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 Post subject: Sabermetrics, Intangibles and the Sample of One
PostPosted: Mon Oct 23, 2006 1:01 pm 
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Over the past few months, I've been dissatisfied with the formulations and definitions of sabermetrics. Namely, I think that a lack of clarity at the roots has led to sabermetricians failing to clearly mark out the limits of their analysis, but that it also has prevented the real value of sabermetric analysis from being properly understood. So I've been working on an essay about the scope and limits of sabermetrics, but it's been slow going. To help work through it a bit quicker, I am going to work on individual parts on posts like these. Here is the first...

Sabermetrics, Intangibles and the Sample of One

There are two things that sabermetrics cannot tell you about. (Well, there are many, for one, it cannot tell you how to make a really good bowl of chili). Sabermetrics is silent about small sample sizes and future events. This does not mean that sabermetrics cannot inform decision making about small sample sizes and future events, but there is no guarentee that the conclusions of any statistical study will hold for the isolated case.

That might seem to be a bit of an odd statement. In fact, at first glance one might read it in such a way that it undermines the entire sabermetric project. In order to clarify this position I need to quickly step back and say something about the types of conclusions that sabermetrics develops. What is the main tool of this type of analysis? Statistical analysis. What exactly is statistical analysis? It is the observation, recording and analysis of past events.

This means that statistical analysis is used as data for inductive inferences - one notices a past probability and uses it to project a future probability. Induction itself is a merely probabalistic mode of inference, which means that we do not have any guarentee that the future will conform to past probabilities. Further, statistical analysis does not even develop probabilities properly speaking. What it develops are the relative frequencies of an event occuring. Even if we take a certain tract in the history of the philosophy of probability and define probability as relative frequency, it is nevertheless relative to a specific sample size.

The last paragraph was a window into some of the guts of the view I am arguing for. Let's take a step back and see what to make of it. What I have claimed is that statistical analysis, at best gives us (a) probable probabilities or worse, (b) relative frequencies that cannot be called useful probabilities at all. Neither option gives us what we thought we wanted - the probability of a future event occuring. We are therefore led to half of the thesis I introduced at the beginning of the article. Sabermetrics is silent on what will happen in the future because it cannot give us any probabilities for future events. All of its conclusions are strictly limited to the sample that generates them. [The upshot of sabermetrics, which I do not intend to defend in this small portion of the project is that it can be used as evidence in inductive inferences about future probabilities. That is, sabermetrics gives us more or less reason to believe certain conclusions about future events.]

What about the second claim, that sabermetrics doesn't tell us anything about small sample sizes? This conclusion is also based on the work we've already done. If the conclusions of sabermetrics are strictly limited to their sample then just as the conclusions do not apply to future events, they do not apply to subsets of the sample. If strikeouts are only marginally worse than all other types of outs and this conclusion is borne out over a number of samples this gives us a very valuable insight, but it tells us absolutely nothing of the value of a single strikeout in a single game.

This is not a particularly noteworthy conclusion. Billy Beane made this view famous with his claim that "his [expletive] doesn't work in the playoffs." He was simply affirming that in a small sample size the conclusions of sabermetric analysis do not hold. In a word, anything can happen.

Although it is not controversial, I think it is important to relate this to the frequent criticism that sabermetrics treats ballplayers as automotons rather than flesh and blood human beings. In whatever job we all hold (from an office to a school), we all see the effects of personal psychology on performance. I'm sure we've all had days where we were a bit down or off-kilter, and our performance suffered as a result. Or conversely, days of confidence that led to tremendous productivity. This happens to ball players to, and absolutely nobody can deny it. Sabermetrics does not deny this claim.

Personal psychology figures into sabermetrics when it has a prolonged influence on a statistical record over a large sample size. Over a sufficiently large sample size these things tend to be minimized. Does it mean that personal psychology and intangibles didn't play a role in each and every game, at bat and pitch recorded in that sample? Nope. What it does mean is that over the duration of the sample size, their impact was not substantive.

I wish to rectify the common error that runs in two directions. One direction is to generalize the claim that personal psychology did not play a substantive effect over a sample to the claim that personal psychology is irrelevant or not substantive in the game of baseball itself. This is clearly false, and results from an improper use of the sample. The other error is to assume that if personal psychology plays an important role in each and every at bat, then any analysis that ignores them is fundamentally flawed. This similarly does not follow, and the error is a confusion between the impact of an event on one event and the impact of similar events on every event of a different sample.

If we are succesful in avoiding this error it becomes clear that human beings play a real and important role in baseball. Not only are humans the ones actually playing the game, the foibles and features of human psychology are intimately bound up in every single event on the field. Nevertheless, we have reserved space for sabermetrics to produce generalized conclusions that have significant value despite not directly engaging with personal psychology.

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PostPosted: Mon Oct 23, 2006 1:33 pm 
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Jeff, great post, but do you have a cliff notes version of that? j/k :)

I find this paragraph to be particularly interesting:

Personal psychology figures into sabermetrics when it has a prolonged influence on a statistical record over a large sample size. Over a sufficiently large sample size these things tend to be minimized. Does it mean that personal psychology and intangibles didn't play a role in each and every game, at bat and pitch recorded in that sample? Nope. What it does mean is that over the duration of the sample size, their impact was not substantive.

What do you mean by the first sentence? Can you give an example? And what precisely is meant by personal psychology in this context?

Doesn't personal psychology always figure into sabermetrics? Since everything players do is affected by psychology? And sabermetrics is merely a statistical picture of everything they do?


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PostPosted: Mon Oct 23, 2006 1:40 pm 
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Anyone who quotes Bertrand Russell is obviously not writing for me.

All I see is mathmathmathwordswordsanalysismathmathstatsstatssamplesize.

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PostPosted: Mon Oct 23, 2006 2:01 pm 
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HarrisPoll,

That paragraph was a bit obtuse. Your paragraph that read:

Quote:
Doesn't personal psychology always figure into sabermetrics? Since everything players do is affected by psychology? And sabermetrics is merely a statistical picture of everything they do?


is, I think, exactly right. I had intended my claim to be of a more mediated sort - namely that the effects of the variations in psychology are often marginalized over large sample sizes. As I work further on this section of the greater project, I intend to reshape some of the language to make this clearer and more precise.

Regarding your other questions - an example of what I meant by that sentence might be a pitcher like Oliver Perez. Say (and this is an assumption) that the problem he has is confidence which leads to changes in his pitching. The effect of that lack of confidence would be a psychological factor that has a substantive (and indeed inseperable) impact on his pitching record over a larger sample size.

My use of personal psychology is intended to be suitably broad to cover all manners of mental phenomena, dispositions, character traits, etc. Nevertheless, I think your question has put into focus that a big part of the confusion I think I caused is that I equivocate a bit between that conception of personal psychology and "variations from a norm" in my usage, and the latter is rather silly. That's something I will have to clean up in subsequent versions.

Thanks for your valuable feedback!

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PostPosted: Mon Oct 23, 2006 2:25 pm 
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Jeff, I misunderstood that paragraph. I thought you were talking about sabermetrics/players/psychological aspects in general. Now that you put it in the context of one player, I get the gist of that paragraph better, which it appears to be mainly about sample sizes.

It appears then that my statement is consistent with your position. I was just coming at it from another angle.

:)


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PostPosted: Mon Oct 23, 2006 3:14 pm 
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A couple of years ago I made proposal that people writing "articles" on the front page of the website use the forum as workshop environment to help refine the article by subjecting it to questions/comments before publication to the public at large. The reaction to this was not good largely because of personalities and mood of the site at that time was that every new post was viewed through the prism of arguments of the past.

Perhaps I'm misreading this but I take your statement "to help work though it a bit quicker, I am going to work on individual parts on posts like these.." to be an invitation to criticism taken in the friendly spirit it is given and free from reprisal. Perhaps I'm wrong but that's never stopped me before so here goes.

It's too wordy.

I know this fault because it's a tendency I share with you and it's easier to see your own faults in others than in yourself. (One look at this post up to now shows you I know what I'm talking about). So please don't take this wrong but I edited your post. Use this as a springboard because having chopped it up it needs some smoothing, or simple ignore it, but here goes:


Sabermetrics, Intangibles and the Sample of One

There are two things Sabermetrics cannot tell you about: small sample sizes and future events. Sabermetrics can help decision making about small sample sizes and future events, but there is no guarentee that those conclusions will hold for the isolated case. That might seem to be an odd statement, in fact, at first glance, one might think it undermines the entire sabermetric project. To clarify this let's ask what is the main tool of this type of statistical analysis?

Statistical analysis is the observation, recording, and analysis of past events. It is used as data for inductive inferences - one notices a past probability and uses it to project a future probability. Induction itself is a merely probabalistic mode of inference, without any
guarentee that the future will conform to past probabilities. Statistical analysis does not by itself develop probabilities; what it develops are the relative frequencies of an event occuring. Even if we define probability as relative frequency, it is nevertheless relative to a specific sample size.

And what about sample sizes, or to be specific, small sample sizes? If the conclusions of sabermetrics are strictly limited to their sample then just as the conclusions do not apply to future events, they do not apply to subsets of the sample. If strikeouts are only marginally worse than all other types of outs and this conclusion is borne out over a large number of samples, this may give us a very valuable insight but it tells us absolutely nothing of the value of a single strikeout in a single game.

This is not a particularly noteworthy conclusion. When Billy Beane said "his [expletive] doesn't work in the playoffs", he was simply affirming that in a small sample size the conclusions of sabermetric analysis do not hold. In a word, anything can happen.

I think it is important to relate this to the frequent criticism that sabermetrics treats ballplayers as automotons rather than flesh and blood human beings. In whatever job we all hold (from an office to a school), we all see the effects of personal psychology on performance. I'm sure we've all had days where we were a bit down or off-kilter, and our performance suffered as a result. Or conversely, days of confidence that led to tremendous productivity. This happens to ball players too, nobody can deny it. Neither does Sabermetrics.

Personal psychology figures into sabermetrics when it has a prolonged influence over a large sample size. Over a sufficiently large sample size these influences tend to be minimized but that doesn't mean personal psychology and intangibles don't play a role in each and every game, at bat, and pitch recorded in that sample. What it does mean is that over the duration of the sample size, their impact was not substantive.

To pit these two seemingly contradictions against each other is a common error that runs in two directions. One direction is to generalize the claim that personal psychology did not play a substantive effect over a sample to mean that personal psychology is irrelevant in the game of baseball itself. This is clearly false, and results from an improper use of the sample. The other error is to assume that if personal psychology plays an important role in each and every at bat, then any analysis that ignores them is fundamentally flawed. This similarly does not follow, and the error is a confusion between the impact of an event on one event and the impact of similar events on every event of a different sample.

If we are succesful in avoiding this error it becomes clear that human beings play a real and important role in baseball. Not only are humans the ones actually playing the game, the foibles and features of human psychology are intimately bound up in every single event on the field. Nevertheless, we have reserved space for sabermetrics to produce generalized conclusions that have significant value despite not directly engaging with personal psychology.


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PostPosted: Mon Oct 23, 2006 3:29 pm 
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Willie STILL should have bunted in the bottom of the ninth instead of putting up Floyd. :evil: :evil: :evil:


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PostPosted: Mon Oct 23, 2006 3:30 pm 
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Putting aside my other criticism I have a question. Why is it that:

Personal psychology figures into sabermetrics when it has a prolonged influence over a large sample size. Over a sufficiently large sample size these influences tend to be minimized but that doesn't mean personal psychology and intangibles don't play a role in each and every game, at bat, and pitch recorded in that sample. What it does mean is that over the duration of the sample size, their impact was not substantive.

It seems to run counter to a more pop psychology approach and I wonder if the numbers don't back it up. Take the old argument about clutch hitting. You admit that being in a funk or being supremely confident affects each single event. Confidence, which we all know, doesn't come out of nowhere like a headache. It comes from past events. It may be by accident that someone appears clutch in Event 1, but once it gets to Event 50 or 250 wouldn't that become a self-generating psychology which would be substantive to his performance? Papi now knows he's clutch when he steps into a clutch situation which has to affect his psychology and the psychology of the pitcher. Is there an important difference between sample sizes when that means many players over many events and sample sizes of individual players over many events?


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PostPosted: Mon Oct 23, 2006 3:55 pm 
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dougdilg wrote:
Putting aside my other criticism I have a question. Why is it that:

Personal psychology figures into sabermetrics when it has a prolonged influence over a large sample size. Over a sufficiently large sample size these influences tend to be minimized but that doesn't mean personal psychology and intangibles don't play a role in each and every game, at bat, and pitch recorded in that sample. What it does mean is that over the duration of the sample size, their impact was not substantive.

It seems to run counter to a more pop psychology approach and I wonder if the numbers don't back it up. Take the old argument about clutch hitting. You admit that being in a funk or being supremely confident affects each single event. Confidence, which we all know, doesn't come out of nowhere like a headache. It comes from past events. It may be by accident that someone appears clutch in Event 1, but once it gets to Event 50 or 250 wouldn't that become a self-generating psychology which would be substantive to his performance? Papi now knows he's clutch when he steps into a clutch situation which has to affect his psychology and the psychology of the pitcher. Is there an important difference between sample sizes when that means many players over many events and sample sizes of individual players over many events?


Regarding your first post, you are spot-on that I posted with the intent of constructive criticism and discussion, so your thoughts are valued. I have not yet had a chance to read through your edit yet and give it any thought, but I intend to this evening.

I do have time for a response to your second post, so for now I'll stick with that one. I am not sure I fully understand your post, but one confusion in the quoted paragraph might explain it. Allow me to begin with my take on your example:

Let's say Ortiz becomes so convinced of his clutchness, that he brings that confidence with him each and everytime he steps up to the plate. Confidence in each at-bat improves his skill at the plate, making him a better hitter. This would be evidenced in his statistical record, as it would be statistically indistinguishable from his skill set. In other words, his confidence would simply become part of the ability of Ortiz, and would show up in the record of his achievments.

This phenomena might not, however, appear in a study of all players. What I mean by that is that clutchness factor might not come out of a large sample size where we learn that it is not something exhibited by larger groups of players. The conclusions in each case of they hypothetical study would be relative to the sample, but in virtue of them being different samples, rather than one being of numerous players and one being of a single player.

I actually think this raises some fascinating questions about the clutch question, and right now my thoughts on it are awfully confused and will need considable clarification. But what I'm starting to wonder is if studies about clutchness are making a category mistake - that is, they are searching for a single quality that is applicable to all players rather than a more subtle and nuanced account of individual psychology having common factors. In other words, maybe there is a common thread between psychological states that we call clutch that is not a quality that all players exhibiting clutchness possess.

I might have been confusing in that paragraph by making it seem as if I assumed that all psychological occurences would wash out in the laundry. I had meant that paragraph as a hypothetical about studies in which the psychological effects do marginalize (though, once again, I seem to have slipped into treating psychological effects as deviations from a baseline norm), but I did not make that explicit.

Lots to think about! And yikes, even my response was wordy! :lol:

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 Post subject: Re: Sabermetrics, Intangibles and the Sample of One
PostPosted: Mon Oct 23, 2006 5:29 pm 
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Being a renegade from philosophy in academia - I feel like I can address this somewhat articulately.

I should say, at first, that I am no skeptic about induction. That is, I think that inductive inference is rationally permissible. And it's warrant is the general uniformity of nature. And rational permissibility of beliefs + warrant + truth, in most contexts, produce true knowledge claims. I say this not to argue for it. But because I doubt I'll agree on much of anything with anyone who disagrees with much of what I've just asserted. whew.

Quote:
This means that statistical analysis is used as data for inductive inferences - one notices a past probability and uses it to project a future probability. Induction itself is a merely probabalistic mode of inference, which means that we do not have any guarentee that the future will conform to past probabilities. Further, statistical analysis does not even develop probabilities properly speaking. What it develops are the relative frequencies of an event occuring. Even if we take a certain tract in the history of the philosophy of probability and define probability as relative frequency, it is nevertheless relative to a specific sample size.


I am muddled about the metaphysics of probability and the epistemology of inductive inference. But it seems to me that the nature of probabilities and the nature of inference are pretty much independent. Any attempt to define "probabilities" in such a way that we can form deductive arguments about them aren't really probabilities. They're something else, like relative frequencies.

Of course there is no gaurantee in inductive inverence (if by that you mean no chance of being wrong). But why not consider statistical measures of a player's performance as supporting inferences about the causal powers of that player? Even supposing determinism (I don't), perfect inferences about player's causal dispositions wouldn't be possible absent the ability to hold other causes of an outcome fixed. (e.g., the opposing pitchers stuff, the roar of the crowd that day, the player's argument with his wife). Still, apart from uncertainty, which I expect, I see no reason to consider the enterprise as somehow ill-defined. That's why the best science, the science that really gets at the causal dispositions of events and things, is experimental. It seeks to isolate certain causal powers by holding others fixed. Any post-facto data mining is almost inherently flawed, comparitively. Still, post facto data mining saves lives.

And I believe this is the common understanding. After all, understanding statistical measures of performance as measures of abilities (i.e. causal dispositions) allows integrating statistical measures with other measures, measured bat speed for example.

As for the probabilities of inference you discuss... well - they're usually considered subjective probabilities - determined by rules for manipulating arbitrary prior probabilities (at least, before any evidence is in). They're just something else. I'd rather not talk about them. They confuse me.


Quote:
What about the second claim, that sabermetrics doesn't tell us anything about small sample sizes? This conclusion is also based on the work we've already done. If the conclusions of sabermetrics are strictly limited to their sample then just as the conclusions do not apply to future events, they do not apply to subsets of the sample. If strikeouts are only marginally worse than all other types of outs and this conclusion is borne out over a number of samples this gives us a very valuable insight, but it tells us absolutely nothing of the value of a single strikeout in a single game.


This is all grist for the realist's mill. The *reason* that sabermetrics don't directly address the small sample is that a single stat measures the causal powers of a single event type. That event type is not the sum total of properties instanced by certain individual event (i.e., game situation) Still, what you say about the strikeout isn't quite right. It tells us if the causal background of the strikeout is similar to the causal background of other strikeouts, then this strikout is marginarlly worse than some other out. The trouble is, the very concept of a representative causal background is of something unfocused. (It's a collage, it's gotta be).

The best way to focus the causal background is to be familiar with the abilities of the players playing in this game in this situation in other ways. There's no neat and mathematical way of doing this. But that's life. That's why doctors talk to patients.


Cheers,

Dan-o[/quote]


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PostPosted: Mon Oct 23, 2006 8:12 pm 
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You've given me a number of really interesting things to think about Dan-o16!

I am not intending to produce any counter argument to your questions and objections but I do have some questions.

1. Your point about being a skeptic about induction is well taken. I am skeptical about the justificatory basis for it, but I consider that an abstract question with little bearing on people getting by in the world. I would like to avoid committing myself to this skepticism, and I think I slipt into it by trying to dip my fingers into both inductive inference and frequency interpretations of probability simultaneously and sloppily at that.

2. One notion I am curious about is the true causal power of the player. I am not sure how to get at any such thing, if it even exists. Actually, to be clearer, I'm not really sure what it would consist in. Is it a causal power to effect a certain outcome a certain percentage of the time? Or is it an infinite series of powers to cause a certain outcome in the corresponding situation?

I think this is the most important topic you bring up. My skepticism rests on the inability to generate useful predictions for small samples and individual events. If I take your criticism correctly, you are placing the causal power of the player as an intermediate entity. While I was worried about using relative frequency to approximate future probabilities, you are claiming that we can use relative frequencies to estimate ability which helps us make sense of what these future probabilities are. It is a powerful point, and so I am keen to make sense of what the causal ability of the player would consist in and the appropriate use of relative frequency claims as evidence for the causal power of the player.

3. I think your point about the application of large sample sizes to small sample sizes being conditional is really interesting. My concern is that a relative frequency is still strictly limited to the sample its based upon, so the conditional would be of the form: "if this strikeout is part of the sample x then it is worth the same as any other out." Do you think that we can abstract away certain principles from a sample that all conclusions based on that sample apply to?

Thanks again for the great feedback! I haven't responded to all of your points, but that's not for lack of thought.

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PostPosted: Tue Oct 24, 2006 9:30 am 
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Maybe unrelated ... but you made me think about something, the impact of in-game psychology on players.

For example, if you are in a game with two mediocre pitchers (Steve Trachsel versus Jeff Suppan, for example), with both pitchers off to a good start and an improbable (yet possible) pitching duel emerges, should the statistics from that game be treated with the same weight as say a game where two aces square off, don't have it, and the teams beat up on each other's bullpens?

I am wondering if a metric can be applied to show a player's performance, relative to the game at hand. In other words, a scale that would show you that going 1-for-4 with an RBI in pitchers duel had as much (or more( of an impact as going 3-for-6 with a HR in a blowout.

One would think sample size, over time, would really flatten this out, but I am not so sure. I know win-shares somewhat covers this topic ... which in my eyes makes it a valuable measurement, but I think played psyhcology does have an impact on each game (not just per player, but as a group).

If the metric were relative to those of your teammates, you'd also get more accurate measurements on a players value ... everyone knows that plugging any player into the Yankee lineup is an instant stat boost, but where is that reflected accurately when you are comparing the career of Bernie Williams, who spent his entire career in the middle of a powerhouse lineup that literally psyched out opponents before games even started, to someone like Geoff Jenkins, who existed in almost the opposite scenario for the majority of his career. One has to wonder how nice Jenkin's numbers might look if he spent 15 years in the middle of the Yankee order, on a team that was always tearing through someone else's weak bullpen arms, in a lineup with less pressure knowing you were going to always get ABs with RISP, people in front and behind you would hit, etc.


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