Quantization Analysis of Deviation Propagation Effect Results from Error-Estimated Table Tennis Players' Ratings ∼ A Monte Carlo Simulation Approach

USATT rating system, initiated since 1970s, had been the most well-known sports rating system in the world. The rating system uses single parameter logistic model derived from Item Response Theory (IRT) to quantize a table tennis player's playing strength. Because it is easy to perform, including ITTF, the system had been widely adapted with some deviations all over the world. As a computer programmer and table tennis enthusiast, I wrote a computer program and devoted in table tennis players rating calculation for the past decade in Taiwan (TWTT Rating System). There had been 36,737 table tennis players registered in our database while 3,147 events and 522,101 matches were recorded for calculating and analysis. A Mote Carlo simulation program was developed in this research to analyse the effect of error-estimated ratings problem. Each simulated player has two rating scores, one represents his real playing strength and the other imply the observation from computer program which might be equal or deviated from his real ability by manipulation. The outcome of all simulated matches were determined by two opponent's real playing strength using single parameter logistic probability model while the observation rating score will be re-calculated according to the outcome above in every simulated match. Deviation between real playing strength and observation rating for error-estimated players and whole population could be thus analysed iteratively. We hope that this simulation can help us for the development of the automatic rating adjustment process for the error-estimated players in the future.