CHIRPMAN-ZEETHOOT INC

# QUANTUM BASEBALL®

A Mathematical Model of Professional Major League Baseball

Baseball is an example of a process that can be successfully simulated. The game is complex enough that a theoretical analysis is difficult, but it is an orderly and well documented process. Past data can be fed into a computer, and the computer can then "act out" the game.

On the basis of two teams statistics (batting and fielding averages, slugging percentages, steals, and so on), it is possible to simulate different situations (hits, strike outs, fly out, ground out, bunt, double steal, etc.). A player's statistics can be determined and expressed as a probability of occurrence. Strat-o-matic, APBA and Pursue the Pennant use DICE to simulate the probability of an appropriate outcome. Quantum Baseball uses playing cards.

The MATHEMATICS of DICE GAMES

When a player's batting statistics are expressed as a probability along a line segment, the portions along the line would represent the percentages of times a batter flies out, grounds out, strikes out, walks, singles, etc. ... Let us assume, for example, that a player has a batting stats as shown below.

 RESULT PROBABILITY Fly Out 0.110 Ground Out 0.210 Strike Out 0.220 Walk 0.140 Single 0.220 Double 0.050 Triple 0.025 Home Run 0.025 1.000

We can simulate this batter at the plate by generating a random roll of dice. If one die is red and the other is white, there are 36 possible combinations. There is only one double 1 and one double 6 combination, hence 1/36 chance for each to occur. Percentages wise this means, there is a 2.8% chance of occurrence. If a player hits a home run only 2.5% of the time (example: 13 HR at 502 at bats), then rolling dice, a double 1 roll could represent a home run, etc...

Other batters are treated in an analogous manner. Base runners likewise have statistics, such as the number of bases that they will advance in different situations ... so do pitchers. In this way an entire game can be simulated. As a result, if played enough times, the laws of probability will average out to yield the players past performance. There are many other variety of dice baseball board games, however they all fall short in the realism. Strat-o-matic ranks as the best dice game with its 85% approximation of the real effects occurring in professional baseball.

When the laws of probability are applied to playing cards, more advanced mathematical techniques are required utilizing probability matrices of Markov chains and eigenvalued problems. In addition, some 400 hours of mind boggling number crunching was required to find a basic consistent pattern, to unfold an accurate baseball game, enough to satisfy the most demanding baseball fanatic. At the same time, the objective for a good and easy card game was essential with relatively few rules.

From the point of view of John Von Neumann's game theory, an advanced mathematical technique, Quantum Baseball is more than a stoic Markov chain of probabilities. Quantum Baseball is more than a Monte Carlo method of simulation, although these features were instrumental in following the thread that lead to its modeling. According to Category Theory, another advanced branch of mathematics, baseball is indeed a game that is in the class of games identified as a Finite Non-deterministc Automaton.

However, in the actual play of this game, no one ever is required to have any knowledge of mathematics, let alone the advanced concepts used to find a mathematical model of professional baseball. All one needs to know are some preliminary basic rules of baseball. The rest unfolds as if the game was physically being played by real ball players.

The MATHEMATICS of PLAYING CARDS

There are twenty four (24) different possible initial states of the base paths when a batter comes to the plate (bases empty, runner on 1st, runners on 2nd and 3rd, no outs, one out, ... etc.). The player's batting statistics are subject to the conditions on the base paths as well as his hitting capabilities. The EVENT of his batting performance, which can be translated into a probability transition matrix, has an effect on the situation on the field. A home run clears the bases and produces a run(s). A double advances the runner(s) with some possibly scoring. A line drive to short stop could become a double play or it can lead to either a fielder's choice or a ground out. Some plays advance runners, others do not.

The amazing similarity of the above equation to both Schordinger's wave equation and Heisenberg's matrix equation led to the conjecture that if the laws of nature in Quantum Baseball were to be replaced by the rules of baseball, then the mathematics of the matrix equation would describe an accurate mathematical model of professional baseball. Hence the name, Quantum Baseball.

In the application of this mathematical model to playing cards, incorporating every situation generated in baseball, a deck of 60 playing cards are required. Such a deck would use a standard deck of 52, plus four jokers and four "ones". This arrangement generates an accuracy of 98% of the events of professional baseball. As a result Quantum Baseball is unique amongst all baseball games. Since it is based on a mathematical model, an equation, it is not a simulation.

This has never been accomplished before! All previous attempts to obtain an accurate card game were met with little or no realism. Quantum Baseball, not only captures the realism of baseball that the top dice board games accomplish, but also, is the only game that incorporates the complete drama and excitement of major league baseball by developing the complete count (balls and strikes) on the batter. Dice games do not. One merely throws the dice and the event happens! With Quantum Baseball, you are in effect playing an actual game of baseball, pitch by pitch, without the physical exertion.

My children and their friends, everyone, not only learn the rules of the card game quickly, but they also recognize the strategies of baseball. In all the excitement of play, they discover the wonders of baseball.

| Game Board Elements ||White Dwarf Studio| Strat-o-matic |