Basketball = Math
So we watched the UNC-Duke game last night with some friends (GO HEELS!).
I've been on a dynamics kick lately, and I started wondering what it would take to model the dynamics of the game.
The model that pops into my mind is that of a 'random walk' a quantity that goes up or down randomly as time passes. These kind of things produce graphs like you see associated with the stock market, very jagged and complicated looking with lots of changes in direction.
I was thinking you could use such a thing to model the difference in the scores between the 2 teams (call it X). So at the beginning of the game X = 0 since both teams have the same score (0 points). If team A scores then X goes up, and if team B scores then X goes down. So if X is a big positive number team A is winning by a lot, or if X is a small negative number then team B is winning by a little.
Basketball seems like a continuous motion, but it can actually be broken down into discrete parts. When a team gets the ball, they either score or they turn the ball over, so their possession can be summarized by the number of points they score from it: 1, 2, 3, or 0 (if they turn the ball over).
For simplicity's sake, I will assume that a team either scores 2 points or none. You can make a sequence based on the result of each possession that might look something like this: 0, 2, 2, 2, 0, 0, -2, -2, -4 etc... where the entries alternate between the possessions of A and B. In this particular sequence, team A scored on their first possession, but then team B scored 3 in a row.
For me, the interesting things happen when you incorporate the skills of each team. To me, the better a team is, the higher their probability of scoring when they possess the ball. We can measure this. So if team A has a 60% chance to score when they have the ball we can say P1 = .6. If team B is not as good as A, they may only have a 45% chance to score when they have the ball, so we can say P2 = .45.
In the sequence, what will happen is when A has the ball, X has a 60% chance of going up by 2, while when B has the ball, X has a 45% chance to go down by 2. What I wonder is what the long-term behavior of such a sequence would be. Would it be chaotic? My intuition says no, but I would have to do some actual work to figure it out.
Oh yeah, and the Tar Heels won. Yay!
I've been on a dynamics kick lately, and I started wondering what it would take to model the dynamics of the game.
The model that pops into my mind is that of a 'random walk' a quantity that goes up or down randomly as time passes. These kind of things produce graphs like you see associated with the stock market, very jagged and complicated looking with lots of changes in direction.
I was thinking you could use such a thing to model the difference in the scores between the 2 teams (call it X). So at the beginning of the game X = 0 since both teams have the same score (0 points). If team A scores then X goes up, and if team B scores then X goes down. So if X is a big positive number team A is winning by a lot, or if X is a small negative number then team B is winning by a little.
Basketball seems like a continuous motion, but it can actually be broken down into discrete parts. When a team gets the ball, they either score or they turn the ball over, so their possession can be summarized by the number of points they score from it: 1, 2, 3, or 0 (if they turn the ball over).
For simplicity's sake, I will assume that a team either scores 2 points or none. You can make a sequence based on the result of each possession that might look something like this: 0, 2, 2, 2, 0, 0, -2, -2, -4 etc... where the entries alternate between the possessions of A and B. In this particular sequence, team A scored on their first possession, but then team B scored 3 in a row.
For me, the interesting things happen when you incorporate the skills of each team. To me, the better a team is, the higher their probability of scoring when they possess the ball. We can measure this. So if team A has a 60% chance to score when they have the ball we can say P1 = .6. If team B is not as good as A, they may only have a 45% chance to score when they have the ball, so we can say P2 = .45.
In the sequence, what will happen is when A has the ball, X has a 60% chance of going up by 2, while when B has the ball, X has a 45% chance to go down by 2. What I wonder is what the long-term behavior of such a sequence would be. Would it be chaotic? My intuition says no, but I would have to do some actual work to figure it out.
Oh yeah, and the Tar Heels won. Yay!