Individual Poster Page

See copyright notice at the bottom of this page.

List of All Posters

DIPS year-to-year correlations, 1972-1992 (August 5, 2003)

Posted 7:45 p.m., August 5, 2003 (#27) - Arvin Hsu
  I'll toss my hat in the ring and side with Erik.

The r^2 of .4 for 1b vs. .3 for 2b should result solely from less variance in the number of singles, because you have more observations of the number of singles per pitcher per year.

-Arvin

PS> In fact, if you control for # of observations decreasing the variance of the binomial, you might actually get a higher _actual_ degree of control for xbh.

DIPS year-to-year correlations, 1972-1992 (August 5, 2003)

Posted 1:26 a.m., August 14, 2003 (#89) - Arvin Hsu
  guys, this is fantastic stuff. I dropped in 2 weeks ago, and have been too busy finishing my Master's thesis to pop back in. Boy was I surprised to see how far you guy's have taken this. outstanding job.

It seems we have a statistical model now:
k ~ Bin(n,p)
p ~ Norm(mu,sigma)
sigma ~ Chi-sqr(tau)
mu = alpha-pitcher + alpha-park + alpha-defense
alpha-pitcher ~ Norm(pitcher-sample-mean,pitcher-variance)
alpha-park ~ Norm(0,park-variance)
alpha-defense ~ Norm(0,defense-variance)

Since in any one year we have a different mix of park/defense/pitcher, we can evaluate the model

That's awesome, and it can be evaluated. Someone can evaluate it classically if they want. After I get my Master's(Sept) I'll grab Lahman2002 and run it through a Bayesian engine. I should be able to get probability distributions for alpha-park for every ballpark, and alpha-defense for every team-year, and alpha-pitcher for every pitcher across seasons.

DIPS year-to-year correlations, 1972-1992 (August 5, 2003)

Posted 1:36 a.m., August 14, 2003 (#90) - Arvin Hsu
  Other notes:

1) I did this a couple years ago and posted to r.s.b, I think. You shouldn't need to do year-to-year correlations. You should get _much_ better estimates of pitcher ability if you aggregate seasons. Keith Law came up with original idea, iirc. So, here's how you do it: pitcher-A: odd-season $H correlated with pitcher-A:even-season $H. You can use Lahman to exclude all pitchers with ooh.. <800 IP, and exclude all seasons with <50 IP. That should give you a few hundred data points, that may turn up with much stronger correlations than you've been getting.
Actually, now that I think about it, you don't need to exclude <50IP seasons, you just aggregate the seasons before calculating $H.
I'll do this in Sept, too, if no one gets around to it earlier. I predict much higher r^2, than you've been getting.

2) binomial population variance vs. observable sample variance.
I need to think about this. Chris, this may be where you had been planning to go. I figure we should be able to calculate, rather than simulate what our sample variance _should_ be. This would be an "exact" formula, in the words of Carl Morris.
I'll think about this for a few days, and post back if I've got it.

-Arvin

DIPS year-to-year correlations, 1972-1992 (August 5, 2003)

Posted 2:10 a.m., August 14, 2003 (#92) - Arvin Hsu
  one other clarification point Re: binomial distribution

X ~ Bin(n,p) is the distribution for Random Variable X.
X is the expected number of events to occur with prior prob. p.

When ppl quote std-Bin = sqrt(n*P*(1-p)), this is the std for r.v. X.
It is _not_ the std-dev for p-hat = X/n, or what ppl use as the best-estimator for the population parameter p.
p-hat is a proportion.
X is an integer.
The variance for p-hat is calculated as follows:
Var(aX) = a^2*Var(X)
p-hat = X/n
Var(p-hat) = Var(X/n) = Var(X)/n^2
Since Var(X) = std(X)^2 = n*p*(1-p),
Var(p-hat) = n*p*(1-p)/n^2 = p*(1-p)/n
std(p-hat) = sqrt(p*(1-p)/n)

Note that this is the SAMPLE variance and standard deviation.
p-hat is the best estimator for the population parameter p.
std(p-hat) is NOT an estimator for the population variance of p.

What does this mean for us? It means as N increases, the sample std-dev of the sample will decrease. This explains, perfectly, Erik's findings in post #58:
BIP #seasons std(p-hat)
200-299 1446 0.032
300-399 812 0.0268
400-499 592 0.0245
500-599 507 0.0221

to take two numbers:
n=250, std(p-hat )= .032
n=500, std(p-hat) = std(p-hat(n=250))/sqrt(2) = .032/1.41 = .0226
You're std(p-hat) for n=550 is .0221!!!

The question you really want to ask is: what is the relationship between p-hat, or std(p-hat) and my POPULATION Variance for p?? That question is a bit more difficult, and is mentioned in my previous post. a start, at least:
pop-variance should be distributed Chi-Sqr.
One next step would be to calculate the MLE(Maximum Likelihood Estimator) for pop-variance.
There are other estimators, as well, though MLE should be fine.
It should be calculated already, if anyone wants to look it up in a stats textbook.

That estimator only begins to answer the questions posed, since we need to then combine with a model for multiple values of n, in order to find an estimator for the population variance.

-Arvin

DIPS year-to-year correlations, 1972-1992 (August 5, 2003)

Posted 2:26 a.m., August 14, 2003 (#94) - Arvin Hsu
  damnit, stop drawing me away from matlab.

Chris:
I had considered this, but I don't think it is a problem. I certainly think it would be interesting to calculate, rather than simulate, what the pitcher variance should be, but if the simulation is done correctly, the answers should be very similar.
True. In fact, as I mentioned, it's difficult to calculate it with the differing N's, and the simulation seems to work well enough. The two reasons to do it are: 1) interesting, as you said, 2) it would give us a better idea on what factors affect the observed std(p-hat).

Eliminating the simulation variance would help, but the dependancy between park and defence factors, and the lack of a good estimate of defence variance relative to pitchers are larger issues.
Totally agree. But they can be unlinked. The big problem is ballpark v. defense. I think the key here is to take multiple seasons, and hold ballpark constant, but defense as adjustable.
But, you don't have enough degrees of freedom. Hrmm...

Each pitcher on a team shares the same defense each year. They also share the same home ballpark each year. How do you disentangle home ballpark from defense without using pbp data? Home/away splits for each pitcher would do it, but that's still unavailable/not easy to crunch. you can't use offense numbers to calculate alpha-park, there's a dynasty bias.
10 seasons * 5 starting pitchers = 50 data points
1 park factor, 10 defense factors, 5 pitcher factors = 16 variables
plenty of room to get good estimates.

but once you collapse pitchers on a team, you get
10 seasons = 10 data points
1 pf, 10 defense factors = 11 variables.
and that's not identifiable.

grrrr... any suggestions?

DIPS year-to-year correlations, 1972-1992 (August 5, 2003)

Posted 2:35 a.m., August 14, 2003 (#95) - Arvin Hsu
  Chris,

could you define your proposed variables a little clearer?
So far, I understand:

defence-team variance (.008)
pitcher variance (est. at .007)

Everything else in your post, I'm a bit fuzzy on:
What is defense-pitcher variance?
Is defense-team = inter-team variance,
is defense-pitcher = intra-team variance?

-Arvin

DIPS year-to-year correlations, 1972-1992 (August 5, 2003)

Posted 10:51 a.m., August 14, 2003 (#101) - Arvin Hsu
  Tango:

It seems like you're introducing a lot of variables. Are you planning to use pbp data to identify all the values?
It seems like you want to say each pitcher is a combination of
the following over 21 years(72-92):
one of 28+ park factors
one of 28*21 IF defense factors
one of 28*21 OF defense factors
his own pitcher IF factor
his own pitcher OF factor

Is this correct?

You're using up df very fast this way, and may run into identifiability problems. Also park factors may also have an IF/OF split

-Arvin

DIPS year-to-year correlations, 1972-1992 (August 5, 2003)

Posted 10:55 a.m., August 14, 2003 (#102) - Arvin Hsu
  yah, it looks like 28*2 park factors.
adding it up:
assume 500 pitchers, avg. of 5 years per pitcher
data points:
5*500 = 2500

variables:
28*2 = 56
28*21*2 = 1176
500*2 = 1000
total: 2232

Well, 2232<2500 which makes it theoretically identifiable. But
this is immense.

-Arvin

DIPS year-to-year correlations, 1972-1992 (August 5, 2003)

Posted 3:36 p.m., August 15, 2003 (#114) - Arvin Hsu
  1) Regarding UZR: you guys are way over my head. I haven't looked at the methodology close enough to begin to understand it.

2) tango: Actually, Arvin, I'm assume "league average" for everything else. For example, I already published the DER park factors over the 21 year span. The standard deviation (50% home, 50% road) was .004. I'm assuming that over that many years and BIP that the observed and expected would come in at pretty much the same thing.

Why would the STD of both stats be the same? .04 std for DER should be stat dependent, and shouldn't have anything to do with the population std of the defenses using this binomial p model that Erik is using.

-Arvin

DIPS year-to-year correlations, 1972-1992 (August 5, 2003)

Posted 6:43 p.m., August 16, 2003 (#116) - Arvin Hsu
  Tango...

thanks for the explanations. The methodology makes sense now.

As for formulas... I think the numbers you've been simulating, Erik, can be approximated by assuming that the variance's add.
IOW,
k ~ Bin(n,p)
p ~ Norm(0,sigma^2)
Var(k) = n*p*(1-p)
Var(p-hat) = p*(1-p)/n <---- this is what we expect the Binomial to contribute to our data.
Observed Variance of Data = Var(p) + Var(p-hat)
= sigma^2 + p*(1-p)/n

So... Using your data: sqrt(p*(1-p)/n+.012^2)
200-299 1446 0.032: .0309
300-399 812 0.0268: .0269
400-499 592 0.0245: .0244
500-599 507 0.0221 .0226
600-699 579 0.0210 .0213
700-799 454 0.0204 .0203

------------------

Also, if you have multiple sources of variance, they will also
add similarly:

Total True Variance = True Defense Variance+TrueParkVariance+TruePitcherVariance

.012^2 ~= .0075^2 + .008^2 + .004^2 = .0117^2

I'm not entirely comfortable with the simplification that the Norm Variance and the Bin Variance will linearly add, but it appears to fit the data well.

-Arvin

Using your data: sqrt(.0075^2+.008^2+.004^2) = .012

DIPS year-to-year correlations, 1972-1992 (August 5, 2003)

Posted 6:44 p.m., August 16, 2003 (#117) - Arvin Hsu
  btw, Tango...

in your most recent post you said UZR team std = .010,
whereas in Erik in his prior calculations was using .008.
Which one is correct?

-Arvin

DIPS year-to-year correlations, 1972-1992 (August 5, 2003)

Posted 10:53 p.m., August 17, 2003 (#120) - Arvin Hsu
  Tango: Like I showed above:

k ~ Bin(n,p)
p ~ Norm(0,sigma^2)
Var(k) = n*p*(1-p)
Var(p-hat) = p*(1-p)/n <---- this is what we expect the Binomial to contribute to our data.
Observed Variance of Data = Var(p) + Var(p-hat)
= sigma^2 + p*(1-p)/n

Hrmm... now that I re-paste it, I can see that it's a bit impenetrable. How's this?

Observed Variance = Binomial Variance + True Variance

So...

(Obs. Std)^2 = p*(1-p)/n + (true Std)^2

And this is what the chart that I posted after that showed for Erik's numbers. Oh, p is the avg. rate for the binomial: eg. .281, but it would be different if the team fielded at, say, .300, or whatever...
And n is obviously the number of BIP.

-Arvin

DIPS year-to-year correlations, 1972-1992 (August 5, 2003)

Posted 1:46 a.m., August 18, 2003 (#122) - Arvin Hsu
  Tango:
n=4500 in your example. You're data has 120 observations of a
Binomial distribution where n=4500. The std-dev observed is the
std-dev calculated on the binomial distribution, and is an estimate
of the combination of the binomial variance and the underlying(true)
variance.

-Arvin

DIPS year-to-year correlations, 1972-1992 (August 5, 2003)

Posted 6:55 p.m., August 18, 2003 (#129) - Arvin Hsu
  tango: that sounds like a good idea.

I have a few thoughts on the theory that could be included. I'll post later about it.

-Arvin

DIPS year-to-year correlations, 1972-1992 (August 5, 2003)

Posted 11:01 p.m., August 18, 2003 (#130) - Arvin Hsu
  tango:

wow... you're thoughts move faster than mine:

.006 ^ 2 = [(t/7)^2] * 7

(That is, each position is on average getting 1/7th of the plays, and there are 7 positions. See post 115 for more info.)

t = .016 = true avg single fielding position

I read 115, and I still don't understand what you're doing here...
isn't it: .006^2 = [t^2]*7??
That means that on any one play, a fielder gives .0023?

Here's how I interpret it:
.006 is the std(variance) of defensive ability, independent of park or pitchers. If every fielder contributes .0023 std (variance), than that creates a teamwide std (variance) of .006.

Alright, but on any one play, the ball can only be fielded by one fielder, sometimes two, very very rarely three. So what does that mean?

.006^2 is the variance of the underlying distribution that governs the binomial p... On one play, or one Bernoulli trial, you have a p that is determined by 1) pitcher's alpha, 2) park's alpha, and 3) defense-alpha.
3) defense-alpha ~ Norm(0,.006^2)
Thus, 65% of teams have a defense-alpha within +-.006.

What about on a play? That entire variance should be attributed to the fielder, I think, or divided in half(using Pythag) and given to both fielders, or all 3 or however many are involved in the play.

That means that if you have 7 fielders, all at +.006, then you would have teamwide defense at ... +.006. Because on any one play, the ball only goes to one of the fielders.

-Arvin

DIPS year-to-year correlations, 1972-1992 (August 5, 2003)

Posted 10:32 a.m., August 19, 2003 (#132) - Arvin Hsu
  I think it comes down to why we're adding variances:
In a normal distribution, you add when you add two random variables.
eg. X ~ Norm(3,.05^2), Y ~ Norm(4,.03^2)
Z = X+Y
Z ~ (7,.05^2+.03^2)

Although I'm not yet convinced it works this way for a normal p affecting a binomial, the sims seem to bear it out. Why? Well it makes sense. On some level, you're adding two r.v.'s, the binomial
and the normal. So, on any one play, who can affect the ball? Only our 1-3 fielders. Thus, the fielder's variances can never really _add_, since they each affect _different_ plays. We add park +pitcher + defense specifically because all 3 affect the _same_ play.

-Arvin

DIPS year-to-year correlations, 1972-1992 (August 5, 2003)

Posted 10:34 a.m., August 19, 2003 (#133) - Arvin Hsu
  In fact, what you probably have is a single fielder std somewhere around .0059, and it averages out to .0060 once you add in plays where two fielders can make the play, as well as three. If you have these numbers we can try to calculate it, but I figure .006 is strong enough an approximation for now.

-Arvin

DIPS year-to-year correlations, 1972-1992 (August 5, 2003)

Posted 1:59 p.m., August 19, 2003 (#136) - Arvin Hsu
  observed ^ 2 = .010 ^ 2 + .006 ^ 2 + .004 ^2 + luck ^2 = .020 ^ 2
solving for luck = .016
Or... you could just say:
Binomial distribution, n=700, p = .281
std: sqrt(p*(1-p)/n) = .0169

the extra .009 is probably rounding error, since we only have one significant figure on a lot of these numbers.

-Arvin

DIPS year-to-year correlations, 1972-1992 (August 5, 2003)

Posted 4:31 p.m., August 19, 2003 (#138) - Arvin Hsu
  so... back to figuring out the impact of a single player.
Anyway, since we've established for fielders that 1 stdev is .016, and if they average about 650 plays each, that gives us 1 stdev = 10 plays per season, or about 8 runs. That's 1 stdev for fielding runs for an average fielding position.
If we redo this approximation, we get:

(.006)*650 = 3.9 balls/season.

Most ppl would agree that the number seems low. 65% of starting fielders are within +- 4 plays/season from average? It definitely seems low. So how to account for it?

Well, let's start by pointing out the weaknesses in the approximation:
a) BIP are not distributed evenly. SS's obviously get more BIP than RF'ers, or 1B-men.
b) +-.006 is 1 STD for the team defense. This means that individual positions may have a higher STD.

Let's also point out two general items which will bias judgment:
a) 1 STD is just that. One standard deviation ~ The best players may be 2 or 3 or even 4 standard deviations from average(Erstad, anyone?). At this point, we have no reason to believe that the underlying skill distribution is normal. It may, in fact be, student's t, or Beta, or whatever, and the tails may be considerably longer. However, many ppl may see the small STD and say that it just can't be, without realizing the statistical significance of it.

b) How errors are counted. As I understand it, an Error is counted as an out from the pitcher's POV. The presence or absence of the error is not present in our binomial calculations at all, except as another BIP that resulted in an out. I think, that, to evaluate fielding, we will have to add error rate as an extra factor on top of the +-.006 std for fielders, thus giving fielders 17% responsibility for the $H, but an added responsibility for converting "oughtta_be_outs" into "actual_outs." This, shouldn't affect our DIPS calculations, but _will_ affect our interpretation of UZR as a "control," so to say, since IIRC, UZR counts Errors as balls that the fielder failed to get to, which will increase UZR variance rates, but will not affect our DIPS variance rates.

-Arvin

DIPS year-to-year correlations, 1972-1992 (August 5, 2003)

Posted 4:40 p.m., August 19, 2003 (#139) - Arvin Hsu
  We know very well how to estimate the former, and not
very well the latter. Since the BABIP figure is not
reliable for an individual pitcher, it's more accurate
to use say 50% lg, 40% team, 10% pitcher to estimate
his expected BABIP. But, that estimate will come with
a very wide margin for error.

The conclusion stands that you need to separate
things, and you can't rely on a pitcher's past BABIP
to predict the future (much like you wouldn't use his
ERA). Still outstanding is WHAT to use for BABIP.
I'll contend that PZR would be that measure. But,
that has yet to be implemented by anyone.

The answer, I hope, will be around the corner. I'll be free after the first week of Sept(Master's finished), and I'll be able to do some more in-depth work. I've been planning to run some data models of hitter's, using component rates over career arcs inside a Bayesian framework, but I'll put that on hold now. What we have is the structure of a tangible data model that is experimentally testable. I should be able to enter DIPS data into a Bayesian engine that will simulate(MCMC) and establish likely data points for all pitchers, parks, and team-defenses. I'll need home/away splits to do that, but that should be all the pbp data necessary. We should come up with some very nice estimates that would be perfect for predictions.

IOW, the simulation should come up with precise distributions(mean/std) for each pitcher, each ballpark, each defense. And that would be the numbers you use to predict next year's $H.

-Arvin

Evaluating Catchers (October 22, 2003)

Posted 1:38 p.m., October 27, 2003 (#15) - Arvin Hsu
  Great stuff, as always, Tango.

For 28 of the 29 catchers, the "other catchers" was between -1 to +1. Benedict was compared to a +2 baseline. In essence, by doing this huge meshing, we are just about capturing a league average baseline.

When you did this, did you do a weighted average? If so, what were the weights based on, IP(caught) for each pitcher, then weighted for the catchers the pitchers caught?

That's a good point... no I did not.

hehe. Doing the more difficult adjustment before looking at the easier one. :)

Colinm: . Then you can add up the deltas, and multiply them by ActualPA/WeightedPA to get the total for a career.

I'm not grasping what you're trying to do. Doesn't the multiplication undo what you did by taking the lower IP-weight?

-Arvin

Evaluating Catchers (October 22, 2003)

Posted 2:42 p.m., October 27, 2003 (#18) - Arvin Hsu
  In the example in the article, I would take Foote's rate, and apply it to the 2176 PAs with Rogers. I do this with all catchers that Rogers had. This tells me how good the "non-Carter" catchers were. And I repeat the step, etc, etc....

wow. fully weighted and recursive. very nice.

Cities with best players (October 23, 2003)

Posted 3:02 p.m., October 23, 2003 (#9) - Arvin Hsu
  San Francisco has:

Barry Bonds

Joe Montana/Jerry Rice

Wilt Chamberlain/Rick Barry

Top That!

Cities with best players (October 23, 2003)

Posted 3:08 p.m., October 23, 2003 (#10) - Arvin Hsu (homepage)
  Ranking of top 100 North American Athletes of the Century
http://espn.go.com/sportscentury/athletes.html

For SF:
Mays #8
Chamberlain #13
Montana #25
Rice #27

Bonds would rank up there now.
I would say:
Bonds/Mays (2 of top 3 baseball players)
Chamberlain (1 of top 3 basketball ever)
Montana/Rice (2 of top 5?maybe top7?)

-Arvin

Cities with best players (October 23, 2003)

Posted 5:42 p.m., October 24, 2003 (#27) - Arvin Hsu
  so using the arbitrary top 10 lists posted above,
and assigning points from top-down(10-1):
San Francisco has
Bonds(9)+Mays(4)+Montana(6)+Rice(8) = 27

And If you count Chamberlain(9) as half points: 31.5

Results of the Forecast Experiment, Part 2 (October 27, 2003)

Posted 6:01 p.m., November 1, 2003 (#76) - Arvin Hsu
  One of the problems is that there are two factors which determine what the "curve" will look like - one, the distribution of a binomial (will the player get a hit, a walk, a home run, etc., in each PA or won't he?), and two, the distribution of possible changes in true talent level, which is presumably based on things like chnages in age, physical condition, injury, "learning," and mental and psychological factors. The former should produce a normal curve, by definition - the latter, who knows?

Actually, the former does not produce a normal curve. It produces a binomial. The latter produces what statisticians often call the beta-binomial. There resides a beta prior distribution on the binomial theta(or p) value. This beta distribution has it's own mean and std. This is what contains the day-to-day variation. This does not, however, account for overall shifts in ability, ala the Loaiza example.

-Arvin

ALCS Game 7 - MGL on Pedro and Little (November 5, 2003)

Posted 7:48 p.m., November 5, 2003 (#6) - Arvin Hsu
  FWIW, my take on the matter.

there is evidence that pitchers do NOT have good and bad days

I am guessing that MGL is referring to the fact that what seems like good & bad days to casual observers models exactly what we would expect from random noise due to a normal or a binomial distribution.

If that's the case, the issue can be restated thusly:
A is what we observe as fluctuation in performance.
A can not be distinguished from random noise B.
What do we mean by random noise B?

One interpretation is this:
B results from the binomial distribution. e.g. a machine bats a ball with a certain ability .300. This means there will be some stretches where the machine will go 0-5, and some days the machine will go 4-5.
These hot & cold streaks are strictly the result of having a probabilistic engine governing the underlying event.

Another interpretation is this:
B results from random variation, eg. like that seen in a normal distribution. We expect the batter to bat .300 on average, but he fluctuates above and below that, and it looks like he has a variance of .0004(or std-dev of .020). Thus, in 67% of samples taken, he's within +/-.20 of .300.

This latter interpretation is problematic: Every measurement in the world has an aspect of indeterminism to it, and what distinguishes the fact that some things have small variance and some things have large variance are due to causal factors underneath. These causal factors may be "good and bad days." Why do they look normal? Central Limit Theorem. Everything looks normal when taken with enough samples.

-Arvin

PS> this is my 20-second take on the matter. I haven't thought it through

Converted OBA (December 15, 2003)

Posted 4:27 p.m., December 15, 2003 (#2) - Arvin Hsu
  Tango: Why do you want to convert everything into a binomial distribution? I can understand an ease-of-use argument, but the multinomial isn't that much harder to use. And the multinomial describes all the events precisely, without the loss-of-accuracy, as long as you agree with the premise (which you have to in order to use the binomial as well).

-Arvin

Converted OBA (December 15, 2003)

Posted 7:31 p.m., December 15, 2003 (#8) - Arvin Hsu
  Tango:

Your Ben matchup idea is interesting. I played around with a matchup similar to this for real OBP a while ago. It used the same system as Chess ratings and Sagarin power ratings.

Essentially, all batter/pitcher matchups are equivalent to a chess match. Eventually, you should come up with a rating for each pitcher and batter. The higher the rating, the better the ability to "win." Win is defined as keeping players off base for pitchers, getting on base for batters.

Wikipedia has a good intro to the ELO rating system.
http://en2.wikipedia.org/wiki/Elo_rating_system

Once the true values are determined, batter/pitcher matchups should be able to be predicted with precise % success rates (eg. probability of getting on base).

-Arvin

Converted OBA (December 15, 2003)

Posted 1:15 p.m., December 16, 2003 (#10) - Arvin Hsu
  B=Batter rate
P=Pitcher rate
L=League rate
B*P/L = X

So you did (.391)*(.391)/(.342) = .447??

Then you take the .447 and back-derive the constituent HR,BB,etc?

-Arvin

Converted OBA (December 15, 2003)

Posted 4:57 p.m., December 16, 2003 (#14) - Arvin Hsu
  Why do people think the League average should be involved at all?

Assuming true rates for each event, the batter and pitcher abilities should be all that is taken into account.

-Arvin

Converted OBA (December 15, 2003)

Posted 12:06 p.m., December 17, 2003 (#19) - Arvin Hsu
  Patriot:

You are correct. That's why I said assuming "true rate."
IMO, the best way to do a prediction is to first regress the observed rates. IOW, what you predict batter A and batter B's true rate will be in their next matchup. Then, you do the comparison, and you shouldn't care about league. (park or D may matter, but that's a whole other can of worms).

-Arvin

Converted OBA (December 15, 2003)

Posted 2:03 p.m., December 17, 2003 (#22) - Arvin Hsu
  it sounds like we are on the same page... but still not quite.
Once you regress, IMO, you're done. You don't need league anymore.
Of course, you can use park effects and defense and such, but that's different.
And we have a lot of practice at regressing to find true talent level, so I would use the work that's been done there already. Once you have the regressed true talent level for both batter and hitter, you can throw league out the window.

-Arvin

Converted OBA (December 15, 2003)

Posted 5:42 p.m., December 17, 2003 (#24) - Arvin Hsu
  Aaah... I see what you're saying now.
For any given performance, there are multiple factors at work:
alpha = player's true ability
beta = park effect
gamma = year effect

For a batter v. pitcher matchup like we have, there are two alpha's, but only one beta and one gamma.

For events that are in the field-of-play, you also have
delta = defense effect (subdividable by type of play, if you wish)

-------------------------
Bonds v. Pedro
alpha1 = Pedro's true OBP
alpha2 = Bonds' true OBP
beta = Coors/Astrodome
gamma = 1994/1980

============================
My initial confusion was that I was thinking of true talent level as a true talent level estimated for a particular year(specifically b/c of aging curve effects). Thus, my erroneous assumption was that
Bonds' true OBP for 1994 would be a function of alpha2+gamma, which I thought of as one effect, but which in fact, is two effects. In some ways, this translates into a very weird concept of "true talent level." As of 2004, we can predict Bonds' true talent level, but it shouldn't be the best prediction of Bonds' performance(ignoring parks and pitchers faced). The best predictor would be a function of both Bonds' true talent level and a predicted league-year effect for 2004.
In essence, the value which we assign to each player as "true talent," has no direct correlate in measurable stats.

Request for statistical assistance (December 17, 2003)

Posted 5:52 p.m., December 17, 2003 (#1) - Arvin Hsu
  short answer: yes, you should.

long answer:
depends on your assumptions, specifically what the statistical model is behind these "catcher deltas." Tango, what exactly are the "catcher deltas", and how did you calculate them? I don't remember the previous catcher breakdown thread too clearly.

Request for statistical assistance (December 17, 2003)

Posted 6:14 p.m., December 17, 2003 (#2) - Arvin Hsu(e-mail)
  Feel free to email me if you want.

Request for statistical assistance (December 17, 2003)

Posted 8:37 p.m., December 17, 2003 (#4) - Arvin Hsu
  That uses the same formula we used for figuring out defensive contributions. _That_ formula was an approximation, but it worked.
This one, I don't know. Let me read up on your catcher's delta tonight.
I may have a statistical model tomorrow.

-Arvin

Request for statistical assistance (December 17, 2003)

Posted 3:46 p.m., December 22, 2003 (#26) - Arvin Hsu
  So to continue,

δPB = (µ=-10.5, σ² = 48.4)

ΔPB = δPB *5500/8104 (in this case)
ΔPB = (µ=-10.5*5500/8104, σ² = 48.4*(5500/8104)²)

Request for statistical assistance (December 17, 2003)

Posted 3:47 p.m., December 22, 2003 (#27) - Arvin Hsu
  ΔPB = (µ=-7.1, σ² = 22.3)