An orthogonal set of predictors for wins in major league baseball

Abstract

In quantum mechanics theory the state of a system may be represented by a linear combination of what is known an orthogonal set of wave functions. The word, orthogonal, means that one wave function does not interfere with another in determining the properties of the system; rather, each wave function contributes independently to the properties of the system, each one by an amount a _i , where the subscript, i , refers to one of the wave functions in the orthogonal set. Thus, designating a given wave function by ψ , the so called state vector of the system (or simply, “the state of the system”) would be given by S = a ₁ψ₁ + a ₂ψ₂ +…+ a_n ψ _n , where n represents the total number of orthogonal wave functions in the set. Further, the sum of the must equal 1, i.e., ; the latter ensures that the sum of each wave function’s contribution to the state of the system adds to a 100% contribution overall. In the work which follows we proceed according to the above model in an attempt to develop seven “orthogonal categories” associated with the game of baseball, viz., singles, doubles, triples, home runs, {walks + hit batsmen}, errors, and ERA, which can be represented by φ _i, i = 1, 2, 3, … , 7 , such that S = a ₁φ₁ + a ₂φ₂ + … + a ₇φ₇ with .We then utilize further mathematics borrowed from the same theory of quantum mechanics in order to determine the expectation value of the number of wins, W, associated with any given sample size of future games. Using the statistical record associated with the National League Clubs of 2009, we were successful in predicting the number of wins for a given club to within 8% on average. Of interest is that our findings show that by far the largest contribution to success on the diamond comes fromthe two defense categories, errors and ERA, with an overall theoretical contribution of 71% associated with the two combined.

Keywords:

• Major League Baseball
• offense categories
• defense categories
• predictors for winning