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Validating the Favorite Toy (June 9, 2003)
Discussion ThreadPosted 2:01 p.m.,
June 9, 2003
(#3) -
Warren
I remember looking at the Favorite Toy once, and I found that the formula really only works for the type of players that ever reach important milestones - that is, good/great players. The predicted number of remaining seasons formula, if I remember correctly, is quite inaccurate for most players - if way overestimates the number of remaining years. Only for players that we already know are good does that estimate seem to work okay. That doesn't invalidate the method by any means, but it's something that people should be aware of - just because it works with great players does not mean it will work for other groups of players.
After Sabre-School Special (June 19, 2003)
Posted 9:15 a.m.,
June 20, 2003
(#10) -
Warren
I just wanted to follow up on what Vinay said - he's exactly right that when you're looking at pennants added, you get a different picture. One thing I thought about when playing around with this pennants added stuff is that we shouldn't necessarily come up with a single baseline (average, replacement, random), but rather look at *every* baseline. A player with a very high peak is more valuable to a poor or average team, but a consistent player is more valuable to a great team. There's no right or wrong answer as to who the better player is - like many things, it depends on the environment.
One other baseline, and one more important from a value perspective, is his actual team's performance (subtracting out himself, I suppose). It's certainly possible to have two players that would theoretically have equal value on a average or random team, but that have additional value because of the types of teams they play for (a high peak player on a bad team, or a consistent player on a great team).
Livan Hernandez and Scouting (September 10, 2003)
Discussion ThreadPosted 3:08 p.m.,
September 10, 2003
(#3) -
Warren
FYI - I'm not statistician, as my comments will undoubtably show...
I guess the first questions to ask is if a scout guess at a player's true rate is exactly analogous to a certain number of batters faced (or innings or plate appearances) of a sample. So, taking the example above, if the scout believes both Livan and Orlando now have a true rate of 25%, can we treat that as equivalent to having some extra data suggesting that they had a rate of 25% in (say) 500 batters?
If so, then the issue of margin of error goes back to however you determine that based on your sample size when you have no scouting data. If the error is +/- 5% at 200 batters, and +/- 3% at 700 batters, then it would also be +/- 3% at 200 batters with scouting information. You could then "rate" scouts according to their "effective sample size". You would also regress the sample towards the mean as you would normally do.
Time for some educated guessing to Tango's questions...
1. Livan has 200 batters at 25% and 500 "fake" batters at 25%. So we have, in effect, 700 batters at 25%. Let's say we regress 50% of the way toward the mean at a sample size of 700 batters. So Livan's true rate is 20% +/- 3% (the 3% being from the fake numbers above).
2. Orlando has 200 batters at 15% and 500 "fake" batters at 25%, giving him 700 batters at 22%. Regressing halfway, gives us 18.5% +/- 3%.
3. Pasqual has 200 batters at 25%. If we regress 75% of the way at a sample of 200 batters, then his true rate is 17.5% +/- 5%.
The real question, of course, is how many batters is a scout's opinion worth? 0? 500? 5000?