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Advances in Sabermetrics (August 18, 2003)

Posted 11:20 a.m., August 20, 2003 (#25) - Jim R
  Tango,

Maybe I'm missing something because there are other factors that you and the more learned posters here are using, but I'm not sure I understand how regression to the mean would be a recent advance either.

Let me take your two examples:

Little Johnny Walker: I wouldn't have a clue based on this information alone as to what his talent level would be.

Johnny Walker: I still wouldn't venture to guess, but my best guess would be .340+ in that context.

The reason that I point this out is that I would offer the evaluation in this context is not based on simple regression to the mean. True, in large sets of data, the data will typically take on a normal distribution, but I don't see the applicability in this concept for individual or isolated players. Either Johnny Walker may be underperforming their true talent level with the .380 MNP and we have no empiracle method of determining this from that data alone.

What I have seen many of you talented researchers do is look for strongly correlated points of data that show consistent indicia of talent. That is, attributes that are not likely to wildly fluctuate from year to year.

For example, you could give me and A-Rod four at bats against an A-ball pitcher, with these results:

Arod 1: Liner caught on the warning track.
Arod 2: Dinger
Arod 3: Missle right at a deep playing center fielder.
Arod 4: Popup.

Me 1: The Whiff
Me 2: The whiff
Me 3: squibber the roles down the 3b line and goes for an IF single
Me 4: The Whiff

This is a scenario that would not astond probability. We would both have an OBA .250, the league average could be .330, and you still aren't able to determine that A-Rod has a talent way above .330 and I have a talent way below .330.

Replace me in the extreme example with Tony Womack for 60 AB. Replace Womack with Furcal in 800 AB, and you still end up with the same scenario.

Now what you may be able to do is find attributes that are constant despite a small sample. For instance in the me and A-rod example, you may be able to determine, bat speed, approximate exit velocity of the baseball, and overall athleticism.

In the Womack example, you may also use (1) and (2), but they will be pretty close in (3) for just an observer without other instrumentation. Also this skill may reach an apex without the use of additional instrumentation. You may add other observation variables, such as ability to make contact on different pitches, swings at good and bad pitches, etc..

In the Furcal example, its entirely possible that my (1) (2) and (3) aren't noticeable without instrumentation. (I know ARod hits it harder but bear with me.) Some of the Womack observation criteria also start to break down, but some may be able to let you make a meaningful determination. Also at this point, it becomes a little more difficult to observe and remember, so you add instrumentation and start recording results. At this level, you can probably take away meaningful differences by using things such as slugging and walk rate.

In essence, the more data you have the more able you are able to discern the true ability from past performance. Each time, your data set increases, you start to include measures that are relatively constant within those intervals.

Nevertheless, regression to the mean does not help you better predict any single player. If you give me a data set that includes all players who overperformed the mean for a specific interval, I can guess for each player that their performance will drop. In doing this I would be right more times than I am wrong. If I can make bets or gain credibility by doing this, I would derive income and prestige.
Yet, using a regression to the mean would not help me with any given player. I will be right more times than I am wrong if I guess their performance will drop, but it doesn't help me in any way determine what that players true ability level would be.
Baseball performance is entirely different than running a simulation on a widget. When I run a simulation on the widget, I know that its true performance level is constant when I begin the exercise. Each subsequent rerun of the simulation can allow me to determine a different mean, and a level of confidence on this being the true performance level.
A single baseball player is different, because (1) their true performance level will differ over time with variables that are difficult to account for and (2) the basis of comparison are other baseball players who themselves have differing levels of a true performance level.

For instance, if you pose the following hypothetical (which is closer to Brady Anderson):

Johnny Walker Blue in 600 AB- .380 OBA
Johnny Walker Blue career in 1800 AB - .360

The model is closer to where you can use regression to the mean to determine Johnny Walker blue's performance in his next 600 AB.

Correct me if I'm missing something.

Advances in Sabermetrics (August 18, 2003)

Posted 4:12 p.m., August 22, 2003 (#38) - Jim R
  "A player will always play to his true mean for every play, and this mean will be different play to play. As his sample number of plays approaches infinity, his average performance level in those plays will approach his average true talent level over that time span of plays."

I was with everyone until this clarification by Tango. So, I'll do what I always do, when I'm confused--I'll try to impose my own language and see if you guys will tell me where I'm wrong.

First, I think we have two different means that we are talking about

(1) Performance Mean - This is what it is. This is a player's mean performance in some category over some interval. You can adjust the performance mean for other factors, but the performance is the same. By definition, this is a straight line, backward looking measure and thus it does not regress. We can hypothesize that it will regress in the future (more on this later). When tango is saying "...100% ..." we are referering to performance mean that has an interval of 1. Its reasonable to presume through documented evidence that the performance statistics of all major league baseball players take on a normal distribution in the interval of one season after performance statistics are adjusted for the most egrgious factors affecting our performance instrumentation (e.g. park).

(2) Ability Mean - This is either a hypothesis/theorem/law (herafter hypothesis), and is the primary tool we use for making projections. We hypothesize that a player has a true talent level within any interval. We hypothesize that the number of variables that affect ability mean are not so large or egregious as to make the ability mean of all major league players within a single season not take on a normal distribution level.
By definition ability mean can include an interval for future events. We do not have the instrumentation to measure ability mean, but pursuant to the law of large numbers, we hypothesize that ability mean and performance mean converge for a single set of data when the interval becomes large enough. While it is true that a player will have the same ability mean for any interval (not necessarily 1), we are not able to observe what this mean may be.
Because of our previous hypothesis, we can presume that ability mean and performance mean for all major league players over the course of a season are equal within a tolerable degree of error.
However, we hypothesize that the data set for a single player in one major league season is not large enough where ability mean and performance mean converge.
Rob hypothesizes that 9971 AB is an adequate sample where ability mean and performance mean will converge for a single player. Tango says that it is not large enough to make this judgement.
If we pick a random player with no performance data and do not have any other information about their performance level, we can say with x degree of confidence that this player's ability mean will match the league ability mean, which equals the league performance mean. Thus we can project his performance mean to be equal to the league performance mean.
If we can pick a random player with some performance data, we can say with y degree of confidence that his ability mean is the same as his performance mean. Yet because the numbers are too small, the y is usually going to be too small for us to have any degree of confidence.
Instead, we can start with a guess of x degree of confidence that his ability mean=league ability mean=league performance mean. We can use his performance measures to adjust our hypothesized ability mean with actual performance numbers. As we do this, we will converge on a number within a tolerable degree of confidence of the player's ability mean.
So the only remaining questions would be:

(1) At what number of events does the performance mean converge on the ability mean. It seems we are in agreement that it is greater than 600 but less than 450,000.
(2) When/How do we adjust for the time dependent variables in each mean (age, era, etc.)

Solving DIPS (August 20, 2003)

Posted 3:55 p.m., August 20, 2003 (#3) - Jim R
  Just a comment on the write up and not the actual information. FWIW, I particularly enjoyed the write up and I thought it was fairly tight. Maybe I didn't save any time from reading the write up as opposed to reading the thread, but I at least had the illusion that I saved time :)

I know you probably have better things to do, and I guess BPrime isn't springing for you to have a clerk, but I do find these items useful.

I think you will find that besides myself, there are people that fit this profile:
(1) Are interested in your work and the work of your contemporaries
(2) Have variable amounts of time we can devote to reading the results (I've been on partial vacation for a week).
(3) Probably have little to offer in the more serious development of the ideas.
Your synopsis provide great utility to me (or us). I hope if not you, BPrime can find a way to keep them coming from time to time.

Making (some) sense of RBI (August 20, 2003)

Posted 5:32 p.m., August 20, 2003 (#2) - Jim R
  Three questions.

(1) Where do you get the data for #1 and #2. I'm guessing this is some combination of Retrosheet and Ray Kirby's ASS, but if you can save me some hunting and pecking it will be appreciated.

(2) If its already written up what is the laborious process for controlling (b) and (c). [Skip this if its not written up]

(3) I just want to make sure my understanding of your (6) based on reading your linked discussion of the RDI. Our resulting number will still only tell us how good above average the player is at the RDI, as you have defined it. If one were to try and build upon this work and determine if there are skills for Ichiro's magic ability to hit a homer when it counts, etc., etc.; or the abiilty of Reggie to hit more clutch home runs than Barry Bonds, we still wouldn't be able to determine this without reconsidering the HR. That is, if the HR has a contextual value it still must be considered?

I ask this not to be a smart ass, but instead to understand and or extrapolate my worldly view on baseball. If one were to accept that (1) some batters were to change their approach on the AB based on the dynamics of the game; (2) they have differing performance parameters based on their approach.

For instance (and I am totally making this up), lets assume the famed Ichiro goes to the plate with one of two approaches: (1) Try to get a base hit and (2) Try to hit a homer. We have the instrumentation to determine the state of mind of the batter. In situation (1) Ichiro has this spread .15 1b; .1 2b; .03 3b; 0.02 HR; 0.04 NBIPOBO; .66 Out/error and in (2) .05 1b .08 2b .02 3b .08 HR 0.02 NBIPOBO, .75 out/error; or (1) .300 BA .340 OBA .520 SLG (2) .230 BA .250 OBA .590 SLG.
Now in probably 99% of baseball situations approach (1) is better than approach (2). I would imagine that if we use your base outs in combination with you win probabilities, we can likely find a neutral situation (that is not dependent on the pitcher, lineup, available personnel) where hitter (2) is preferable. That is trade an increase in 10% of making an out for a 6% increased chance of hitting a home run (or more appropriatly creating a run by driving oneself in). In this particular case, the ability to hit the HR, or make the decision to go for the home run would impact (a) and (b) of your number (5).
(As an aside, this is meant for illustrative purposes. I don't contend that anyone can be Dr. Vidro and Mr. Deer. However, I am inclined to believe that batters probably do change their approach based on pitcher, base/out, instinctual win probability, coaches instruction, count, etc. The differences in approach may likely yield very small changes in probability, and some approaches may in fact yield a decline in probability for any relevant positive event. I pose this just as a question for my understanding of the RDI discussion. Obviously we are not likely to have the instrumentation to measure this phenomena (if it exists) at any foreseeable period. I just want to understand the probable meaning of the outcome. I think I do understand of the macro ramifications of R+RBI-HR as a better predictor than R+RBI.

Mike's Baseball Rants - Sac Flies (August 28, 2003)

Posted 2:55 p.m., September 1, 2003 (#7) - Jim R
  "Maybe so, but we are only awarding statistical credit here for what did happen, not for what was most likely to happen."

David,

I've re-read this a couple of times, and I might not understand your point. If the FBOut does not score a run, it is not a sacrifice, regardless of the batter's intent. If the FBOut, scores a run, we are awarding the sacrifice. Perhaps there is a presumption that the batter did intend to give himself up for the run.

Conversly if a GBOut scores a run, the player usually gets an RBI, but not a sacrifice. Perhaps there is a presumption that the batter did not intend to give himself up. However, in all cases, the SAC is based on our judgment of the batter's intent. Even if the batter squares to bunt and advances a baserunner, we award the SAC because we believe the batter intended to give himself up. If a batter squares or drags a bunt, the official scorer can choose to not give a sacrifice because he believes the batter was not trying to trade his out for the advancement of a baserunner.( 10.09(d)

I would agree that there may be other situations, such as hitting behind the runner where the batter is giving an out and AB for advancing a baserunner. Nevertheless, this would probably create even more wrangling about a hitters intent.

"Furthermore, the only studies I've seen suggest that there is no "ability" to hit a FB in a SF situation that is different than the player's overall tendency to hit FBs. Since that topic has not yet received the detailed scrutiny that DIPS has, I am not going to assume that the conclusion is correct. But I have seen studies which suggest that GB hitters tend to be as good or better at advancing runners on outs as FB hitters are. Yet the FB hitters get all of the credit (in SFs) while the GB hitters get all of the debit (in GDPs). "

If you have links to these studies, please post them. I would really enjoy reading through them.

"IOW, the official statistics in this area are biased in favor of FB hitters, for no good reason that I can see."

This is probably true in the sense of judging a player by his batting average, GIDPs etc., is the prevailing methods by most sports fans. However, this is probably not true for both the baseball insiders (re: Conventional wisdom, etc.) or the hard core data analysts. The latter group, which comprises the majority of the Primate Studies crowd is probably seeking better and more refined methods of value. The former crowd will speak to "productive outs" etc.

"Historical Statistical Preservation Committee of Everything Ever Done Then is Better Than Now"

I know this is Tongue and Cheek, and I realize that Tango is among the most humble in advancing his own research, but I did want to make one comment.

I am not sure that the prevailing wisdom is that its better, its more along the lines of the value of the intended measurement doesn't change for the increase in data collection. The official scoring mechanism when instituted was probably the best conceivable means for achieving the result of most counting and rate stats that were perceived valuable for both performance and projection systems. In that sense, there was a convergence on data performance and data analysis.
In most cases, and IMHO, we want to remove as much subjectivity as we possibly can from a human machine, who must make a decision in a RT system. If we add these judgment calls to the official scoring system, we are going to have a bigger mess than a fix to the problem.
With an increase in instrumentation, we have sought to increase the data recordation to include PBP data. We can get it, and for the most part, its not RT dependent. We can actually wait a few days for the information. Within the last few years, we have even augmented our ability to get zones on batted balls, etc. I'm sure that everyone agrees it would be even more helpful if we could get additional info, like starting position of fielders, trajectory to the balls, et.
Also, the traditional stats from the official scoring system still have value despite the error from the miscounting. A casual baseball fan can look at Barry Bonds numbers and immediately determine he is one of the best hitters in the game. It is more difficult for him to judge the relative value of Bonds vs. Pujols within this season.
Said casual fan may also have trouble determining the value of Giambi versus Dmitri Young etc. They may also engage in frustrating arguments over the career worth of Joe Carter because of the RBIs.
Nevertheless, this frustration index does not disappear when dealing with a casual saber fan, who may also misinterpret the meaning behind statistics that use other methods of data recordation. I'm sure that you will find many people on this board that will attribute a meaning to a statistic that simply does not exist.
IMHO, the answer is not to change the official scoring procedures. They do what they are designed to do. Any changes in them would not likely increase their instrinsic value. The answer lies more into recording what we consider meaningful data into seperate systems and determining if the analysis of that data helps us in gauging the value of performance or enhances our ability into making projections.

Valuing Starters and Relievers (December 27, 2003)

Posted 2:47 p.m., December 28, 2003 (#14) - Jim R
  Interesting thoughts, and I have a question. At some point does it not make sense to vary the utilization patterns of starters as well as relievers. I'm making a lot of assumptions on Tango's unpublished study, but if the advantage a reliever gets would be based on two factors:
(1) Number of times through the lineup
(2) Amount of exertion on a single pitch

If we can decouple these factors, wouldn't we know about how to maximize starter utilization. For instance, I once read a Mike Marshall linked article where he opines that Maddux will take himself out of games after 3 times through the lineup. That certainly accounts for factor 1, but not necessarily factor 2. If a pitcher does do this, shouldn't they be able to recoup some of the 0.60 advantage in ERA. Could they recoup more if we limit it to two times through the lineup. If we start producing and positing some of these limits, wouldn't a pitcher then be able to also start to increase exertion to recoup a bit more.
Obviously this changes the makeup of your personnel and roster in a drastically different way. However, even if not taking to its logical conclusion, shouldn't we be able to look at an individual group of personnel, determine the equlibrium points of usage, and over the course of the season be able to reduce the staff ERA by a significant amount?