Modelling Outcomes in Volleyball Tristan Barnett Alan Brown
Modelling Outcomes in Volleyball Tristan Barnett, Alan Brown and Karl Jackson Swinburne University of Technology
Outline o o o o Scoring Model Probability of winning a set Probability of winning a match Number of points in a set Sports Calculator Conclusions
Scoring o 6 players make a team o A coin toss is used to decide the server at the start of the first set o To win a match, a team must win 3 sets o To win a set, a team must reach 25 (15) points with at least a two point lead o A team can win a point when either serving or receiving o A team serves after winning the previous point in a set o Teams rotate for service each set
Model Assumption: The probabilities of each player in a team of winning a point on their respective serves are identical and constant, irrespective of the score. Model consists of two parameters: p. A and p. B
Probability of winning a set
Probability of winning a set
Probability of winning a set P(A|A, 24) = p. A 2 + p. Aq. A P(A|B, 24) + q. Aq. B P(A|A, 24) P(A|B, 24) = q. Bp. A + q. Bq. A P(A|B, 24) + p. Bq. B P(A|A, 24)
Probability of winning a set
Probability of winning match
Probability of winning match
Probability of winning match
Number of points in a set
Number of points in a set
Number of points in a set
Sports Calculator www. strategicgames. com. au
Conclusions o Markov chain models can be used to model outcomes in volleyball conditional on both the scoreboard and server o Results from the model indicate that there is no advantage in being server or receiver at the start of the match but the receiver has an advantage at the start of the final set. o Similar models can also be applied to beach volleyball, where the rotation of serve is the same as standard volleyball o Fairness in volleyball scoring systems. Paper for 10 M&CS
- Slides: 17