NBA Coaches Need to Hire Mathematicians

Once again, a professional coach in a major game, ahead by plenty of points to win, and with little time left, blows the final game decision and loses as a result. In this latest of numerous cases, it was Orlando's Stan Van Gundy, ahead by three with ten seconds left (really 5 with 1:01 left, but I'll get to that in a minute), who chose not to foul the Lakers, allowing Lakers' guard Derek Fisher to make the game-tying 3-pointer that was their only chance to tie the game, and win in overtime. The need for NBA coaches (and really those for other sports as well) to have a mathematician on the sidelines for such situations screamed out in Gundy's post-game comments:

Van Gundy had his reasons for not fouling. He felt a foul too early would turn the game into a free-throw shooting contest and his team was hitting just 59 percent (22-for-37) of theirs. He philosophically doesn’t believe in doing it until “six or seven” seconds remain in the game.

“It was my decision with 11 seconds not to foul,” he said. “Yes I regret it now, but only in retrospect. I mean, normally to me 11 is too early. You foul, they make two free throws, [they] cut it to one [and] you’re still at six or seven seconds.”

Philosophically? PHILOSOPHICALLY? This isn't philosophy sir, it's basketball, and at these end-game situations it's really a mathematics problem. Further, it is not how many seconds left that dictates when one should start the foul-them-before-they-shoot-and-play-keep-away strategy. It is how many seconds are left relative to how many points ahead you are. The problem across all sports that I've seen for years is that coaches are not mathematically adept enough to be able to make such calculations, so the only time they use this strategy is when there is only one possession left. That's why they need a mathematician on the sideless to help them work out formulas like this:

Play keep away and foul when they cross half court (or when one of their crappy free throw shooters gets the ball) if: [Your Score - Their Score] / [minutes remaining] > 4, and you have possession.

After all, the surest way to insure victory when you have a sizeable lead in basketball is to take away their best hope - three-point shots, and emphasize yours - making free throws and handling the ball to avoid turnovers. The big implication of all this that Gundy (and the rest of the basketball world) is missing is that when you are way ahead, you WANT to turn it into a freethrow shooting contest and a keepaway contest, because you can put your best at both on the floor and you've got a big lead. Being way ahead makes certain skills, like rebunding, playing defense, and shot blocking, far less important than they are in the rest of the game. All that matters at this point is ball-handling and free throw shooting, and the players put out on the floor should be based on those skills and no others. Gundy's aversion to having a free throw contest based on the team's poor shooting throughout the game is irrelevant because many of the players that missed those shots aren't going to be in the game when it matters. Put in the guys that are good at it.

Allow me to illustrate. With 1:01 remaining, Kobe Bryant of the Lakers missed a shot and Orlando's Mickael Pietrus got the rebound with Orlando ahead 87-82. Orlando is now ahead by 5, with 61 seconds remaining and a 24 second shot clock. My rough formula for when the special strategy should be emplyed is when one's lead is greater than 4 points per minute remaining (assuming 24 seconds for your possessions and 6 seconds for your opponents) and one has possession of the ball. This situation qualifies. Now if Orlando just burns the full 24 seconds off the clock on their possessions, and fouls LA on theirs to prevent them from scoring more than 2 on any of their possessions, Orlando wins. Observe how it works even using outcomes as favorable to LA as can be expected:

O - 87 LA - 82 1:01 remaining
Orlando burns off all 24 seconds, doesn't score (they easily could have)
87-82 :35
LA dribbles to half court and is fouled
87-82 :32
LA makes both free throws (odds are they'd miss at least one)
87-84 :32
Orlando again just burns down the 24 second clock without attempting a shot
87-84 :08
LA gets fouled at half court
87-84 :05
LA makes both free throws
87-86 :05
Orlando runs out the clock to victory.

Now of course, it isn't a sure thing: LA could get a steal, or miss a free throw and get a rebound and score, or a whole host of highly improbable events. But then again, Orlanda could easily get a back door layup while killing the clock, or get fouled themselves. LA might even decide to foul back and turn it into a free throw shooting contest. But Orlando is ahead by 5, and has its best free throw shooters on the floor. The odds of them losing that contest are miniscule, far less than the odds of what happened: one guy hitting a three-pointer.

So wake up coaches, you're making it harder than it is. Get yourself a mathematician on your staff, we work cheap, and could mean the difference between winnning a title and not.