Hey Bill, in a pitcher's Game Score, why are unearned runs factored at all? Anticipating your answer isn't "whoops", how would you change the definition of an unearned run to more accurately reflect the pitcher's culpability?

                Well, you’re on the edge of something really interesting there, which is the difference between linear and non-linear logic.    Linear Logic, or what I like to call Asshole Logic, insists that one’s initial assumptions are absolutely true and should be followed through with complete fidelity.   It’s a black and white world; the pitcher is either responsible for the run, or he is not responsible for the run.   He can’t be sort of responsible for the run, which we represent mathematically as half responsible; either he is, or he ain’t. Since in the real world one’s initial assumptions are almost never entirely true, the history of sabermetrics—and the history of every other field of knowledge—is replete with examples of people tripping and falling into a ditch based on Linear Logic.    Regarding Game Scores, the question that people used to hammer me with was the "illogic" of treating a strikeout differently from another out.   "If a pitcher gets an out," stat lawyers would demand to know, "what difference does it make whether it’s a strikeout or a ground ball?  Why should a strikeout pitcher be favored over any other type of pitcher?"

                Eventually, because of Voros McCracken, people came to understand that, of course, a strikeout is NOT the same as any other out, that whereas a strikeout is an absolute out, a ball in play becoming an out is largely a matter of luck.   Of course, after Voros people began to insist that balls in play becoming outs was ENTIRELY luck, and based on that one can derive a pitcher’s "true" effectiveness based on the "three true outcomes", which isn’t true, either; it is merely Asshole logic beginning with a different assumption.    Believing that all balls in play are the same except for luck is not an absolutely true assumption; it is merely a better starting point than the "old" assumption.

Anyway, I have always used non-linear logic, and it always annoys about 40% of my audience.   In the recent article on Sandy Koufax Seasons (Climbing the Stairway to Sandy Koufax), I created a "compromise ERA" which is half-way between a pitcher’s "natural" ERA and his ERA adjusted to the league.   In sabermetrics we use the assumption that league Earned Run Averages rise and fall based on the conditions of the game, that if the league ERA is 4.00 one year and 3.50 the next, this is because the conditions of the game have changed to be more favorable to the pitcher, therefore that a 3.60 ERA one year is equivalent to a 3.15 ERA the next.    But it is not an absolute truth that changes in the league ERA occur because of changes in the conditions of the game; it is merely a working assumption.    Sometimes the league ERA goes down because there are more good pitchers in the league and fewer good hitters; that is probably ALMOST as true, on average, as the other assumption.    If you have to see it one way or the other, the "conditions of the game" argument makes a much better platform for statistical analysis and leads you to fewer false conclusions, but it is not an absolute truth; it is merely a working assumption.   To assume that it’s half one and half the other upsets the literal minded in the audience, but it is probably closer to the truth than the linear-logic assumption.

                In the 1960s and 1970s the United States Supreme Court relied absolutely on Asshole Logic in most areas, with devastating consequences for American liberals and progressives, and for the nation as a whole.    Trials were supposed to follow certain rules (still are, of course), but until the Rehnquist era, the outcome of trials would be reversed because of incredibly picayune violations of the rules.   There were instances of murder convictions being thrown out because of innocuous typos in the jury instructions or typos in a search warrant leading to the discovery of evidence.   It became so commonplace for convictions to be thrown out that there were cases of murderers being convicted of the same crime as many as seven times, each of the first six convictions being vacated on appeal.    The nation’s murder rate tripled in a little more than a decade, which, more than any other one thing, brought an end to the liberal era, and brought Ronald Reagan into office.   Also, it wasn’t good for the people who were murdered. 

                This grew from the desire to ensure the accused a fair trial.    But the problem is, the way to ensure a fair trial is to insist on a fair trial; it is not to insist that every rule be followed with absolute fidelity.    Over time, more and more potentially fatal flaws (for a trial) were fed into the mix, so that the pathway to a valid trial became narrower and narrower.   It was a zero tolerance policy, before the phrase was invented.   Eventually, the pathway to a fair trial resembled a hoarder’s trail between the back porch and the guest bedroom.   The Rehnquist court, under the leadership of Rehnquist and Sandra Day O’Connor, developed the concept of "Harmless Error" (Earll v. State of Wyoming, 1987), which allows a court to look at a trial the way a reasonable person would look at it, rather than the way an Asshole would look at it.   Of course, as in the example of sabermetrics pre- and post-Voros, Assholes never go away; they merely start using different assumptions.    Once we entered the era of the "Harmless Error", judges began insisting that all kinds of things were harmless error which quite obviously were NOT harmless error, but which fit within the absolutist categories used to define the term.   In other areas as well, the Supreme Court began to rely on balancing tests, rather than on absolute principles, which is all to the good, since all real-world decisions require the balancing of costs and benefits.

                Linear logic asserts that numbers never lie.   In reality, numbers constantly mislead us.   Every statistical survey is planted with bombs, in the form of assumptions that are only partially true.   It is the job of serious men to find those bombs and dismantle them before they go off.

                Since linear logic relies on absolute faith in assumptions which everyone knows are not absolutely true, it frequently implores us to pretend that we don’t understand things that, in fact, we understand perfectly well.  Frank Jung, an assistant attorney general in the state of Missouri, once argued in Federal court that the defendant Joseph Amrine should be executed, even if he was innocent in fact—an excellent illustration, I think, of the concept of Asshole logic.  For the process to work we have to respect the process; therefore, if the process sentences an innocent man to death, we have to execute him, even though we may know that he is innocent.

So the real answer to the question, why should un-earned runs be included in a pitcher’s Game Score, is, "Do you want to be an asshole, or do you want to be a reasonable person?"   Because if you are a reasonable person, then you know perfectly well why un-earned runs are included in the Game Score, partially charged against the pitcher, and you know perfectly well that this does not require a change in the rules defining an un-earned run.   Un-earned runs score in part because of the mistakes of pitchers, and in part because of the mistakes of fielders.   Everybody who isn’t playing word games with you understands that perfectly well.

While I am Here

Some of you are about to launch into the familiar explanation of why it wasn’t liberal judges who exploded the crime rate; it was the Baby Boom; in fact, I predict that somebody will have already posted that argument below, having rushed to do so without reading this far into the article.   I have wanted for 25 years to find the space and time to rebut this argument, so I think I’ll pick it up here, noting first that it actually wasn’t "liberal" judges who created the problem; it was judges applying Linear Logic, and Linear Logic is common both among liberals and conservatives.  The liberals happened to be running the show at the time that it became an issue.

The automatic liberal denial of the fact that Supreme Court fiats fed the explosion in crime rates in the 1960s and 1970s is that it wasn’t the justice system, it was an explosion in the numbers of young men in the age groups which are inclined to commit crimes.   Most crimes—goes the logic—most crimes are committed by young men between the ages of 18 and 32; sometimes the age ranges are 16 to 34, 16 to 25, 18 to 26. …whatever.   Most crimes are committed by young men more under the sway of their hormones than under the influence of their elders.    The Baby Boom, beginning in 1946, led to a dramatic increase in the number of young men within that age cadre, therefore to an increase in the crime rate.   Lib’ral judges had nothing to do with it.

This is an empty argument.    It doesn’t work as a statistical analysis, and it doesn’t work as a logical explanation independent of the numbers, but we’re here to deal with the math.  Let’s start with the number of males born in the United States each year from 1929 to 1959, which are the years potentially relevant to what will follow.    It is difficult to find reliable information about how many males were born in the US in each year; that is, it is easy to find information, but the information you find one place is different from the information reliably reported somewhere else.   (About.com cites the Statistical Abstract of the United States as their source, but presents data at variance with the actual source.)    But this is my best effort to find the number of persons born in the United States each year, 1929 to 1959. 

                As you can see, the numbers decreased during the Great Depression, and increased sharply in the late 1940s.  Let us assume that one-half of those are males—an assumption which, if it is not precise, is also not reasonably likely to cause our calculation efforts to fail.   The number of males born each year, then, would be as follows:

                Let us refer to males aged 18 to 34 as the Crime Prone Population, or the CPP for those of you who like acronyms and/or 3^rd-grade barnyard humor.   We can sum up the Crime Prone Population beginning in 1963 by summing up the number of males born between 1929 and 1945, then moving forward one year at a time.   This is the Crime Prone Population, by year:

                Obviously these are not perfect counts.   The number of males in the Crime Prone Population is altered by deaths and immigration, and proportionally altered by disease, epidemics, wars, economic conditions and other factors.   Altered, but not meaningfully altered.  If you take World War II deaths into account. . ..well

                a)  almost no one born in the US in 1929 or later was killed in World War II,

                b)  SOME people are killed in wars in every generation, and

                c)  those numbers just aren’t meaningful in the context of this discussion.   

                We’ll talk briefly about immigration later in the article.   Anyway, let’s look at the murder totals in the relevant years:

                The Crime Prone Population increased by 30% in 11 years.   Murders increased by 140%.   A 30% increase in the Crime Prone Population should not result in a 140% increase in murders, nor has it generally done so when there have been similar population booms in the past.    But the real problem is much worse than that.

                First, almost all crimes, other than murder, increased in those years by much more than the murder rate.    Rape and robbery increased by more than 200%; burglary, by 180%. 

Second, this comparison assumes that the Crime Prone Population is responsible for ALL of the crimes.    In reality, of course, many crimes are committed by women, by boys younger than 18, and by men older than 34.   A 30% increase in the Crime Prone Population does not result in a 30% increase in crimes.

And third, these years—1963 to 1974—express the ability of the increase in the Crime Prone Population to explain the increase in the crime rate near its maximum point.   The more you expand the time line, the less adequate the increase in the Crime Prone Population becomes to explain the increases in the crime rate. 

                How much of an increase WOULD it explain?    It depends on what assumptions one makes about the level of toxicity in the Crime Prone Population.    But if we assume that the CPP is three times more likely to commit a crime than the rest of the population, then the total exposure to crime (TExC) would be:

                3 * CPP  + (Total Population minus CPP)  =  TExC

                With the data given above, the expected increase in crimes between 1963 and 1974 would be 18%--assuming that the Crime Prone Population is ages 18 to 34, assuming that a person in the CPP is three times as likely to commit a crime as a person not in the CPP.

                Of course, we get a different number if we consider the Crime Prone Population as 17 to 26, or 19 to 24, or whatever.  Different, but not much different; the highest expected increase in the crime rate between 1963 and 1974 I could find, using different assumptions about the boundaries of the CPP,  was 19%.    Let’s say it is 20%.   It doesn’t begin to explain the actual increases in crime in those years.

                It’s not a real explanation; it’s not an explanation that works at all when you actually look at the data.    What it is is, it’s a cover.   It’s a dodge.  It is something the liberal can say to avoid accepting responsibility for the explosion of crime between the early 1960s and the late 1970s, which works as long as nobody really looks.   Everybody knows there was a big increase in the birth rate in the late 1940s, and it is generally agreed that young males commit a disproportionate share of crimes.    If you put those two together, it sounds like it makes sense—as long as nobody checks the math. 

                I dropped the immigration issue early in this article—but immigration won’t help you.    If you factor in immigration in the 1960s you have to factor in immigration in the 1990s.   In the 1990s there were much higher rates of immigration (twice as high), combined with only slightly lower birth rates in the relevant years—yet crime rates dropped very sharply in the 1990s.

                Look, this is what really happened, to spike the crime rate in those years, 1960 to 1980.     The police got behind in their work.    There is a criminal population; there has always been a criminal population, very probably there will always be a criminal population.    The criminal population thrives and grows when the police don’t keep up on their homework.

                It wasn’t a prohibitive problem, that the Crime Prone Population was growing.   It was a manageable concern.   The increase in the Crime Prone Population logically required that the size of police forces be increased, and prison populations be increased, proportional to the increase in the CPP—20% to 30%.   Since the population as a whole was also growing—not as rapidly as the CPP, but it was growing—to have increased these things by 20 or 30% would not have been a major undertaking.

                But they were always working behind the problem, always trying to deal with what happened last year.   The ACTUAL criminal population grew, disproportionate to the increase in the crime PRONE population, because insufficient efforts were being made to prevent crime.

                Murder increased more slowly than rape or robbery because, as it became more and more difficult to convict anyone of a crime, resources were focused on the most serious crimes, allowing the crimes on the second level of seriousness to go largely unpunished.    Of course, if you allow shoplifting to flourish it leads to increases in larceny; if larceny is not adequately policed it leads to increases in burglary.    That’s working behind the problem—trying to focus on the most serious crimes because you no longer have the resources to deal with what happens on a day to day basis.  

                In this environment, the United States Supreme Court issued a long, long series of rulings that made it more difficult to successfully prosecute a criminal.   In the words of every prosecutor working in those years, they tied the hands of the police.   These rulings made the problem of working from behind dramatically worse. 

                Did the court do this because they were Liberal?   Yes and No.   It was, of course, a famously liberal court.    It was actually more because they were Assholes than because they were Liberals.  They saw the world as they did because they were Liberal, but also because the law has historically relied on Linear Logic, and they had been trained since law school to think like a train track.   Like Assholes from time out of memory, they stumbled along, relying absolutely on their assumptions, without looking at where this train was going. 

                And where it led us was to tens of thousands of completely unnecessary murders, leading to the Law and Order campaigns of Ronald Reagan and many others.    In a sense we have never really dealt with it; we have never honestly faced the fact that, in this country and in my lifetime, we allowed tens of thousands of people to be needlessly murdered.   There was a holocaust in our country, and we never talk about it.   Liberals dealt with it by denial and obfuscation; Conservatives dealt with it with it by seizing the opportunity that it created for them.  History is dealing with it as it deals with everything, by piling years upon the top of it until it no longer matters.