Originally Posted by RedsManRick
Except we aren't saying that his actual OBP is fixed, just his skill level which produces the OBP. In the coin flip example, the odds of hitting heads stays at 50% as a function of the coin itself. It has nothing to do with how many times you flip it. It's the coin itself, it's design and the process of flipping, that determines those odds. Whether you've previously flipped heads or tails doesn't change those things which actually determine your odds of getting a heads or tails in the future. And as soon as you take a sample of X observed flips (or plate appearances), as you must do in the real world, there's a range of possible outcomes centered around the true skill level.
The gamblers fallacy points out that the odds don't change simply because you have a certain sample in the bag already. The odds are fixed determined by those conditions of the game. A sample simply provides you real life evidence of what those true odds (or true skill) might be. As the sample gets bigger, the more confident you can be that what you've observed is close to the real odds. If for some reason you know what the real odds are, then you're all set. Your best guess about what's likely to happen in the future is based on those odds and is completely independent of what has happened so far.
We are surmising that just like the coin has a "true skill" of 50% heads based on the nature of coin itself and act of flipping it, we're surmising that Taveras has a true skill of 33% on base based on the nature of his abilities and the act of getting on on base. That he's flipped his 33% coin 218 this year and ended up with a 29.5% rate of "on base" doesn't change the odds moving forward.
It's not like Taveras has a bag with 5,000 plate appearances in it with 1,650 times on base among them. If this were the case, you'd be correct. The odds would change after each plate appearance. But the bag of plate appearances from which he's drawing isn't the finite number which he'll get in his career or in this season, but rather an infinite number. That you've pulled 218 from the bottomless bag doesn't change the odds of the next 1, 100, or 1000 of being on base. They all remain 33%.
I understand your point, now. You were working under the assumption that Taveras' skill level is fixed, and I was working under the assumption that his OBP is fixed.
Obviously, neither is the case, since nothing in human dynamics is fixed like it is with a coin flip. I guess the next step is to discuss the relationship between a players skill level and his actual numbers, but I gotta go. Maybe later?
Thanks for the lively, informative discussion. I know I enjoyed it