Thesis Proposal (set 9: graphs)

This graph illustrates the results from the equation used to estimate the prior. On the y-axis we have the estimated probability that the team will win the game given the closing point spread, which is on the x-axis.

Basically, I'm using this to tell us the probability of a team winning a game based on what the closing point spread was. For example if we have a team that is favored by three points (-3), we can see that the probability that they win the game is almost exactly 0.6 or a 60% chance.

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These next two frames show 3D graphs to illustrate the number of times a score margin occurred across the minutes remaining in a game, given that the home team won or lost the game. This first one is for teams that won. So you have minutes remaining on the x-axis with the score margin on the y-axis and the number of occurrences on the z-axis.

Notice how it spreads to the right where the positive score-margins are as the time remaining in the game gets closer to zero.

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You can see that this graph does the opposite by spreading to the negative score-margins as time goes on. That's because this graph is the exact same as the previous one but is for teams that lost rather than won.

These graphs aren't actually showing the results of the conditional likelihood equation, because in reality, a graph representing that equation would require seven dimensions instead of just three. I generated these graphs because I wanted to at least be able to give you an idea for what the spread of the data looks like with respect to two of the variables across wins and losses.

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