Thesis Proposal (set 8: prior pre-decision probability)
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PRIOR PRE-DECISION PROBABILITY 1A
If this frame looks similar it's because we are again utilizing Bayes' rule, but this time it is with the posterior as the PRE-DECISION odds of team C winning the game given the game-state, which is shown on the left-hand side of the equation.
PRIOR PRE-DECISION PROBABILITY 1B
On the right-hand side we again have the prior and conditional likelihood (original and new information). The first term is literally the prior (pre-game) odds of team C winning the game while the second term is the odds of team C being in that game-state given that they ended up winning the game.
PRIOR PRE-DECISION PROBABILITY 1C
The next step is to calculate these two components. Down here you can see that to estimate the first component (the prior) we will be using a logistic regression to predict game outcomes from closing point spreads.
PRIOR PRE-DECISION PROBABILITY 1D
For the second component we will use a multinomial logistic regression to predict the probability of the team being in that situation given that they won the game. In this case X-Prime represents the group of variables that make up the game-state: the score margin, time remaining in the game, field position with respect to the offensive team, current down, yards to go to gain a new set of downs, and an indicator variable for possession with respect to the home team.
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