Run up game distribution

Sterman Karlqvist Eds. Boston:CRC Press. Radzicki, M. Computer-based beer game boards. Worcester Polytechnic Institute, Dept. Thomsen, J. Hyperchaotic Phenomena in Dynamic Decision Making. Systems Analysis and Modelling Simulation, forthcoming. Roberts, E. Cambridge, MA: Productivity Press. Senge, P. New York: Doubleday.

Sterman, J. Instructions for Running the Beer Distribution Game. Management Science , 35 3 , You must be logged in to post a comment. The Beer Distribution Game. By John Sterman.

Beer Distribution Game — Graph 1. In this post I use the negative binomial distribution to better model the how MLB teams score runs in an inning or in a game. I wrote a primer on the math of the different distributions mentioned in the post for reference. A team in the American League will average. This large number of scoreless innings can be described by discrete probability distributions that account for teams scoring none, one, or multiple runs in one inning. Runs in baseball are considered rare events and count data, so they will follow a discrete probability distribution if they are random.

The overall goal of this post is to describe the random process that arises with scoring runs in baseball. The Poisson distribution describes count data like car crashes or earthquakes over a given period of time and defined space. It predicted fewer scoreless innings and many more 1-run innings than what really occurred.

The PD makes an assumption that the mean and variance are equal. The graph above shows an example of the application of count data distributions.

The actual data is in gray and the Poisson distribution in yellow. The NBD is also a discrete probability distribution, but it finds the probability of a certain number of failures occurring before a certain number of successes. From a conceptual stand point, the two distributions are closely related. The second section of the post will discuss the specific equations and their application to baseball.

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An tool like the PokerStars Clock app allows you to input the number of players, starting stacks, and level duration, and gives you an estimated time for how long the tournament will run. In this scenario, the PokerStars Clock estimates a five-hour duration to determine the champion in this tournament. Reducing these breaks to 10 minutes or so will cut down on the total time of the tournament.

The PokerStars Clock app estimates a three-hour duration for this tournament.