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[Ryan J. Parker]

After reading over Dean's The Perfect Score in Chapter 12 of BoP last night, I wanted to get a visual representation of why this happens numerically. Clearly this is because of the affect the standard deviation has on the distribution, and here are the images I came up with to show this:

The image below shows the Bulls points for distribution (far right red distribution) along with three Bulls points allowed distributions: red represents the Bulls optimal points allowed distribution if they were to win 103-83; green represents the Bulls actual points allowed distribution after winning 103-71; blue represents the Bulls points allowed distribution if they were to have won by a 50 point margin (a score of 103-53).



The affect of the large standard deviation really represents itself when the Bulls win by 50 (again, represented by blue):



Thanks to keeping their opponents score low, their points allowed distribution now has their opponents as having a higher likelihood of scoring in the 122+ point range. Clearly this isn't logical, but that's the sideaffect of that sort of win. A similar result takes place when you use a score of say 150-100. The reverse happens, though, and the Bulls are left with a wide array of possible points for that isn't tightly centered around their mean points for.

Here is a representation of the difference distributions, where red represents the optimal win of 103-83, green represents their actual win of 103-71, and blue represents a win of 103-53:



Zooming in around zero and you get a better picture of what's going on:



The Bulls want to get as much of the distribution to the right of 0 as possible, but the large win just doesn't do that for them.

When all is said and done, this really just makes a strong case for regression to the mean as one lopsided result shouldn't alter a team's true expectation that much, but hopefully this gives a good graphical representation of what's going on in The Perfect Score.

[Ryan J. Parker]

After thinking about this a little more, I checked to see if using the margin of victory distribution affected the expected winning percentage in any way. I'm sure this is what Dean was talking about in this post, so yay for rehashing.

The results are below, but it doesn't seem to change much with regards to the perfect score, save for the fact this is much easier to calculate if you're in a hurry.