Neural Network Realization of Project Sport Analytic
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Deep Learning Soccer
Model Architecture and Training
Two-Tower Model
Possession Model: Average length of a possession
It would be nice to focus on sparsity. Tarrak didn't see how to deal with the sparsity problem, other than by reward shaping and upsampling. We could argue that soccer is the major sport with the most reward sparsity and our method deals with it.
Are there special training methods we use to deal with it?
In Sloan I proposed using conditional value for impact: instead of using $Q{home}$, use $Q{home}/(Q{home}+Q{away})$. If this works better than plain Q values it would be another contribution for dealing with sparisity.
Another idea: initialize so that goal actions (or successful shots) are mapped to value 1. This helps with interpretability too, because that's what the reader expects.
The deep mind architecture, where each action is represented as a separate node. Might help with the problem that Q(goal) isn't equal to 1.
Using "possessing" vs. "defending" team rather than home or away team.
Puterman's idea: train the model to learn the difference $Q{home}-Q{away}$. This is also recommended by Gelman. Puterman proves nice convergence properties. If we also learn $Q_{neither}$, we can recover the Q-values through normalization.
These ideas can be combined. For example, training on the difference and initialize the model so that $Q{home}(goal(home))-Q{away(goal(home))}=1$ and $Q{home}(goal(away))-Q{away(goal(away))}=-1$ makes a lot of sense.
Btw, we may be able to get a theoretical convergence guarantee by adapting Puterman's ideas to TD-Sarsa.
It may be tricky to train a model to map a Boolean indicator (home vs. away = 1 v 0 or 1 v -1) into flipping a sign (e.g. $Q(goal)$ flips depending on whether the home or away team scores). Another option is to use the difference as a convergence criterion. So keep updating weights until the max difference between iteration $n$ and $n+1$ is small, for the expected difference quantitity $Q{home}(s) - Q{away}(s)$. (Also converge for $Q{neither}$). We know this works in the discrete case from the previous discrete models by Kurt.
Model Validation
Calibration
Features for bins:
period (1,2)
half (defensive, offensive)
manpower
score differential
Sparsity:
Does $Q_{neither}$ match the number of 0-0 games in the dataset?
Does $Q_{neither}$ always dominate because of reward sparsity? When does it not?
Action Values
We should prominently feature shots. Why:
Modelling shot quality is recognized to be important. We may be able to find baseline models. For example, the caltech guys in the ghosting paper built a shot quality model.
We can explain how TD works: first the system learns the value of shots. Then it learns what situations lead to shots.
Could calibrate against a separate shot quality model, even our own separate model perhaps.
Passing is the most frequent action, another place to focus.