Abstract: We present evidence, based on play-by-play data from all 6087 games from the 2006/07--2009/10 seasons of the National Basketball Association (NBA), that basketball scoring is well described by a weakly-biased continuous-time random walk. The time between successive scoring events follows an exponential distribution, with little memory between different scoring intervals.
More Random Walk Model Basketball images
"Random walk" model reveals when a lead is safe. Physics isn’t all about discovering new subatomic particles and describing the fundamental forces that hold the universe together.
computational random-walk model that accounts for a variety of statistical properties of scoring in basketball games, such as the distribution of the score difference between game opponents, the fraction of game time that one team is in the lead, the number of lead changes in each game, and the season win/loss records of each team.
For the random-walk-with-drift model, the k-step-ahead forecast from period n is: n+k n Y = Y + kdˆ ˆ where . dˆ is the estimated drift, i.e., the average increase from one period to the next. So, the long-term forecasts from the random-walk-with-drift model look like a trend line with slope . dˆ ,
The Marginal Revolution blog has a little discussion.The authors, Gabel and Redner, build into their random walk model the rate at which scoring plays occur, team strength, "anti-persistence" (a score by team A leads to a sharply increased probability that team B will score next, because team B automatically gains possession), and a "restoring force" (teams with larger leads have slightly ...
do arise from random statistical fluctuations. Their study indicated that a simple random-walk model successfully captures many features of the observed scoring patterns in basketball, thus the apparent streaks or slumps seen during a game are simply a consequence of a series of random uncorrelated scoring events.
Random walk model. When faced with a time series that shows irregular growth, such as X2 analyzed earlier, the best strategy may not be to try to directly predict the level of the series at each period (i.e., the quantity Yt).
Lattice random walk. A popular random walk model is that of a random walk on a regular lattice, where at each step the location jumps to another site according to some probability distribution. In a simple random walk, the location can only jump to neighboring sites of the lattice, forming a lattice path.
The Natural Random Walk Natural Random Walk Given an undirected graph G= (V;E), with n=jV jand m=jEj, a natural random walk is a stochastic process that starts from a given vertex, and then selects one of its neighbors uniformly at random to visit. The natural random walk is de ned by the following transition matrix P: P(x;y) = (1 degree(x ...