Volleyball Statistics

Live Script simulating recreational co-ed volleyball with rotating substitutions, analyzing bench-time fairness and set-score statistics.

This Live Script simulates recreational co-ed volleyball sets with a no-more than three guy players rule for a team with N substitute guy players (N = 1, 2, or 3) and three gal players playing against an opponent team of equal or unequal strength. Players are alternately guys and gals and rotate through positions according to standard volleyball rules. Each time a team wins back service, the players rotate positions and a guy rotating into position 1 is substituted off the court and replaced by the next guy player on the bench. Two rotation modes for a new set are considered: 1) 'Line up as we were at the end of the last set" or 2) reset to the original positions.

The script addresses two questions.

(1) Fairness: Is bench time distributed equitably among all guy players as N and the rotation mode change? The script shows that the theoretical mean bench fraction is N/(N+3) for N substitute guys, but that there are large fluctuations from set to set depending on game outcomes.

(2) Statistics: What are the distributions of rallies per set, team scores, and score differences for evenly or unevenly matched teams?

The script may interest coaches, recreational athletes, students of probability and statistics, and instructors of computational in physics and other fields. Try this suggestions are included for further exploration.

For additional educational Live Scripts on probability, statistics, physics and other topics, see the author's MATLAB Central File Exchange contributions.