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Aging Patterns
June 27, 2002 - Gerry
"Age is calculated as of July 1st, with the remainder rounded off."
In other words (and more simply), age is calculated as of Dec 31st.
"One standard deviation means that 68% of all results will fall within .500 +/- .016 probability."
Only because you are sampling from a normal distribution (or a binomial distribution with such parameters as to make the normal distribution a good approximation). Do you know that batting averages or LWR or whatever follows a normal distribution?
"I will define a regular player as someone who has at least 300 PA (AB+SF+BB+HBP) in a season."
Do you stick to that in strike years, when 300 PA were harder to come by? Do you use that same standard for 154-game seasons and for 162-game seasons?
Aging Patterns
June 28, 2002 - Gerry
Ben Vollmayr-Lee wrote,
...for applications where you are determining the confidence level of the mean (say, average OPS of 30 year olds), you do not need the distribution of OPS to be normal. The reason is the "central limit theorem" which basically says that means are normally distributed (once the sample is big enough) even when individual variables are not. This is a very powerful theorem and is basically the foundation of the field of statistics.
Even a theorem as powerful as The Central Limit Theorem has hypotheses, though, and is only valid when those hypotheses are satisfied. I don't think this is the place to get into the details. Let's just say you have to know *something* about the distribution of the variables whose mean interests you - it's not a blanket statement about everything, all the time.
Forecasting 2003
February 12, 2003 - Gerry
I can think of a couple of other ways of making a quick & dirty forecast.
1. Take the median OPS over the last three seasons. Make the age adjustment if you wish.
2. Take a weighted average of the OPS over the last three seasons; say, half 2002 plus one-third 2001 plus one-sixth 2000. Make the age adjustment if you wish.
It might be amusing to see how these do against the other competitors.
I guess the simplest forecast would be to just use the 2002 OPS (with or without age adjustment).
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