Linear Logic and a Horse’s Patooty

April 29, 2014

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.   ( 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 3rd-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:



United States Murders 


























                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.


COMMENTS (41 Comments, most recent shown first)

Ask ANY prison warden what his inmates have in common. (I have.)

Grew up without dads. And so weren't shown the restrained use of strength.

5:28 PM May 6th
Brian, i would never argue that there are plenty of possible confounds. BUT, the numbers in the graph are drawn from DoJ sources (the link I put there has those sources). It may be that they are comparing apples to oranges, but the rate holds relatively constant until the introduction Anti-Drug Abuse Act, and the graphic was obviously not generated to address Bill's assertion (as it came first). As I noted, Bill's assertion may prove true, but right now the evidence is aligned against it, if you can find confounds that support it I would love to hear it.

I might add that the graphic brings up another question, if successfully prosecuting people were the key to reducing crime, wouldn't the massive increase in incarcerations have pushed rates of things back down below the 1963 levels?? We have the highest incarceration rate in the world (USA! USA!), why do we still have high crime rates (compared to many other western countries)?
4:34 PM May 6th
When looking at crime rate stats other than homicides, remember that there are all sorts of ways they can be misleading. Statutes can be changed from misdemeanors to felonies, and vice-versa. That alone can increase or decrease the rate of felonies. Are residential burglaries violent crimes? Messing with that interpretation can mess with the rates of violent crimes. And there are cases when a police chief will drastically change arrest policies to make it look like they have reduced crime rates.

Also, in terms of incarceration rates. Make sure you know-is the study defining "incarceration" or "custody"? Some studies referring to "custody" have included those in the custody of parole or probation. Those people are most certainly not incarcerated for the purposes of crime and punishment discussions.

11:31 AM May 6th
Other folks have noted that there have been many explanations for the rise and fall of crime rate statistics (the Freakonomics people famously suggested the connection between legalized abortion and the drop in crime rates that started in the 90s). I would tend to agree that the problem is very complex and does not follow from any single cause.

That having been said, as I understand Bill's argument, he is suggesting that crime became tougher to prosecute in the period leading up to the spike in rates. Which made me go look for evidence of this, and I am not sure that the assertion holds up. For example, check out this graph on incarceration rates in the US by year:

Ignore the massive rise in incarceration starting in the mid 70s (which may have been a response to the rise in crime). Prior to 1975 or so the rate of incarceration held roughly the same (with a small spike towards the end of the Depression). If crime was growing progressively harder to prosecute, I would contend that you would expect to see a drop in incarceration rate. Of course, a more complex answer is possible. Perhaps post WWII people are becoming more crime prone and the relative stagnation of the incarceration rate would then support Bill's assertion. But without any evidence of such a shift, I think the notion of the Supreme Court and others making it harder to prosecute crime is speculative at best.

3:07 PM May 5th
"So, IMO, it's very important for laws to be revisited every once in a while, just to test the working hypothesis and make sure it hasn't gotten way out of whack with reality.

Right now, the only way American law has to test laws is to appeal them to the Supreme Court"

Not true at all. Laws can be passed at the local, state and national levels. Laws can be repealed at those levels as well. Town charters, state constitutions and the US Constitution all have an amendment process.

Courts are the worst place to go to determine whether a law is "working" or not. That's not the job of the courts. Their role is supposed be to interpret what the law means and whether it violates a law from a controlling authority. Whether a state law, for instance, violates its own constitution, federal statutory law or the US Constitution.

Local hearings, state legislative hearings, Congressional hearings -yes lobbyists too-they all provide information as to whether a law is working. The media is supposed to provide information on that as well. Even constitutuents contacting their legislator.Then the ultimate "hearing" to decide how we view the information that has been provided is the election. And that's all elections -local, state, national. Legislative and executive branch.

That process doesn't always produce the best result, and people get frustrated, but it is terrible precedent to bypass all that and have the courts change laws as they see fit.
2:48 PM May 3rd
Two things:

1. Some "earned" runs are almost unearned-- a failed double play doesn't show up as an error, so runs that follow are earned, even if they would not have scored had a double play been completed and the inning ended.

2. It seems to me that statistics show that people who commit serious crimes don't consider the probability of conviction when deciding whether or not to commit the crime. Either they're determined enough to do it, or they think they'll never get caught. It's hard to imagine that someone after Miranda said to himself "Maybe they'll interrogate me without warning me of my right to remain silent, so I can get away with this murder."

1:17 PM May 3rd
Darn Bill, talk about non-liner logic. An unearned runs question turns into a conservative diatribe on the Warren Supreme Court.

But since you mentioned it, I cannot make the connection between the so called “liberal” Supreme Court rulings and the increase of violence. Yes, it may have let some guilty people off the hook but enough to cause a 140% increase in murders with only a 30% increase in population.

Police and prosecutors saying they had their hands tied is old and worn out. Does that mean they could not get their evidence the old fashioned way, by beating a confession out of their suspects?

10:28 AM May 3rd
(the size of the Supreme Court has never changed, in spite of a vast increase in the population at large)

1789: 6
1807: 7
1837: 9
1863: 10
1866: 9
1867: 8
1869: 9

Size of SCOTUS really isn't that big of a problem. Advancements in technology and travel almost certainly make their jobs far easier. They actually chose to hear fewer cases now than in the past, and certainly could work more if they changed their own rules.

On the flip side... a massive number of cases appealed to them are b.s. appeals on things properly decided below, or reasonable cases that are similar to ones they're taking up (i.e. will be decided by a ruling on another case).

They certainly could work harder and take up more cases. But there's a load of nonsense in the courts.
2:28 PM May 2nd
Brock Hanke
I probably agree with Bill on this, although I use different language. My contention is that a law - ANY law - is a working hypothesis. It may be the best working hypothesis available given the information known at the time, but still, it's a working assumption, not a hard immutable fact. Believing that laws are immutable (essentially, being what Bill calls an Asshole) will, over time, cause the laws to get wildly out of sync with the living conditions of your populace. So, IMO, it's very important for laws to be revisited every once in a while, just to test the working hypothesis and make sure it hasn't gotten way out of whack with reality.

Right now, the only way American law has to test laws is to appeal them to the Supreme Court. Since there are far, far too many laws for the Supreme Court to review them all (the size of the Supreme Court has never changed, in spite of a vast increase in the population at large), the ones that the Court actually takes on are either very important laws, or laws that have gotten REALLY out of whack with the citizenry. I don't know exactly what to do about this, but it's pretty clear that the necessary work is too much for the Supreme Court to deal with, so something else has to be created. And yes, it's very important for the citizenry to accept that laws are not graven in stone and will sometimes need to change. Living conditions change. Technology changes. Laws need to change in response. We don't do enough of that.
6:45 AM May 2nd
The way I've always thought about this subject is that laws/rules/principles all exist for a reason. They are there either to cause something to happen, or prevent something from happening, generally speaking. There's a desired outcome that's being looked for.

If the enforcement of a particular law/rule/principle in a particular instance does not, in fact, help move us toward that desired outcome, then it should not be enforced in that situation. The point of not allowing trials to proceed "as is" regardless of errors and mistakes is to make sure that innocent people don't get railroaded.

However, if enforcing this rule - say, because there was a typo on a stenographer's transcript - does not actually do anything by way of doing this, because a typo on a transcript does not actually affect the outcome of the trail, then you don't enforce the rule in that situation.

One thing I've run into constantly where I work is that many people just don't know how to adapt situationally/apply flexible standards on a case-by-case basis. If you try to move away from one-size-fits-all you wind up with some people getting very confused and unable to make those kinds of decisions. It's really irritating.
7:26 PM May 1st
This is the article that the Forbes piece cited earlier was pointing at:

It's across two webpages, so when you get to the bottom of the first section, click on page two.

Drum also links off to the studies.
2:29 PM May 1st
Tom: thanks for the Canada data. They weren't a specific are focus of the study that doncoffin cited earlier, but they were referenced:

[i]It is tempting to extrapolate the interpretive sketch developed on the preceding pages to this most recent change in the long evolution of homicide rates. Especially as we are looking at a phenomenon that transcends national borders yet again. The years between 1990 and 1993 were a watershed as regards homicide rates across the Western world. They started declining in the United States, but they did the same across much of Europe with the notable exception of the United Kingdom and Ireland. Similarly, homicides rates have been declining since the late 1980s in Australia (from a peak of 2.3 in 1989 to 1.3 in 2005, see Mountzos 2003) and in Canada (from 2.6 in 1992 to 1.8 in 2004). The extent of decline differed and it is relevant to ask why these differences exist. But this does not detract from the main argument developed throughout this paper, namely that the primary unit of analysis for the kind of questions addressed in this paper must be the Western world. Also, I find many of the more conventional explanations offered in the criminological literature rather unconvincing. The similarity of trends across the Western world, for example, makes discussions of how the merits or faults of American criminal policy caused the drop in violence look rather parochial (Blumstein and Wallman 2000).[i]

So not just a similar period of increase, but a similar period of decrease.
2:27 PM May 1st
This article reminded me of a blog post describing what happens when you try to use "non-liner logic" (or Bayesian reasoning) in the real world with doctors and Texas policeman.
2:14 PM May 1st
First off, I believe it was my unpublished HeyBill that is excerpted in italics above, and what a great day in the morning to wake up and find your thinking may be ass-holish :-)

The point of my actual question was this ""how would you change the definition of an unearned run to more accurately reflect the pitcher's culpability?"""

My question actually was not a refutation of using ERA, but a query on how Bill would better improve the definitions between earned and unearned, which we all know can yield such absurd situations as to erase the validity of an entire season's ERA in one afternoon, particularly for a reliever. I would have to do a trace on this, but my memory was stirred by some situation where a pitcher's own errors prolonged his inning, and then HR and HR piled something like 6 unearned runs on, while he emerged unscathed ERA-wise. Probably wound up with a W as well.

What triggered me at the time was Bill's Sandy Koufax article, which combined W, W-L percentage, Ks, ERA, and a league avg Ks to BB ratio, all on just one season. To me, a robust High Quality Start stat of yet-to-be-determined definition could have great value in there, and, in a quick survey I did, the season leaders in even the flawed and despised QS category were very often 1-2 in Cy Young balloting. Sure, they are also tops in Wins and ERA -- but those shape the voting.

Do these flaws even out over a career? Sure, I guess, but not necessarily in a "greatest season" sense, or in a single game score.

Anyway, this reads like a dog's breakfast as I have been cutting and pasting, but if it sits here in the article comments, I'll begin a thread on RP.

PS: the drop in crime during the Giuliani Administration was caused by legalizing abortions 17 years earlier. uh-duh...

12:58 PM May 1st
evanecurb asked about lead as an explanation for a spike in crime. It was, I believe, in the 1930s that tetra-ethyl lead (tel) was found to be an effective anti-knock agent in gasoline, and became widely used. (The Ethyl Corporation, which made tel, foreshadowing the tobacco, climate, and gun lobbies, hired a physician in the 1950s to cast doubt on powerful epidemiological studies showing that ingesting lead harmed the intellectual development of children and could poison adults too.) Anyway, lead had that effect on children, whether because they ate lead paint or inhaled lead from auto exhaust. Children in the 1950s would have been teens and young adults in the 1960s and 1970s and the lead hypothesis says that these affected children grew into young adults who committed crimes at a greater rate than had happened before. The Ethyl Corp's physician finally lost his battle in the 1970s or 1980s and lead was eliminated from gasoline and paint, leading to a drop in crime. That's the hypothesis; I haven't evaluated it myself.
6:29 PM Apr 30th
I think that hankgillete gave us the best example of linear logic, and also a clear insight of where he stands politically. So it was the soldiers that came back from Vietnam after killing babies, of course!

If you read what I actually said instead of filtering it through your own political views, you’ll see that I said I didn’t know the reasons, and gave several possibilities for partial explanations. Nor did I mention anything about killing babies.

The fact is though that 2.7 million Americans served in Vietnam. I don’t see how anyone participating could not have been affected by a war that kept score not by battle won, or by territory gained, but by body counts. Most adjusted when they came back. Some did not.

Most serious drug-related crimes were committed by the organizations that were supplying it, but there were huge numbers of property crimes committed by addicts trying to get the money to buy drugs.

Someone else provided the link to the theory that lead in the environment contributed to crime. There is a correlation to the numbers which is suggestive, but I agree is not proof.

Do you have any theories of your own, or do you limit yourself to misrepresenting what other people say?

6:13 PM Apr 30th
I think that hankgillete gave us the best example of linear logic, and also a clear insight of where he stands politically. So it was the soldiers that came back from Vietnam after killing babies, of course!

Or the drugs, although must of them were done by the "Make love not war" crowd, that although assholes themselves and responsible for a lot of the wrong things happening now did not commit the murders.

Oh yes, of course, it's the environment because... uh, sorry, I really have no idea what he means by this.

They met via internet, hold on, Al Gore had not invented the internet yet.
2:53 PM Apr 30th
Not sure if I'm missing something here. Bill arguing that a 30% population increase shouldnt lead to a 140% murder increase seems to imply that the two should have something closer to a 1 to 1 relationship-- but one individual can commit more than one murder.

So many possible contributing factors here, across the western world apparently, from CPP to liberal courts, hell maybe even to climate change if more crimes are committed in warm weather. EvaneC's regression analysis approach seems interesting, not sure how easy it would be to separate signal from noise.
11:51 AM Apr 30th
"Asshole" judges may certainly have been a factor. But to say that they were the only factor engages in that same linear asshold logic, no? Other factors (besides the increase in CPP):

Leaded gasoline:

There is a controversial theory put forward by economist Steven Levitt that the increased availability of legal abortion after the Supreme Court ruling in 1973 on Roe v Wade meant that fewer children were born to young, poor, single mothers. This, says the theory, stopped unwanted babies in the 1970s and 80s from becoming adolescent criminals in the decades that followed. See Freakonomics.

" It began with a very public change of heart, that inner-city black youth, primarily, used their new freedoms to reject society, and after many tumultuous years ended in an almost completely silent, but equally dramatic change of heart to end it. " (he actually has some data there to back up his thesis).

A sociologist at Tufts University, John Conklin, says a significant factor behind the fall in crime in the 1990s was the fact that more criminals were behind bars and therefore unable to offend.

The fall in violent crime that began in the early 90s can be partly explained by the fall in demand for crack, says Prof Blumstein, co-author of The Crime Drop in America.

Are all these people wrong and Bill James correct? Or are there many factors in play here, some interrelated, some independant, such that it cannot be concluded 100% - by way of linear thinking - the one true cause of the 60's and 70's crime wave?

10:52 AM Apr 30th
The government agency in Canada (Stat Can) has a well-organized site, showing data of all kinds.

A couple of click later, and it shows these murder numbers (these are total murders, not per capita):
1975 633
1974 545
1973 479
1972 479
1971 426

1970 433
1969 347
1968 315
1967 282
1966 222

1965 243
1964 218
1963 215
1962 217
1961 185

That's an enormous jump (though naturally, relatively low compared to USA murder rates). There's this interesting note:

"Excluded from the reporting system are communities of less than 750 population, and communities of more than 750 which do not have police forces or contracted police protection.

In 1962, there were 698 urban communities in Canada with a population of over 750 operating their own police forces, and reports were received from 91.4 percent of these communities (although some respondents submitted reports for only part of the year as it was the inaugural year of the Uniform Crime Reporting System). In addition, of course, reports were submitted by the RCMP, the OPP and the QPP.

Because nearly all of the non-reporting communities were small in size, it is estimated that this non-reporting and part-year reporting resulted in a national statistical under-enumeration less than 2 per cent of crime recorded by police.

So, it might also be the case that the REPORTED numbers are not the ACTUAL numbers. Still, the presumed affect noted is a small percentage.

Rape (or rather REPORTED rapes) followed the same pattern, at about 3x of number of murders, year after year:

1975 1,848
1974 1,823
1973 1,593
1972 1,285
1971 1,230

1970 1,079
1969 1,019
1968 892
1967 773
1966 652

1965 641
1964 745
1963 549
1962 579

9:16 AM Apr 30th
I mentioned muggings in San Francisco & Times Square, as the first time my family came to Manhattan, in 1992, we saw a Japanese tourist get mugged right in front of us. The culprit grabbed and ducked into the subway. My father turned to my mother and said, "did we come to America for this."

At least we didn't have to re-enforce our front door.
2:06 AM Apr 30th
Thanks Bill for another well-thought and thought-provoking article.

I'm organizing a weekly high school class to teach kids "probability and decision making through games & sports." Would be a great final class to see if they are able to understand something like this.

And as someone who grew up in other countries (as well as in early-90s New York), I find it hard to understand how someone can not think that a state unable or unwilling to prosecute criminals consistently won't keep getting more and more crime until they do. Or anyone who's watched Game of Thrones, for that matter.

I live in New York again now, twenty years later. Not a big fan of the police, but who else will keep the crime in check, especially from professional & repeat criminals? Israel is the only (urban) place I've been to that has an effective citizen militia. And the petty violations that the police in New York overlook, or which people can easily get out of... like aggressive begging, cabbies talking on the phone while driving, etc, well you see those every day.

Last spring I saw a woman get her purse snatched in broad daylight in downtown San Francisco. Right next to a high-end shopping mall, at three o'clock on a Sunday. Something that wouldn't happen in today's Times Square. And something I saw & would hear about frequently in Italy as a kid. While in Russia... the #1 import we brought back from Italy was a 8-bolt lock system to install for our apartment. Taking off front doors wholesale was all the rage in Moscow, circa '91.

Very different states of the justice system. Then again we ate plenty of lead paint in Russia too, so that could have been a part of it.
1:57 AM Apr 30th
I don't have anything original to add, but I'm reminded that last summer The Economist devoted a fair amount of space to the shocking reduction in crime rates in the Western world. Here's one of the articles from that issue:​tion-not
1:27 AM Apr 30th
Two people mention lead. I have no idea what this means. Would like to hear the explanation
12:53 AM Apr 30th
While I think the 60's and 70's SCOTUS decisions may have contributed to the crime spike, I've always been leery of single-point explanations for it (which your isn't, but pegs these decisions as the key factor). I've heard that the crime spike was caused by a) lead in the air and water; b) population growth; c) the welfare state; d) not enough welfare state; e) abortion; f) not enough abortion; g) the decline of religion; h) the decline of the family; h) not enough cops; i) cops that were too violent, etc. etc.

In reality, I think it was almost certainly a combination of factors. A parallel would be the power spike of the "Steroid Era". Steroids played a role, but so did small ballparks, small strike zones, the acceptance of strength training, small bats, batters standing on the inside corner, etc.

The crime spike was probably the same. SCOTUS decisions contributed as did other factors. I'm not sure what exactly caused it. I do know that crime has plunged over the last twenty years, so whatever mistakes we were making have clearly stopped.
10:23 PM Apr 29th
I have written many, many times more positive words about the legal profession than negative. And stop whining.
8:30 PM Apr 29th
The statement that "the law has historically relied on Linear Logic, and they had been trained since law school to think like a train track" is not accurate in my view. Numerous core legal concepts are based on vague standards and "balancing tests." "Reasonable doubt" "comparative negligence," the "reasonably prudent person" test, hundreds or thousands of other examples, many of which try and do exactly what Bill is describing as non-linear logical thinking---apportioning responsibility. I get that Bill has never had a good word to say about the legal profession but I think the above is an oversimplication.
7:43 PM Apr 29th
I would recommend that people give thought to doncoffin's post and the study that he linked to. It's not a USA issue. It's very clear that in the rest of the Western World that a similar decline occurred (which ties into Bill's "starting point"), a similar significant jump, and then a similar decline.

The Warren Court wasn't in all those countries. One could try to point to Western Euro Liberals similar to the Warren Court, but you can look at individual countries and study them a bit, you're going to have problems tying that up in a nice bow.
6:47 PM Apr 29th
I think it is a huge leap to show that population increase does not account for the rise in crime to deciding (on absolutely no evidence that I can see) that the reason for the increase in crime (including murder) was solely because the Supreme Court made it harder to get convictions.

How did that work? Did potential murderers actually decide to commit a murder that they wouldn’t have based on their belief that their chances of being convicted had been reduced to an acceptable level? Or, do you think that all the additional murders were committed by repeat offenders who were not convicted of previous murders an thus were able to kill again?

I don’t know what explains the increase in crime during that period, but I doubt it was any single one thing. Some possibilities for partial causes:

1. The Vietnam War trained a large number of men in the risk group to
use weapons and gave many of them a lower regard for human life.
2. The drug culture of the era gave many people contempt for the legal system and the use of drugs decreased their inhibitions and mental judgement.
3. Lead in the environment.
4. The population increase led to a critical mass where it was easier for potential criminals to meet and commit crimes that they wouldn’t have committed by themselves.

I don’t understand how you can latch onto this Supreme Court theory to the exclusion of everything else when you demand evidence in other matters.

5:03 PM Apr 29th
I really liked both these commentaries, and thank Bill for them. I've never been fond of the tradition of not attributing "unearned runs" to a pitcher. Sometimes the "unearned runs" go error, walk, single, HR. The single, walk, and HR are just as much the pitcher's responsibility as they would have been without the error, unless you believe the error makes everything the pitcher does harder to do.

As for the asshole logic on the court, while I am unwilling to accept that it's the entire reason for the increase in crime rate--I see correlations but no real statistical analysis--I do believe that the Supreme Court makes lots of asshole decisions. Just look at all the decisions that focus on the 14th Amendment, some of which reach diametrically opposed conclusions. And recent decisions about campaign finance, in which the majority has written that unlimited money doesn't distort or create the impression of distortion of elections, were written by assholes. (I would have been far less upset if the majority had written simply "We cannot see how to limit financial contributions to campaigns without running afoul of the 1st Amendment.")
3:53 PM Apr 29th
Another contributing factor to the crime explosion might have been the wider use of narcotics which I've heard was greatly accelerated by the Vietnam War - in various ways: spread by soldiers, product coming back in body bags, etc. That fits the timeline well, considering it likely had a long lingering effect. There again, court leniency probably didn't help there either, but I echo the sentiments of the contributors below that it was a complex issue with many causes. The subsequent reductions in crime probably has many causes as well - such as improved policing techniques aside from balanced tests in the courts.
3:02 PM Apr 29th
My point, to the extent that I have one, is that something that is happening across countries and across legal regimes is likely (but not guaranteed) to have similar causes. So while I think Bill may be on to something, I also think the issue is substantially more complicated.
1:22 PM Apr 29th
FWIW, some academic work, looking at a longer time period, and for Europe--where, as it turns out, murder rates rose about as fast as they did in the US:

Modernity Strikes Back? A Historical Perspective on the Latest Increase in Interpersonal Violence (1960–1990)
Manuel Eisner

There is a plethora of criminological explanations why criminal violence increased during the three decades between the early 1960s and the early 1990s. This paper argues that most available interpretations are lacking in three respects: they lack a historical perspective that anchors the three critical decades in a wider understanding of long-term trends; they take the nation-state as their unit of analysis and disregard important commonalities across the Western world; and they pay insufficient attention to different trends in broad categories of physical violence. This paper therefore takes a macro-level and long-term perspective on violent crime, focusing on European homicide during the past 160 years. It demonstrates that the period of increase was preceded by a long-term decline and convergence of homicide rates from the 1840s to the 1950s. Also, it shows that both the decline and the increase primarily resulted from temporal variation in the likelihood of physical aggression between men in public space. It argues that explanations of these common trends need to take into account broad long-term cultural change common to Western societies. In particular, the paper suggests that shifts in culturally transmitted and institutionally embedded ideals of the conduct of life may provide an explanation for long-term change in levels of interpersonal violence.

You can find the entire study (,pdf) here:​
1:10 PM Apr 29th
12:41 PM Apr 29th
Glad you were finally able to get that off your chest, Bill. Your argument is very persuasive, as pertaining to baseball and crime. But, of course, such Linear Logic is present everywhere humans are: in politics (on both sides, as you pointed out), employment, marriages, parenthood, religion—perhaps especially in religion, where the stakes ultimately are highest. I think you’ve done us a service by exploring it and laying it out in the open. I’ll now be more wary of it in myself and in others.​
12:10 PM Apr 29th
The rise in crime rates during this period creates an opportunity to learn from the past. Let's look at each of the factors that may have contributed. None are the sole reason, but it seems to me that there ought to be a way to run a regression analysis on those variables that can be quantified:

1. size of crime prone population
2. Convictions as percentage of reported crimes
3. Number of police
4. Characteristics of areas that experienced largest / smallest increases in crime (by population density)
5. Unemployment and median income levels in the areas listed in number 4.
6. Prison capacity
7. Population increases in warm climates relative to colder climates (crime rates are higher in warm weather than in cold weather)

and so on. You could come up with 10 or more variables, test them all, and quantify their impact on crime rates. You could split the study into subgroups: areas where crime rose the most and areas where crime grew the least, and test the variables in each subgroup.

The point is, I think many factors contributed, and I think most of them can be quantified. I don't know how to do it, but it makes more sense to look at as many variables as possible than to limit the discusssion to two variables.

I live in a law-and-order state (Virginia). High rates of convictions, no parole for serious offenses, high rates of capital punishment relative to the rest of the nation. Crime rates are down so most people are happy about that. Richmond used to be known as the Murder Capital; not so much anymore. This is a good thing. But there is a perception among many (myself included) that the pendulum has swung too far toward law and order. Overcrowded prisons are unsafe for the inmates and fair trials difficult to obtain.

I think it's important to find out which law-and-order practices achieve their desired results and which ones do more societal harm than good. We know that there is collateral damage from too much leniency, just as there is collateral damange from too much power in the hands of cops and prosecutors. The key is to strike a balance.
10:31 AM Apr 29th
This partial v binary approach certainly scares people. The best example is the WAR implementations at Fangraphs (fWAR) and Baseball Reference (rWAR).

At its core, fWAR is FIP, which is based solely on the "three true outcomes", which therefore ignores all batted balls, baserunning plays, and sequencing of all events.

And at its core, rWAR is RA9 (runs allowed per 9IP), which presumes that the pitcher has complete responsibility on the batters that manage to get on base, and the runners that manage to score, and the sequence of all that.

The true answer is somewhere in-between. But, try selling to someone the idea to weight things differently. And at its core, that's what Game Score is. It weights runs allowed with hits allowed, even if a hit doesn't lead to a run. Game Score gives partial credits and debits for each event.

Anyway, that's why I happily accept what rWAR and fWAR are doing, and I simply take a position half-way between the two. I don't know what the true answer is (one-third one way and two-thirds the other? three-fourths the other and one-foruth the first?), but taking a 50/50 spot puts me in a comfortable position, enough that I don't have to take a political position of going all-in on one or the other.

10:23 AM Apr 29th
Television. It may be oversimplifying but when murder and mayhem are brought into virtually every home in America on virtually every night of the week over and over and over, it changes the way people see such things. Never mind that the bad guys always get caught, it plants the seed. Well, I see where they went wrong. I won't get caught.
9:31 AM Apr 29th
Bill I take extreme umbrage at this article. It seems to me that you take a very dismissive view of "3rd grade barnyard humor." My life has been greatly enriched by such humor. I tried to prove its worth using math but, well, it quickly descended into 3rd grade barnyard humor.
9:23 AM Apr 29th
I'd like to cautiously agree with gregg, below. In this period we started our third war in three decades--couldn't the real reason for the spike be several reasons? [court rulings-35%, CPP-5%, law enforcement not having data/resources-25%, differing parenting styles-10%, "white flight" from inner cities/de-emphasis on maintaining urban core-15%, general societal callousness due to 3 wars in 3 decades-10%]. I'd really like to see the breakdown of WHERE these murders were taking place--did the percentage of urban murders as compared to overall murders shift in this period we're talking about, for instance?
8:42 AM Apr 29th
Bill, your refutation of CPP as the sole cause is convincing. But I'm less convinced than you seem to be that limits on law enforcement from the courts is the central reason for the spike in crime. The years in question (1963 to 1974) had more social disruption and dislocation than any similar period in recent memory, for example. A breakdown in respect for authority and tradition in general (which is not the same as fear of punishment) pervaded the era. There may have been many other reasons, other than criminals perceiving that their chances of getting punished were diminishing.

Your article starts out talking about the errors of linear logic, of simplifying conclusions about cause and effect. But your last paragraphs seem to fall into the very error you highlight, as well.​
7:30 AM Apr 29th
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