With 16.6 seconds left in overtime and his Los Angeles Lakers up by one, Kobe Bryant had to decide, in an instant, whether to take the shot or drain a little more time from the clock and deny the Boston Celtics a chance to score.
Bryant moved within 30 feet of the basket at TD Garden as the clock ticked down. Fifteen seconds. Fourteen. Thirteen. With 12 seconds remaining and Celtics guard Ray Allen coming up fast, it was crunch time. Bryant could milk the clock and leave the Celtics only a few seconds to answer, or go for a quick three but risk missing and leave Boston time to attempt a game-winning shot. He split the difference, making his way to the free throw line and taking a jump shot.
A recent study suggests Bryant, like many NBA players, made the wrong choice.
Brian Skinner, a physics research associate at the University of Minnesota, explored the nature of shot attempts in the NBA. In his paper, published in the online journal PLoS ONE, Skinner said he wanted to determine when a player should take the shot.
"It just depends on how much time I have left." -- Kobe Bryant "Within this model I derive an answer to the question 'how likely must the shot be to go in before the player should take it?,'” Skinner wrote.
He discovered through an analysis of scoring situations that NBA players often wait too long to shoot and it could cost teams an average of 4.5 points per game. Rather than take the sure thing early in a possession, players wait it out, taking time off the clock and hoping to make another, possibly tougher, shot pay off. Although that denies their opponent a chance to respond, it also deprives their own team of a chance at a basket before the shot clock expires.
Although Skinner specifically didn't examine end-of-game situations, Bryant's performance in last Thursday night's game against Boston could highlight that finding.
With 12 seconds on the shot clock and no other defender besides Allen to harry him, Bryant used up six seconds fighting Allen to the left corner of the free throw line. As Celtics forward Kevin Garnett joined the fray from the right corner of the line, Bryant spun away from Garnett and took a turnaround jump shot with five seconds remaining. The ball clanked off the rim. The Celtics collected the rebound, but it was too little, too late.
That the Lakers were up by one point afforded Bryant the luxury of taking a tough shot. Although he didn't necessarily have a good opportunity for a high-quality shot just a few seconds before, Skinner's research suggests Bryant's decision to drain time from the clock was typical of the league. He found players tend to be overly reluctant to shoot early in a possession and therefore miss scoring opportunities.
"NBA players may be unwilling to settle for only moderately high-quality shot opportunities early in the shot clock, believing that even better opportunities will arise later," Skinner wrote.
He also notes that the likelihood of a turnover plays into the equation.
"If the players believe, for example, that their team has essentially no chance of turning the ball over during the current possession, then they will be more likely to hold the ball and wait for a later opportunity," he wrote.
Yeah, whatever, Bryant responds. He told Wired.com after a recent matchup with the New York Knicks that there are countless variables, and his decision to shoot -- or not shoot, as the case may be -- depends upon who's on the floor, where they're standing and how much time is left on the clock.
"If I can kick it to somebody, a lot of times I wind up getting a hockey assist, so it just depends on how much time I have left," Bryant said. "If there's a chance to pass and swing [to another player] for another opportunity, that's fine. If there's not, then I have to create space and get a shot up, understanding that there are two [players] on me and it's going to be a great opportunity for us to get an offensive rebound."
Except in this case, the Lakers didn't get the offensive 'board. In the end, though, it worked out for the Lakers when forward Pau Gasol blocked Allen's last-second shot for the Celtics. The Lakers won, 88-87, in OT.
In analyzing teams' shot quality, shot rates and shot percentages, Skinner found that the average NBA squad has a 4 percent probability of shooting the ball when left with 15 seconds on the shot clock in their final possession. The ideal rate is 12 percent.
Skinner didn't offer guidelines for exactly when a team should shoot. So many variables exist, particularly the subjective nature of defining a quality shot, that it's difficult to say for certain when a shot attempt is worthy. But Skinner's data showed teams could increase their average points-per-possession from .86 to .91 if they took the ideal shot instead of milking the clock. That works out to about 4.5 points per game.
Lakers head coach Mike Brown isn't convinced. Asked about his late-game philosophy, Brown said, "If we're down [one point], we need to [shoot] right away to extend the game. If we're up, hey, hold it and let's try to milk as much clock as we can."
Bryant found himself in essentially the same situation Sunday against the Toronto Raptors. Down 92-91 with seven seconds left, Bryant received an inbounds pass in front of the Raptors' bench, dribbled toward the baseline and lofted a shot. The ball sliced through the net with 4.2 seconds remaining. The Raptors made one last attempt but came up short. The Lakers won.
No matter how the clock is managed, sometimes it pays to have a great player.
UPDATE, 3:45 p.m. EST Feb. 15: An earlier version of this post said Skinner's research focused on end-of-game situations when in fact he considered "risk neutral" situations in the beginning or middle of the game. We've updated the post accordingly.
