An Example of TWP Calculation
by Andrew Foland
I scanned in about 20 points of WP by hand from the New Orleans-Seattle game WP chart, and used the previously described method for generating the “TWP” that combines the WP model with the input MWP (which favored NO by 59%, in this case.) The plot of the TWP is shown below together with the WP chart.
As you can see, late in the game the MWP consideration doesn’t change the WP very much. This is actually as expected. The better team is expected to have already done better by late in the game. If it is not already ahead, the high randomness of the few remaining possessions overwhelm the average expected advantage of the better team. This is a restatement of the “variance is the friend of the underdog” motto.
Also note the plot starts off with TWP=59%, per Brian’s published probability for this game!
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4 comments:
Alright, now how can we convince Brian to spend more of his free time to make this automated?
That's the conversation I hope to stimulate, if Brian has any interest in marrying the game probabilities to the WP calculator (at least as an option.)
There are various places where the specific model I described is clearly improvable. I laid out the reasoning in gory detail because I think the reasoning is going to be pretty generic in any attempt to incorporate. But there are various details that attention will have to be paid to, in order to make it "really right". I've said I think remaining improvements will be numerically small, but that should be substantiated / contradicted (as the case may be.)
In the meantime, I've uploaded a mwp(t) calculation Excel sheet which makes part of the job relatively easy.
Though the spreadsheet does make one tiny fudge relative to the described procedure, in calculating Delta(0) directly in the stochastic model rather than from the point differential table. Which reinforces the point, that there are still things to think about here. I'm already finding little tweaks here and there to the procedure I described.
Amazing work!
Wow - just found this 5 part series from Brian's post. Excellent, excellent stuff.
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