 seconds to play you need a 13.5-point margin, which means a 16-point lead with the ball or 17 without. The curse of Dale Brown. Actually, I would guess Dale was cursing up a storm when that happened.

My editor, doing his due diligence, found one game in which a team lost after holding a safe lead. On March 2, 1974, North Carolina trailed Duke, 86-78, with 17 seconds to play—a safe lead for Duke. Duke had repeated misadventures in in-bounding the basketball and wound up losing the game in overtime. That was before the human typo was hired to coach Duke, but ... does anybody know where I could get a tape of that game?

My little formula, over the course of 40 years, has wormed its way into our family's college basketball experience. Early on in every game, usually once in the first half when the score is about 23-21 and again midway through the second half, I will observe soberly, in my best faux-expert voice, that "the lead is not safe," and my wife will look at me not only as if I were an idiot, but as if for some reason she is surprised by this. In the closing minutes of a tense game, it gets serious: "Is that it? Is the lead safe yet, Dad? How much more?" They are waiting to exhale, waiting to unbundle their nerves. They know that every time the clock stops, when I should be scoping out the cheerleaders, I am recalculating the lead in the back of my head. I've been doing it so long, I can do both at the same time.

I hope you get something out of it.

And if you do, tell Ralph Nader. It's over, man. Go home.

Correction, March 17, 2008: This piece originally misstated a possible heuristic for determining whether a basketball lead is safe. Rather than "[t]he game is over when the number of points you are ahead (or behind) is more than 10 times the number of seconds left in the game," it should have read "more than one-tenth the numbers of seconds." (Return to the corrected sentence.)

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