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# Up Three, Without the Ball: To Foul or Not? New Insight

Many statistical experts feel that NBA coaches are too timid in intentionally fouling when their team is on defense, up three points, in the closing seconds of a game.

It's an old coaching question. Now there's some new evidence to inform the debate.

The idea is that a good foul would give the opponents a measly two free throws and your team the ball. Presto, you've eliminated the possibility of a game-tying 3! Tidy! Nice! If all goes according to plan, that would ice the game, right?

Is it true? Does that work?

The Situation
It's one complicated thing to study, because all does not often go according to plan. Some potential complications of fouling, for instance:

• Away from the basket, the foul could lead to three free throws.

• The trailing team could make the first free throw, miss the second, get the rebound (NBA teams grab about 14% of their own missed free throws) and hit a shot (2 or 3) to tie or win.

• A player intentionally trying to foul can be called for a flagrant foul, a clear path foul or an away-from-the-play foul, which gives the trailing team one (clear path, away from the play) or two (flagrant) free throws and the ball.

• Other weird stuff could happen, like a turnover.

This is an end-game strategy, but how do you know when it's the end of the game?

That's the debate. Everyone knows intentionally fouling with ten minutes left really hurts your team. But at some point, as the buzzer approaches, that changes.

When Does Fouling Become Useful?
If you're up three with, say, eight seconds left, the mere passage of time is valuable. Don't you just know it in your bones that a 3-point lead with eight seconds left -- that could be three possessions! -- is not nearly as secure as the same lead with two seconds left? What is the cost of taking that time pressure off your opponent?

With two seconds left, however, I'd imagine the numbers would show fouling to be brilliant. But with nine seconds? Who knows? At what point does it become useful?

John Hollinger has written about this quite a lot, and makes it clear that opinions differ as to at what point this strategy starts paying off.

I'm a big advocate of fouling when up by three in late-game situations, especially when the opponent is out of timeouts, but generally you need to be in single digits on the clock to make it worthwhile. Stan Van Gundy said his own rule of thumb was six seconds, while Jackson said his was five; regardless, it sure as heck isn't 11.

Hollinger makes a tremendous point: It matters if your opponent has a timeout left or not. With one, they can shoot their free throws, foul you to get the ball back, and then call a timeout to move the ball and strategize their next play. A timeout also lets the trailing team stop the clock in the event the leading team misses its final free throw.

Ten Seconds is Likely Too Many
In his new book "Mathletics," Wayne Winston -- Indiana University professor and consultant to the Dallas Mavericks -- tackles this issue, and offers some new data. First, he faults two of the main studies on the topic, by Lawhorn and Annis, for failing to account for the many different ways games can unfold. Neither, he says, embraces the idea that a game has an unknowable number of possessions left.

Then Winston does something delightfully simple. He asks: Has it worked? He presents, for the first time I'm aware, the evidence:

A student in my sports and math class, Kevin Klocke, looked at all NBA games from 2005 through 2008 in which a team had the ball with 1-10 seconds left and trailed by three points. The leading team did not foul 260 times and won 91.9% of the games. The leading team did foul 27 times and won 88.9% of the games. This seems to indicate that fouling does not significantly increase a team's chances of winning when they are three points ahead.

He adds a key footnote:

We believe more work needs to be done to determine the definitive answer to this question. We are working on a simulation model of the last minute of a basketball game that should help settle the issue.

No Hard and Fast Rule, Yet
About the time I wrote that, David Thorpe called. I asked him if, when he coached, he had a rule to foul with a certain number of seconds left.

"I would not have a hard and fast rule," he explained. "I'd have a fluid game to game strategy."

What he'd direct his players to do would depend on many factors, including personnel. "If I thought they could execute a foul on the dribble, I'd do it. But if there was a player in the game that I didn't trust to make the right decision, I might just tell one or two players to make that play if someone dribbled near them. If you foul a player who is standing with the ball, they have an opportunity to make it look like they were in the act of shooting. Do you have five guys you can trust to handle it? You also have to think about the referee. Did you cuss him out five minutes ago? Is he a grandstander who'd love to turn a game on an intentional foul call? You also have to ask yourself how likely the other team is to rebound their own free throws. It's pretty nuanced." (UPDATE: IMG Academies' Mike Moreau adds: "This has to be practiced well before you try to execute it in a game. You have to foul a guy on the dribble, before he can gather. That takes practice. And even then, the execution can get screwed up in the heat of the moment.")

If he decided to foul, however, Thorpe said he could make the call from the sideline when the clock got into single digits, with the realization it takes a while to actually achieve the foul. "You'd be lucky" he says, to actually achieve the foul in two or three seconds.

Where does all that leave us? Although the sample sizes are small, it seems hard to make the case that fouling, up three, with "1-10" seconds left is clearly advantageous. What about with six or fewer seconds on the clock -- does that change things?

In time, I suspect we'll get a real answer to something like that. Soon we will probably know the point on the clock after which the odds favor fouling over just playing defense.

But even when we get there, the odds will only ever be the odds. As in, C3P0, hollering in Han Solo's ear about how impossible it is to successfully navigate an asteroid field.

Coaches will still have the opportunity to be Han Solo, which will make them look brilliant if they can muster the insight and skill to steer against the odds, through the asteroid field, to land safely inside the giant space worm of victory.