Does reliever over-use lead to poor subsequent performance?

MGL

You say: only included those who had no starts in back-to-back years. First I split each pitcher included in the study (back-to-back years with no starts) into two groups: One, less than 70 innings in year X (and any number of innings in year X+1), and two, 70 or more innings in year X+1.

And then you say: Group I, the low innings pitchers, averaged 33.7 innings per pitcher in year X and 35.5 in year X+1. In group II, the high innings pitchers, each pitcher averaged 86.7 innings in year X and 64.9 iinnings n year X+1.

How can group 2 only average 64.9 innings in year x+1 if your criteria specifies that to fall in that group IP > 70

With all due respect to statistical genius and the baseball world's zeroing in on measuring reality through numbers, I wonder what has happened to the human arm. What happened to the prototype work horse?...the complete game?....the 300 strikeout season?

It seems strange that we have witnessed the rise of the reliever over the past 30 years and simultaneously witnessed the increase in personal trainers and medical breakthroughs. We live longer, physically healthy lives and yet arms are falling off like leaves. Something doesn't add up here. There was a controversial article about Mike Marshall printed on yahoo last season describing his Florida academy and alternative approach to pitching techniques. I say controversial because Marshall sees himself as the balck sheep of baseball because MLB clubs blow him off as a charlatan. I know nothing about pitching mechanics, but what do we lose by trying new methods?  

An interesting point etan. But in that vein, I have to wonder if in the past, our comparative ignorance to the health issues forced a natural selection of only those pitchers capable of handling such great workloads. Many great pitchers may have fallen by the wayside in college or the minors due to abuse. Also, I believe that career length, as measured by years has increased over time.

Perhaps it's not that pitchers today are weaker in some way, but that teams are choosing to use their pitcher career's worth of innings over a longer number of seasons, as doing so minimizes risk of catastrophic injury and helps maintain the highest level of effectiveness. I really don't know how many promising young careers in the 50's and 60's were ruined at age 27 or 28 after the strain of a few 280+ IP seasons. I'm sure there's been a study on this done by the guys at THT or BP.

John, thanks, you caught 2 "typos."  One, I meant "year X" as Tango says, and two, I meant "worse" rather than better.

When I first read the article quoting Fregosi, I thought, "Well, that is an easy thesis to test."  After working on it though, I realized that with all of the regression and selective sampling issues, it is not so easy, especially if we are looking for small effects.  Which is one reason why I "concluded" that there is no significant evidence that an "over-use" effect exists, rather than something stronger, like, "There is clearly no over-use effect."

Another thing that I thought was interesting was how many relievers do in fact pitch in one year and not in the subsequent year.  In fact, there were more innings or relievers (I can't remember which) who did NOT pitch in a subsequent year than who DID pitch.  That creates a huge (.2 or so in ERA) selective sampling issue if you want to look at things like aging or what I was looking at.  I don't think you have nearly the same magnitude of the "dop out" syndrome with starting pitchers.  The only starting pitchers who drop out from one year to the next, I think, are the truly awful ones who have not had a track record of being good, and the old ones who also probably pitched badly in their last year.

So, for pitching aging studies, I think you should only use starters (of course, then the results are really only limited to starters, although I am not sure that relievers should have significantly different aging patterns), or try and reconstruct what would happen the next year if the pitchers who dropped out were still pitching, or something like that.

1) We all know ERA is a rather poor indicator of pitcher performance, especially for relievers (due to inherited/bequeathed runners).  So why not use DERA or some other measure tied to the 3 true outcomes?

2) You could solve most (though not all) of your qualitative issues between the two groups by simply imposing a lower bound on IP for Group 1.  In 2007 there were 43 pitchers who had 70+ IP in relief and 44 who had between 60 and 69 2/3.    It's not critical that the 2 groups be that close in number, but it helps.  The difference in ERA between them is modest (3.27 vs. 3.46).  The biggest difference between the two is that the 70+ group contains only 6 full-time closers vs. 12 in the other group.

1) When you are doing a pitching study involving large groups of pitchers and your sample or samples is unbaised (with respect to parks, defense, opponents, etc.), ERA is just fine.  Who said that ERA is a rather poor indicator of performance?  That is not true.  There is more noise as compared to something like ERC, but in the long run, ERA will converge with any better short-term measure.  And the (old) notion that ERA is really bad for relievers is nonsense.  Again, because some relievers come in or leave in the middle of innings, there will be more noise, but when working with large unbiased samples of relievers, ERA is fine, and just as good as it is for starters. 

2) I'm not really sure what you are getting at here.

The_Real_Neal, thanks for the lessons in sabermetrics and statistics.

"Delete this and put up your new, corrected study, preferably with a little less of the 'Fregosi and his ilk' condescension."

I'll get right on it. 

In all seriousness, my wording in some of the sentences you quoted, and probably others from the article, were not so great.  However, anyone who has a mentality over the age of around 12 AND understands a bit about sabermetrics or statistics should understand exactly what I was saying, which was 100% correct.  You apparently do not fall into that category, although I am not certain which shortcoming you have, only that it is one or the other.

Snarkiness (yours and mine) aside, as I said, some of my words and sentences were awkward, such as "true mean," however it should have been fairly obvious what I meant.

When a pitcher posts an ERA (or any other sample of peformance) of X, "our estimate of his true mean ERA," and by that I mean his "true talent ERA" over that same time period, or what his ERA would be if he were to pitch an infinite number of innings (thus removing all sample error) with the same average talent he had during that sample time period, AND what we would expect his ERA to be in any other time period (assuming that his true talent has not changed due to age or anything else), is X regressed toward the mean (will fall between X and that mean) of the population of pitchers (we are sampling from a population) from which this pitcher comes, whether we define that population as all MLB pitchers, all relievers, all LH pitchers, all LH relievers, etc.  That also assumes that we know that there is SOME spread (variance) of true talent among the pitchers in the population.  If there is not, then the ERA in that "other time period" will be exactly equal to the population mean of course.

That is all I meant.   "A pitcher's true mean" makes no sense anyway.  (We usually refer to a pitcher's "true talent.")  If I stated that in the article, what I meant simply was "the mean of the population of which the pitcher is part."

All of the analyses and calculations were done based on the correct assumptions, regardless of whether I spoke (in the article) awkwardly or incorrectly, which I admit that I did.

An individual pitcher certainly has their own "true talent" which may or may not (probably not, again, assuming some spread of true talent among pitchers within that population) be equal to the population (of which the pitcher is part) mean.  We never know exactly what that true talent is.  Never.  We can only estimate it from the statistical record of samples of his performance as well as scouting and other observational and other data.  In the case of the article and most sabermetric research, we are only dealing with samples of statisitical data of course, in this case, ERA.

In any case, I am not arguing a controversial point or trying to defend a position of which you or I may be right (or wrong).  I am presenting uncontrovertible facts above.

Honestly, I am not sure whether you and I are on the same page (that you understand how regression toward the mean works with respect to baseball - sabermetric - analysis, such as that done in my article) and that you are simply not understanding the true meaning of some of my admittedly awkward words and sentences, or that you do not fully comprehend how regression toward the mean works in the context of these types of analyses.

In either case, I am quite sure that I have a full and correct grasp of the issues at hand.  I have been a professional sabermetrician for almost 20 years, I have an extensive background in statistics, and ALL of these issues have been vetted countless times among numerous other statisticians and sabermetricians.  If you would like, send me your address and I will send you a free copy of "The Book."

Oy Neal!  There is nothing to "try" (and tell me).  Although I am not a pure statistician by trade, I am a trained and experienced "applied statistics person."  At least you are persistent though!

You don't need to "clear up" anything with me.  I know exactly what I am doing (at least with respect to the statistics stuff in this article).  As I said, either you don't (know exactly what you are doing - no disrespect intended - just making a statement), or you are misunderstanding my words (and are apparently the only the one - that I know of at least - so my words cannot be THAT unclear).  Let me see if I can help YOU (to either understand the concept of regression towards the mean or to understand what I wrote).  Before you get all bent out of shape (if you haven't already), just be calm, and carefully (and with as much dispassion as possible) read the following:

"You should never use a mean of a population to determine regressing towards the mean in this fashion."

Without the "in this fashion" that is exactly what regression towards the mean IS.  When we sample a population more than once, the results of the first sampling will "regress" towards the mean of the population in subsequent samplings.  That is the DEFINITION of "regression towards the mean."  Of course, we often do not know what the mean of the population is.  In fact, we usually don't.  In these kinds of baseball analyses, we often have an idea or we can estimate it.  When we use the data to compute a regression equation, inherent in the equation will be the population mean, so we can infer that value from the equation. 

I don't know what you mean by "in this fashion" but regardless - you are misinterpeting my analysis, as evidenced by the next thing you wrote. 

"Lets say the study consisted of six pitchers."

OK we are sampling some pitcher performance and we get the following sample results.  No problem there.

"In year one the pitchers had the following ERA's and innings:

1. 2.5 ERA 80 innings

2. 3 , 80

3. 3.5, 80

4. 4.5, 40

5 5.0, 40

6. 5.5, 40

Now the mean ERA for all these pitchers (non-weighted) is four. "

 Still no problem there.

"So we are going to use that as your 'mean of the population' to regress to. "

Big problem there!  I don't know if you mean "we" as in "you" or as in "what you think I would do."  But that is not how regression toward the mean works.  "We", or at least "I" will not be using the SAMPLE mean of those 6 pitchers to regress ANYTHING towards. Those 6 pitchers are not a "population," therefore that is NOT the mean we regress towards.  "Regression towards the mean" involves taking a sample, which you did in your example. The sample is N pitchers with performance Y for X innings each, or whatever you want to call it.  It is actually 6 independent samples, but it doesn't really matter.

Keep in mind as you read this that am reading each section for the first time and commenting one section at a time.

I did read ahead that you are going to look at another year (the next year, which is fine) and that we should expect to see each pitcher or group of pitchers regress toward the mean.  That is absolutely correct.

The mean they would regress to is not necessarily known.  As I said, it is NOT the mean of the sample of pitchers or groups of pitchers.  That would make no sense.  It is the mean ERA of the ENTIRE population of pitchers that this sample is drawn from.  We don't know exactly what that is and you have no told us what "kind" of pitchers they are in your example.  The population could be relief pitchers, starters, LHP, RHP, etc.  What we usually do in baseball studies that require us to do a regression toward the mean is to simply narrow down as best as we can the population that we think a sample of players comes from, using pertinent, relevant, and material characteristics.  In my article/study I basically used the mean ERA of all exclusive (no starts) relievers who pitched for 2 or 3 years straight.  Sometimes it is not that important to "nail" the population that your sample comes from.  In baseball studies, it usually isn't. 

"The 80 inning group had a mean ERA of 3, and the 40 innings one of 5. According to the theory we should expect to see both groups ERA's regress towards the mean in the next year."

Again, that is exactly true, but not towrds the mean of this SAMPLE of pitchers.

OK, I lost you in the rest of the post so I cannot comment beyond this. 

Of course, any individual pitcher can and will have any ERA in year 2.  Each individual pitcher has a "true ERA" which as I said in my last post, is always unknown.   We "expect" any individual pitcher's ERA in ANY year, regardless of what it was in any other year to be exactly equal to his "true ERA" (duh).  However, since we don't know what is, we HAVE TO assume that all pitchers true ERA (and what we expect in any other year or time period) is somewhere between that which we see (in year 1 or whenever) and the mean of the population that we think the pitcher comes from.  Using your example, we will expect all of those pitchers to have an ERA in year 2 (assuming that their true talent has not changed singificantly of course, from year 1 to year 2) of somewhere between their year 1 ERA and the mean ERA of the population the come from.  Obviously for 6 pitchers, the chances of that occurring is not that great because of random fluctuation among only 6 pitchers.  However, if each pitcher were a really large group of pitchers (with each GROUP having an average ERA of 2.5, 3.5, etc.), then it is almost certain (depending on how many pitchers there are in each group) that all 6 groups will show an average ERA of somewhere between what they showed in year 1 and their population mean.

I sort of take back what I said about not using the mean of all 6 pitchers as our mean to regress to.  If that is all we have (we don't know the mean ERA of ALL pitchers or all reliever, or whatever), then the (weighted by innings) average ERA of all 6 pitchers IS in fact an unbiased estimate of the population mean AND we can in fact use it as the mean that we regress to in year 2.  That is assuming that these 6 pitchers are randomly (or somewhat randomly in practice) sampled from a certain population.  Again, because we only have 6 pitchers, that unbiased estimate is going to have a large uncertainty as well and could easily be off by quite a lot (e.g. even though it is 4.00, these pitchers could easily come from a population of pitchers with a mean ERA of 3.00, in which case their year 2 ERA's will tend to regress toward that 3.00 rather than 4.00, and we won't know it.

Other than that, I really don't know what you are trying to say.  There are probably many mistakes in The Book, and I did not write the whole thng, but the way we handle regression toward the mean (which comes up a lot in sabermetric research) and the way I discuss and handle it in the article AIN'T one of them! Trust me on that.

If you write me at mglcardinals@yahoo.com and give me your brother's or your address, I'll be happy to send a book. 

I've just skimmed these latter comments, but I have to say that I think Real_Neal is correct. MGL, your approach appears to suggest that *all* pitchers should regress towards ONE common mean, which simply doesn't hold up to scrutiny; as mentioned by Real_Neal, this would imply that Greg Maddux has simply been "lucky" to avoid this "regression" for his entire career. In fact, a much more reasonable explanation is that his "individual mean" is drawn from a *population* of pitcher means (talent levels), and his particularly talent level is in the tail of *that* distribution.

 More to come later, hopefully.

"I (and I think Real_Neal) disagree with the bolded part of the statement. A "bad year" for Johan Santana may still be better than league average for starting pitchers, so wouldn't we expect him, in subsequent years, to regress to his individual mean rather than to league average? "

Nothing to disagree with.  Honestly.  What I wrote is exactly correct.  You guys don't know enough about statistics (with all due respect) to be debating this.  You are mixing up terms, for one thing (among many mistakes).

No one "regresses to their individual mean."  No one has "an individual mean."  If you mean his "true talent," (I think you do), or what his ERA would be if he pitches an infinite number of innings, then in subsequent years, we "expect" him (of course, he probably won't, but that is our best estimate) to post an ERA EXACTLY what his true ERA (I think you call this his "individual mean" or something like that) is.  But of course, we NEVER know a pitcher's true mean.  We can only estimate it from his sample performance, which is the whole point of these types of analyses and the whole goal in forecasting players.  If you read up a little about sabermetrics and how regression to the mean and other statistical techniques are incorporated into it, rather than shooting off your less-than-fully-informed mouths (again, with all due respect - I'm sure there are plenty of things you know better than I - I am somewhat of an "idiot savant" with respect to baseball), you would KNOW that our best estimate of a pitcher's true talent (or individual mean or whatever you call it) is his sample performance regressed toward the mean of a population of players he comes from (whatever and however we determine that to be - absent any other information other than he is an MLB pitcher, we use the mean ERA for all MLB pitchers, perhaps from a certain era, if we know when this pitcher pitched).

You could do a regression (not to be confused with "regression" as in "regression to the mean" although they are related) of year 2 ERA on year 1 ERA and IP, and it might yield some useful information.  I would have to think about that and/or do it (which I won't because I don't have the time) and see what comes up.  The problem with regressions of course, in these types of analyses, is that they do not necessarily address cause/effect, only relationships, as you well know.

You are welcome to do that and see what you come up with.  If you are a student at a University or high school (I assume the former), you might get some extra credit!

Cyberwolf, in your last post about Maddux, etc., you are simply not understanding what we mean in these kinds of analyses, and I don't think you fully understand regression toward (or towards) the mean in general.  I suggest you look around the web for some primers on sabermetrics and statistics, particularly with respect toward regression toward the mean and similar statistical concepts.  There is a difference between asking questions about something which you know a little about, but not enough to nearly be considered as an expert, and "arguing" with people who are genuinely experts in the field.  David and I are truly experts in the field (sabermetrics and statistics), although neither one of us are "expert" statisticians (though I can really only speak for myself).  Not to say that you can't add to the discussion.  You both seem like intelligent, if not obstinate, fellows.  It would be like if I took some courses on cosmology or astrophysics and then thought I could correct Stephen Hawking.  Not that I am comparing Hawking to myself.  He is way smarter than I (though he could not stand up to me in sabermetrics of course - I assume).

Santana and Papelbon will of course "most likely" pitch to their own true talent (ERA or whatever) next year.  But since we don't know what that is, our best estimate (that is where all these projections come from!) is their prior ERA regressed toward the mean of the population we think they come from.  That is how it works.  Actually not too complicated.

You can test this quite easly!  Remember that when you test things like this, you take lots of similar players (including similar in the sense of what you want to test - e.g. ERA, IP, etc.) in the past and then look at what they did in subsequent years.  For example, look at all pitchers (you can limit it to relievers if you want or RH relievers, and/or of a certain age, or however you want to classigy your pitcher in question, as long as you don't classify him by the stat - like ERA - that you are testing) in history who had an ERA of less than 2 in their first 2 years (or any 2 years) and then look at their ERA in the next (or any other) year. That should approximately equal your projection for Papelbom.

If you do that you will find that all similar pitchers will in fact have an ERA of those 2 years regressed toward the mean of all simiular pitchers, similar pitchers pretty much being young RH relievers (NOT pitchers who posted low ERA's in their first 2 years or any 2 years!).

In the case of Papelbon, you could even use as your mean, all closers, although that is a bit problematic as one reason he is a closer is BECAUSE of his great first 2 years.  Regardless of what you use, you will find that he (and all other similar pitchers in history) will likely post an ERA in the subsequent year of his prior years' ERA (say, 1.7), regressed toward something like 3.50 (the mean of the population of pitchers he comes from - NOT pitchers who are great pitchers - that is what we are trying to find out - to what extent he is likely to be a great pitcher!  We don't KNOW that he is a great pitcher - there is a finite chance that, albeit very small, that he is an average pitcher who got REALLY lucky or even a better than 1.7 ERA pitchers who got a little unlucky, etc., although we don't think a pitcher like that exists, so that won't be part of the equation).

How much we regress the 1.7 toward the 3.5 (or whatever that mean is) depends on two things:  One, how many innings of data we are using for his sample performance (the more IP, the less we regress, because our sample error on that 1.8 ERA would be less), and two, our estimate or knowledge (which is never perfect, but we can estimate it with a decent degree of reliability) of the spread (variace) of true talent in the population of pitchers we think he comes from (i.e. how many "true" 1.80 pitchers there are - probably close to zero - how many true 1.90, true 2.00, true 3.00, true 4.00, etc.).

Read, listen, stop arguing, and learn!  I try to tell my son this all the time.

If you have the mean ERA for one pitcher, why would you regress any one season's ERA toward's that mean?  You'd just use his mean (or a weighted mean).

 The ARod example is ridiculous.

 You regress an individual pitcher's ERA towards the population he's a part of, which is MLB pitchers.  The more data you have, the less you regress.  We're not projecting Johan Santana to post a 4.50 ERA next year because that's MLB average.  He only gets regressed a touch, because there's a very small likelihood he's been extremely lucky over the past four seasons.  If you had evidence that a certain set of MLB pitchers performs differently from MLB pitchers overall (say, knuckleballers), then it would make sense to regress pitcher is that group towards the group mean.  If we had scouting data on a player, it might make sense to regress past performance towards the mean of players with similar scouting reports.

Now that I've got my head on straight about the utility of regression to the mean, I've still got a bit of an issue with the methodology of this study, with the main issue being the choice of ERA to regress towards.

Your analysis assumes that all relievers will regress towards 3.86, a number arrived at by averaging the performance of all relievers in the study. However, in your introduction, you point out (correctly, I believe), that relievers who pitched 70+ innings in year X may have a "population" ERA lower than those who pitched < 70 innings.  If this were the case, then wouldn't you want to regress them towards this mean (say, 3.5) than towards 3.86? Despite the fact that you consider "comparable" pitchers in year X-1, I would argue that they are *not* comparable for the purposes of projecting future performance by virtue of the fact that one group pitched 70+ innings and the other <70, which likely correlates strongly with pitcher skill.

In other words, it seems reasonable that in your "experiment", group I pitchers are those regarded as having relatively little talent in year X-1 and hence are not used extenstively in year X. Group II pitchers, on the other hand, are regarded as talented/promising, and are given more opportunities not only because of their better-than-average performance, but because they are thought to be performing up to their actual talent level. If this is the case, then Group I pitchers constitute a sample from the population of "journeyman" pitchers (say, with a true population ERA of 4.0), but Group II constitute a sample from the population of "better-than-average" pitchers (say, with a true population ERA of 3.6). 

So, with this in mind, does regressing towards 3.86 for both groups still make sense? I'd be interested in hearing an explanation. 

Thanks for the help, Guy and SkyKing.  Another example for cyber is if you take a coin out of your pocket and flip it 10 times and come up with 6 heads and 4 tails or 6 tails and 4 heads (which is fairly likely of course).  That is an unbiased estimate of the the coin's true heads/tails ratio, yet you would NOT use that to estimate the coin's true ratio and you would NOT predict that to be the most likely result ifyou flipped it another 10 times.  Why is that?

Because, as Guy explained, you have other information which makes it a Bayesian probability problem (look up "Bayesian probability" on the web).  The information you have is multi-fold.  One, you can see that the coin has two sides that appear to be equally likely to land on, two, you know from past experience that coins tend not to be biased, etc.  Quantitatively, you KNOW that pretty much all coins are fair and that the mean heads/tail ratio for all coins is around 1.

So in estimating the true ratio for this particular coin that you flipped 10 times, you would actually regress the 6/4 ratio that you got (your sample result) toward mean of the population (of all coins or even all coins that might be in your pocket), which is around .5 heads and .5 tails (you can also establish a good estimate of that population mean by flipping lots of coins lots of times).

How much do you regress?  Remember, we said that how much you regress a sample result depends on two things:  One the sample size of your sample result (in this case, 10) AND the variance (apread) of true heads/tails ratio in the population (in this case, zero).  If the variance is zero in the population, as it is in this case, then the regression is exactly 100%.

Keep in mind that if we are sampling only one element from the population (one coin or one pitcher) regression occurs only if we have "other" information, which we do with pitchers and coins (this "other" information is called "a priori" probabilities in Bayesian terms).  If we have no other information (a priori probabilities), then yes, that one element's result becomes our best estimate for that population and for that element itself. 

Now, if we change the coin flipping  scenario a little, we can create a situation which is exactly like a pitcher.  Let's say that we do in fact have some coins, even all coins, that are biased.  Let's say that all coins are biased and that the true heads/tails ratio of coins vary from coin to coin with a mean of 1 (.5 heads and .5 tails).  So that is the mean of the population of coins.  However, this time we have some coins that actually are .6/.4 heads/tails, .4/.6 heads/tails, .7/.3, etc.   IOW, if we flipped on of those .6/.4 coins an infinite number of times, it would land on heads 60% of the time.

Let's also say that the distribution of true heads/tails ratio is approx. normal, with a mean and median of .5.

Now what happens if we flip a coin 10 times chosen randomly from this population and come up with 8 head and 2 tails.  You might be tempted to say that our estimate of its true heads/tails ratio is 8/2, since there are indeed some coins in our population that are true 8/2 coins.  No!  Why is that?  Because in a normal (or roughly normal, or at least one where that around the mean is overrepresented) distribution there are many more coins that are near true .5/.5 than .8/.2.  Mathematically (and this can be easily cacluated using Bayesian probability and the properties of normal distributions, namely z scores) it is much more likely that we picked a .5, .45. .4, etc. (close to .5) coin and just got a little lucky or unlucky (with our 8/2 flips) than we picked a true .8/.2 coin and got what was most likely in 10 flips.  Why is that?  Because there are many more close to fair coins in our distribution to chose from and it is not all that hard to get 8/2 in 10 flips with any coin. 

Now, mathematically, if we use Bayes Theorem and all the einformation we have, we can actually estimate the true head/tails ratio of that coin by regressing the 8/2 that we got in 10 flips, or .8 heads, toward the mean of all coins that we drew this coin from, which is .5.  How much we regress depends on 2 things:  One, the 10 flips.  Why is that?  Because, as I said, it is not that hard to get 8/2 in 10 flips whether I have a true .5 coin or a true .8 coin.  If I got 80/20 in 100 flips it would be a lot harder to do that with a .5 coin than with a .8 coin, so there would be a much greater chance that I happened to pick a .8 coin even though there were many more .5 (and close to that) coins to choose from in my population of coins.

The second thing that affects how much we regress is the variance in head/tails ratio in my population of coins/  Why is that?  Because if my variance is small, then there are WAY more coins near .5 to choose from so the chances that I have a near .5 coin and just got 8/2 as a fluctuation is WAY larger than the chances that I chose a true .8 coin (or true .9, .85, .78, etc.) simply because  there were hardly any of those coins in my population.

But, the larger the variance of true heads/tails ratios among my coins, the more of those very unfair coins there are (as a percentage of the population), so there is a much better chance that I actually chose a very biased coin and that is why I got a .8/.2 sample result (even though it is STILL more likely that I chose a coin closer to .5 than .8.

This is EXACTLY the same scenario we have with pitchers.  We have a population of pitchers (coins) with a mean ERA of whatever (say, 4.50), which is the same as the coins' .5.  We have a distribution of true ERA's among that population of pitchers with a variance of whatever.  So when we randomly select a pitcher from that population, no matter what ERA we get in any period of time it is always more likely that we chose a pitcher who has a true ERA closer to the population mean that his own sample ERA, simply because our assumtion is that there are many more pitchers with a true ERA around average than above or below average, which is a true assumption, more or less. 

After all the flamewars you've gotten back to the point I tried to make days ago.  Yes, you have to regress to the mean.  But it's not just a question of how far you regress (which depends upon the amount of data you have on each individual pitcher) but also what population mean you regress toward.  If you know nothing about a pitcher but his 2007 ERA you have no choice but to regress to the MLB average ERA.  But if you know he throws 95+ you will almost certainly do better by using the mean of the population of pitchers throwing 95+ than you will with the overall population. And if you know he throws 95+ AND he's a lefty you will probably do even better by looking only at that population mean. 

Of course, for each characteristic you add you cut down the size of the population.  Before long you will find yourself with nobody left but the pitcher you started with.  So it is a constant balancing act: you need enough data to calculate a reliable mean for the population as a whole while at the same time excluding pitchers that having little in common with the one you're interested in except their MLB employment status.

In this particular case all we really know is that we have a group of pitchers who may (or may not) have been overworked by throwing 70+ innings.  We now need a control group of pitchers who are similar to them but who did not throw as much to create the population.  Clearly we can't use all MLB pitchers or even all relievers because there are major qualitative differences between them.  The combined ERA for our 70+ group was 3.27.  The combined ERA for all relievers (20+ innings) was 4.22.  The combined ERA for all those between 20 and 70 innings was 4.40. 

Now you have to ask yourself:  what is the likelihood that an ERA differential of 1.13 was caused by "luck", defense or other factors having nothing to do with the true talent of the pitchers?  Simple intuition tells us the probability is very low.  Sometimes intuition is wrong.  But in this case statistics strongly supports us in rejecting the null hypothesis.

So now we need to find a population larger than our 70+ group which includes them and which does not appear to be significantly different in true talent.  That might be very hard to do.  Fortunately in this case it's quite easy.  Here are the ERA's by IP groups.

70-94 3.27

60-69 3.46

50-59 4.26

40-49 4.34

30-39 4.91

20-29 5.05

Aha!  We have a pattern.  Pitchers who pitch a lot do better than those who don't.  No surprise there.  But what was surprising (at least to me) is that