A linear model for estimating optimal service error fraction in volleyball

Tristan Burton 1  and Scott Powers 2
  • 1 Bay to Bay Volleyball Club, Campbell, CA, USA
  • 2 Statistics, Stanford University, Stanford, CA, USA, e-mail: sspowers@stanford.edu
Tristan Burton and Scott Powers


Volleyball coaches are frequently forced to address the question of athlete service errors as a part of their overall service strategy. This is usually done in an ad hoc fashion with an arbitrarily selected maximum allowable service error fraction or maximum allowable service error-to-ace ratio. In this article, an analysis of service outcomes leads to a mathematical expression for the point-scoring fraction in terms of service ace fraction, service error fraction, and opponent modified sideout fraction. These parameters are assumed to be monotonic functions of an athlete or team’s serving aggressiveness and a linear model for the service error-to-ace ratio is used to close the point-scoring optimization problem. The model provides estimates of the optimal service error fraction for individual athletes based on their service ace fraction and the opponent modified sideout fraction against the server overall and also when restricted to only serves that led to perfect passes. Case studies of the Bay to Bay 17 Black Boys’ USAV Juniors team and the Brigham Young University Men’s NCAA Division I team are used to demonstrate the application of the model and standard errors for the predicted optimal service error fractions are calculated with bootstrap resampling.

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