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Expected Value Models

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Soccer

Model expected value of possession given location ball, players, defenders, etc.
Assign players value based on successful passes/movements of the ball/converted shots

https://arxiv.org/pdf/2011.09426.pdf

Soccer

For example, can break pitch up into boxes, calculate the probability of the possession resulting in a goal for each box
Treat soccer as a Markov chain, an idea introduced by Sarah Rudd (http://nessis.org/nessis11/rudd.pdf)
If a player dribbles from one box to the other, or completes a pass into a different box, they are rewarded with that value
Exepected Threat takes this one step further (https://karun.in/blog/expected-threat.html)

https://statsbomb.com/2019/02/attacking-contributions-markov-models-for-football/

Markov Chains

Finite number of possible states
Probability matrix tells you the probability you go from state B given that you’re in state A
Markov assumption: these probabilities only depend on your current state, no the history of the system/how you got there

https://qph.fs.quoracdn.net/main-qimg-feb4de879cdea1e7eafab76c4c55d120.webp

Basketball

Expected possession value computed from spatial tracking data
Use EPV at start of player’s possession minus EPV at end of player’s possession to evaluate player actions

https://arxiv.org/pdf/1408.0777.pdf

Basketball

https://arxiv.org/pdf/1408.0777.pdf

Volleyball

UTSPAN project: obtained data from UofT women’s volleyball team with each hit in a rally and the quality
Use expected point value before/after a player’s touch to assign credit
E.g. If opponent just did a “good” attack, we have P(win point) = 0.3, if a player responds with a “good” dig, maybe that goes up to P(win) = 0.5, so that player gets credited 0.2

https://docs.lib.purdue.edu/dissertations/AAI10607243/

https://arxiv.org/pdf/2402.01083.pdf

Football