Abstract
Individual tennis points evolve over time and space, as each of the two opposing players are constantly reacting and positioning themselves in response to strikes of the ball. However, these reactions are diminished into simple tally statistics such as the amount of winners or unforced errors a player has. In this paper, a new way is proposed to evaluate how an individual tennis point is evolving, by measuring how many points a player can expect from each shot, given who struck the shot and where both players are located. This measurement, named “Expected Shot Value” (ESV), derives from stochastically modeling each shot of individual tennis points. The modeling will take place on multiple resolutions, differentiating between the continuous player movement and discrete events such as strikes occurring and duration of shots ending. Multi-resolution stochastic modeling allows for the incorporation of information-rich spatiotemporal player-tracking data, while allowing for computational tractability on large amounts of data. In addition to estimating ESV, this methodology will be able to identify the strengths and weaknesses of specific players, which will have the ability to guide a player’s in-match strategy.
A Appendix
A.1 Theoretical ESV
Letting T(ω) denote the time at which a point following the path ω ends, the point’s outcome for player i then is a deterministic function of the full resolution data at this time,
A.2 Additional time notations
The notations τt and δt will be defined as:
where ε is the temporal resolution of the player-tracking data. In this case, ε will be equal to 1/25 s.
A.3 Strike/return subset definitions
Let 𝒮 contain every strike contained in the dataset, which includes who struck the shot, its strike state and its corresponding strike category.
Let ℛ contain every return contained in the dataset, which includes who is returning the shot, its return state and its corresponding return category.
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