Thursday, July 26, 2012

Jeremy Lin vs The Ghost

At the height of Linsanity, when I read everything I found about Jeremy Lin, I came across The Evolution of Jeremy Lin as a Point Guard at New York Times. As I read about a drill/game called "Beat the Ghost" that Jeremy Lin plays while training to improve his 3-pointers, I thought about questions I could ask my math students. Here's the text:
Lin’s perfectionist tendencies came out in a 3-point-shooting drill called “beat the ghost,” in which Lin earned 1 point for every shot he made at the arc and the “ghost” earned 3 points for every shot Lin missed.

On one occasion, Lin made 17 3-pointers but lost 21-17, then kicked the ball in anger, Scheppler recalled with a chuckle. He refused to stop until he beat the ghost. It took 14 games. When Scheppler tallied up all of the scores for the day, Lin had converted 71 percent of his shots from the arc. “That’s the beauty of Jeremy Lin,” Scheppler said. “It’s not about moral victories. It’s ‘I have to win.’ ”
Question 1: Assuming each shot is independent of the others and his probability of making a shot is 71%, what is the probability that Jeremy Lin beats the ghost (essentially he makes 21 shots before he misses 7)?

Question 2: According to the article, it took him 14 games to beat the ghost. Is this typical? On average, do we expect him to take this many games before he wins (he was unlucky with his shots) or do we expect it to take longer than 14 games before he wins (he was lucky he beat the ghost in only 14)?

Here's a video of Jeremy Lin's former teammate Steve Novak, the NBA leader in 3-pt field goal percentage last season (2011-2012), in his pre-game routine making it look easy.

It's not all that surprising when you read that one of his feats of marksmanship include making 96 out of 100 3-pointers during a pre-draft workout with the Spurs in 2006 (espn).

Question 3: Assuming each shot is independent of the others and his probability of making a shot is 96%, what is the probability that Steve Novak beats the ghost (essentially he makes 21 shots before he misses 7)?

You can probably guess where I'm going next.

Extension Question: Assuming each shot is independent of the others and a player's probability of making a shot is p, what is the probability that the player beats the ghost (essentially the player makes S shots before F misses)?

I haven't worked it all out yet. I'll get the calculations, diagrams, and simulations up when I get some time to finish them. In the mean time, I thought you'd enjoy doing some math as the school year approaches.

Jeremy Lin vs The Ghost
Jeremy Lin vs The Ghost (Finding Patterns)
Jeremy Lin vs The Ghost (Simulation)

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