Quote:
Originally Posted by Hynh
That's wrong.
The PDO disbelievers would expect the hot weather to continue forever and use the 15 days as proof. The PDO users would expect the average temperature over the next 15 days to be 20, for an average of 25 degrees.
If you flip a coin 100 times and it comes up 75 heads and 25 tails, you don't bet that the next 100 will be 75 tails and 25 heads. You bet that there will be 50 heads and 50 tails, or 125 and 75 total. Flip the coin until you have 1000 results and the PDO users would expect there to be 525 heads and 475 tails. Do it until there are 10,000 results and the expected split is 5025 and 4075.
If you flip that coin 1 million times, the expected result would be 500,025 heads, 499,975 tails. Instead of 75% of results being positive, only 50.0025% are.

Though, of course, no matter how many times you flip a coin the chances of it being 50% heads and 50% tails on a number that ends with 3 or more zeros is frightfully insignificant given that coin flipping is considered the paradigm for the proposition that defines regression to the mean.
I am not sure what to say about PDO that hasn't already been stated. Formulas that prove that the middle of the pack will act like the middle of the pack given enough data points while telling us nothing pertinent about outliers (other than that they can't be included because they are outliers) doesn't seem to have anything very profound to add to a discussion in which there are only 30 sets of data involved.
Telling me after the fact that my team's collapse was predictable because they had an unsustainable PDO to start the season would be more impressive if really good teams didn't sustain their high PDO over the season.
And extending the data collection to 5 or 10 years in order to make the data prove the conclusion may be esthetically pleasing I don't think you would find many hockey fans surprised at the notion that their team tends to suck after a number of years of being very good or that bad teams improve given enough time.