Originally Posted by bucksfan2
RMR you are complicating this. OBP is an average correct? To say that Taveras is a .330 OBPer is somewhat incorrect to me. Basically when all is said and done the middle point of Taveras OBP is .330.
IMO you could take all different data points and date ranges and come up with all different kinds of answers. If you believe that over the course of a season WT will have a .330 OBP then logic would suggest that he is going to improve on his current statistics, baring an unknown outside factor, from now to the end of the season.
Let me ask you this. I am going to flip a quarter 1000 times. At the start I ask you how many times heads will come up, within a margin of +/-10. What would your answer be? Logic would say 500 would be the choice. Now lets assume that after 200 flips it is heads 110 tails 90. If you were give a chance to change, would you? Or would you still stick the fact that the variances will even out?[/QUOTE]
Given your example, my new estimate for the total number of heads would be the current number of heads, 110, plus the number I expect to see in the remaining 800 flips based on my knowledge of the "true skill" of the flip -- 50% of 400 heads.
So my new estimate for the number of heads in THIS sample of 1000 flips is 510. That's what you're missing, this season is still just a sample against that "true skill". His true skill is not what his number will be at some point in time (say, the end of the season), but rather what his performance will be moving forward. At the beginning of the season, with 0 PA under his belt, .330 was our best guess. But at this point in the season, with a ~200 PA of a ~.300 OBP already having occurred, our estimate for his end of the season number changes. You are fixing .330 as his end of the season number when it's actually his rest of the season number.
It's actually simple. We're talking about 3 numbers.
1) OBP to date
2) OBP moving forward
3) OBP at the end of the season
The formula we've been discussing is 3 = 1 + 2. His OBP at the end of the season (3) is a combination of how his current OBP (1) and the OBP he puts up the rest of the way (2).
#1 is completely simple. We know what his OBP so far is and in how many PA.
#2 is what we've been calling is "true skill". This number doesn't change unless we think he actually has become a worse or better hitter. This whole conversation is based on the assumption that his actually ability to hit doesn't change throughout the course of the season. It's his performance that varies. These are two different things. A streak of 6's doesn't mean you've gotten better at rolling 6's -- just that you rolled a few 6's.
#3 is based on a combination of #1 and #2. At the beginning of this season, #1 was zero, since he didn't have any plate appearances. Thus #2 and #3 were the same thing (.330). But now that he's had a few hundred plate appearances, the math changes.
Beginning of the season:
(.000 OBP in 0% of his PA this season) + (.330 OBP in 100% of his PA this season) = .330 OBP this season
(.294 OBP in 35% PA this season) + (.330 OBP in 65% of his PA this season) = .317 OBP this season.
Again, the trick is that we only expect this season's OBP to be the same as his true skill when we have no information about how he's performed so far. They are not fated to be equal. It's just our best guess absent any other information. But if we know how well he's performed this far, that doesn't change how we expect him to perform moving forward. Our anchor point is .330 moving forward, not .330 by the time he accrues 600 PA.