BILL JAMES ONLINE

Xavier University Business School Speech

April 21, 2017

2017-21            

            Thanks and acknowledgements. . . . .

 

            The peculiar fact of my career is that I am often given credit for doing something that I had no thought in the world of doing when I started out.     When I started writing about baseball, my goal was to make a living as a writer.   I wasn’t even worried about making a GOOD living as a writer.   I grew up poor, and I kind of figured I would always be poor, and all I wanted was just a job that would pay the bills and, as Red Smith said, did not involve heavy lifting.  As a young man I admired the work of the great sports columnist Jim Murray, and I wanted to be Jim Murray or Red Smith.  If I could have gone to my local newspaper and been hired to cover the local high school sports teams, I would have been fine with that.      

            I was not the kind of person who could have gotten a job like that.   Newspapers were looking to hire nice young men, and, this being the 1970s, a few nice young women.   I was pretty rough around the edges.   In order to make a living without heavy lifting, I needed to figure out some way that I could do that without depending on people to take a liking to me.

            I had written a few articles for Baseball Digest.    I had read the Baseball Digest for years, so I knew what they liked, and it wasn’t too hard to produce that.    They would pay $60 for an article, or, if they liked the article a lot, maybe $70.   This was the 1970s, and $60 then was more like $125 now, maybe more, I don’t know.  

            Anyway, after writing a few of their routine Baseball-Digest type articles, I tried to sell them on what I thought were BETTER articles, articles which challenged traditional assumptions, rather than buttressing them.   I went through the Box Scores for an entire season’s worth of baseball games, and I figured the Run Scored in Support of each starting pitcher, which is routine information now, but which was not available at that time.   I probably put 50 hours into writing that article, but they would not publish it.    Not only would they not publish what I thought were better articles, but they became suspicious of ME because I wrote them.   After that they were reluctant to publish my new articles, because they were suspicious that I might be trying to sneak something in them that was not in keeping with what they had done for years. 

            I had other experiences like that with other publishers, and after a time I decided that I should start my own annual publication.   I was bold enough to try that entirely because I was young and ignorant and didn’t have any idea what I was up against.   If I had understood how difficult it is to publish an annual book and sell it out of your house, I would never have tried it, but I didn’t know.   

            The thing is that I had great respect for traditional sports writing—excessive respect, I suppose—and I thought that I couldn’t do that.    I thought that to be a traditional sportswriter you had to have an understanding of the game built up over decades of interacting with the players and managers in the game, and I didn’t have that, so I would have to rely on the facts.    That sounds different than the way I thought it at the time.    I thought that there was understanding, and there were facts, and that having an understanding was a greater goal than merely having facts.      Anyway, what I was essentially doing was picking up things that baseball people SAID were true, and checking the facts related to those.   It was generally believed that a right-handed pitcher was easier to steal a base against than a left-hander, and there was a superstar of the time who, being contrarian, would argue that a left-hander was actually easier to steal against because the base stealer was looking right at him, so he couldn’t hide anything.   So I went to the box scores, and I counted the number of stolen bases allowed by right-handed pitchers and by left-handed pitchers.    It turned out that the traditional view was correct; there were more stolen bases against right-handed pitchers.  

            That was such a simple act that it is hard to understand how it could be controversial, but it was.   Sportswriters of that era did not check the statistical record before weighing in on issues of that nature—ever.   They did not EVER check the statistical record before weighing in on issues of that nature.    They were reporters.    If they wanted to know what the truth was, they would ask a veteran player or a veteran manager.  

            There were thousands of statements like that, and for a few years I was trying to make a living by checking the facts regarding these statements.    I want to emphasize how modest my goals were.    I was just trying to make a living.     I thought that if I could do this for a few years, I could build up an audience of maybe 2,000 people who were interested in the subject.   If I could sell each of those people a book once a year and make a $10 profit on each book, that’s $20,000 a year.    It was a lot more money than my father ever made.   I was also a certified school teacher, and that was more money than I could make, at that time, teaching school.    I was just trying to make a modest income. 

            But at the same time, I DID believe in what I was doing, and I did believe that somebody should be doing this.   I called what I was doing sabermetrics.    If you go back and read the things I wrote when I was 30 years old, it seems obvious that I believed that there would be an entire field of people doing this kind of research, but, all these years later, I have no idea how it was I was able to convince myself that that was true.  

            Looking backward, the most peculiar thing is how many people would tell me that I would never make a living doing what I was trying to do, and how certain they were that they were right.    It is more than that: what someone would tell me, probably once a week, is that I personally am really interested in the kind of work you are doing, but you will never make a living doing it because there just aren’t enough of us who are interested in this type of work.  

            But I stuck with what I was doing, because of a mathematical extrapolation that seemed to me irresistible.   I lived in a town of about 50,000 people at that time, only a small percentage of whom I personally knew, but I personally knew at least 20 people in that town who were interested in my area of work.   At that time there were about 270 million people in the United States.   If you take 20 people from 50,000 and expand that to a population of 50 million, that would mean that there would be more than 100,000 people in the United States who would buy into the concept.   In order to make a living doing this, I didn’t need 100,000 people; I just needed a couple of thousand.   So this meant that either the people I happened to know were atypical representatives of the American population by some truly phenomenal margin, or there were, in fact, enough people out there for me to make a living by doing this.  

            In essence, I was staking my professional career on this being true, but I wasn’t risking very much, because frankly, my other options were not all that impressive.   If I couldn’t make a living as a writer, I would run a little book store or be a school teacher or something.   It wasn’t like I was turning down big bucks from Wall Street.  

            Well, the time that I have been speaking of here was 1976 and 1977, when I was starting my career as a baseball writer.   By 1983 the Baseball Abstract was selling more than 100,000 copies a year.   By that time a national publisher had taken over the publishing end of it, so I was making more like a quarter on each book, rather than $10, but still, by my own standards I was doing well.    The other thing that happened was that by 1983, other people were imitating my work.

            Back to the beginning of my work, I always wrote as if this was a field of research shared by other people, even though, in reality, it was just me and a couple of other guys.  I think that a key thing was that I knew that what I was doing was actually very easy, conceptually easy. There was really nothing to it, except work, and the work didn’t involve grease or bad smells or loud noises or getting callouses on my hands, so I was fine with it.  

            But also, I must have believed on some level that the work I was doing was important.   I know that sports writing itself is not important work and that nothing we do or say as sports writers is really important, but I always felt that the work I was doing was important relative to the standards of the field.     Traditional sportswriters very much did NOT think that what I was doing was important relative to the standards of the field, and also, it was easy for people who didn’t understand what we were doing to trivialize it.  

            What people who don’t understand what we do in my field THINK that we do is to figure things like what a player has hit on Tuesday night games against left-handed pitchers with the temperature between 80 and 84 degrees.   I find that Tuesday night is the trigger here; whenever anybody mentions Tuesday night in a discussion of statistics, you know that they don’t have ANY understanding of what it is that we actually do, and are thus attempting to marginalize it or trivialize it.   But what we actually do is exactly the opposite of that.    Sabermetrics is the sworn enemy of that kind of statistical information.   Our interest in that would extend as far as asking two questions:   One, is it reasonable to believe that there is an ability to hit on Tuesday nights, as opposed to an ability to hit at other times—no it does not seem reasonable to believe that there would be such an ability—and two, even though it doesn’t seem reasonable to believe this, might there be evidence to support it nonetheless?   But having disposed of those questions, any mention of such things in sabermetric literature would be greeted with ridicule and derision.     I’ll get back to this subject later in the talk. 

            One of the things that we actually do in my field is to try to straighten out the misconceptions that people have, based on misunderstanding the statistics.    One of the largest of these, actually, has to do with the platoon differential.   The platoon differential, for those of you who are not baseball fans, has to do with the fact that left-handed hitters hit better against right-handed pitchers, and right-handed hitters hit better against left-handed pitchers.

            But what almost nobody understands, inside of baseball or outside of it, is that this is not an individual variable.   It’s a condition of the game.   It applies to everybody.

            But we MEASURE what hitters hit against left-handed and right-handed hitters based on individual hitters, year by year.   Because we are dealing with a relatively small advantage and relatively small data groups, the data for individuals is all over the map.   A right-handed hitter may hit .260 against right-handed pitchers, but .420 against left-handers.  That’s called the platoon differential.   This SEEMS to be tremendously important, and, because we measure it on an individual basis, people ASSUME that it is an individual trait.

            But it actually isn’t; it’s a condition of the game that applies to everybody.   There isn’t actually any such thing as a hitter who hits .420 against left-handed pitchers, or a hitter who has a 160-point platoon differential.    That’s just a statistical fluke, just like the guy who hits .420 on Tuesdays.   The platoon differential is basically the same for everybody.  

            But baseball people don’t understand this; they didn’t understand it 30 years ago, and they don’t understand it now, so they talk literally every day and many times every day about platoon differentials, always assuming that it is an individual variable.    Because they grow up with that understanding, and because that understanding is re-enforced every day by selective observations, it takes a long, long time to get people to understand that there is no such ability.    But we will eventually succeed.     A hundred years from now, people will generally understand that there isn’t any such ability, and never was.    

            I should be careful about speaking in absolutes.   There actually is at least one major league player who has an abnormal platoon differential.    Adam Jones of the Baltimore Orioles is a right-handed hitter who actually does hit better against right-handed pitchers than left-handers.   But he is probably the only one. 

            Well, somewhere I have lost the thread of what I was supposed to be talking about.    By the early 1980s there were 100,000 people a year buying my books, and generally buying into the concept of more sophisticated analysis of the game.    That audience consisted of about four segments.     One was the public, which was, surprisingly, much more receptive to complicated analysis than was generally believed.    A second was baseball writers, who generally were at that time hostile to what I was attempting to do, and were generally dismissive of it.   A third audience was professional baseball men.   Professional baseball men were portrayed by the reporters of the time as being on their side—that is, completely dismissive of what I was attempting to do—although I don’t know whether this was accurate or not.   I know that many years later, it became extremely common for old baseball guys, scouts and coaches and executives, to come up to me and say that they had been reading my stuff and had been fans of my work since I started writing.    I don’t think these people are lying to me; I don’t have any reason to believe that they are.   I think they were just generally quiet about it at the time, because the perception was that this was oddball stuff that wasn’t useful inside baseball, and they didn’t have any incentive to say the opposite at the time.  

            But the fourth audience was young people.   When I started off on my own path, about 1977, after a couple of years of trying to write mainstream baseball material. . .when I started off on my own path, I thought that I was writing to adults.   In fact, that is one of the main ways that I defined what my audience was.   We all used to have this view of the "mainstream", which was generated in a world in which there were two or three large radio stations in each city and a couple of TV stations and one or two big newspapers, that to fit into that audience you had to do things that were consistent with ALL of the potential audience.    A television show couldn’t get on the air if it was unsuitable for any portion of the audience.   The same was true across the spectrum.   A sports writer had to write stuff that EVERYBODY could understand.   Otherwise, it didn’t belong in a daily newspaper.

            Well, a lot of what I was writing was somewhat difficult to understand, so it was de facto banned from the mainstream.   When I went off on my own, my notion was that writing for everybody meant that you were writing for children and for stupid people, so I would not do that; I would focus on writing for that subsection of the audience which was educated and which was capable of understanding things like market forces and correlations.   I would sort of halfway define things so that a less educated reader could keep up, if he tried.   I remember once that I wrote that the standard deviation of batting average was "about what your average deviant would hit".    It’s not a REAL definition, but it gets the un-educated reader past the question of "what’s a standard deviation?"    At that time it was necessary to do that, because sports writing had never used vocabulary like "standard deviation."  

            What I didn’t understand until years later was that there was a subsection of my audience that was really bright young people, then 10 to 18 years old, and that these people were actually the most important part of my audience.   I could not really re-shape the thinking of baseball people or of sports writers, because they had been thinking about these problems in certain ways for decades, and they were both unwilling and unable to go back and re-think these issues.   For example, sports writers and sports casters wrote and spoke daily about a player’s ability to perform in the clutch; did then and still do.   I was arguing, and others in my field were arguing, that there was little or no evidence that any player’s ability to hit in a clutch situation was any different than his ability to hit at any other time, or his ability to shoot a free throw at any other time.    A sports writer generally was not capable of considering the possibility that clutch hitting was a mythical beast like a dragon or a unicorn, but to a young person just sorting out the world, the argument was less difficult.  

            Ultimately, those young people were the most important part of my audience, because it is amazing how rapidly kids grow up and start to change the world.    We lived in Boston for a couple of years ten years ago.   My son was at that time 13 years old, and he had a friend who went to baseball games with him sometimes because I could get them in to Fenway Park.   That was ten years ago, and that young friend now works for the Seattle Mariners, doing work that is pretty much a direct outgrowth of the work I was doing in the 1980s, although it is much more advanced and more sophisticated than what I was doing at that time.  

            Well, these young guys who were reading my books in the 1980s grew up, and they became sports writers and sports broadcasters and executives and scouts and even a few of them became players.    Some of those young people are now managers.   Some of them have been managers for ten years now.   Several young people who were reading my books then are now much more famous as writers than I am.   

            Those young people, really, were the foundation of my reputation.   It was THEM who disrupted the market, not me.    There are a couple of other stages that are crucial to understanding what really happened, how the market for this kind of information was created.    One is that, once I had established that there was an audience for a different way of looking at sports, other writers began to enter that market is significant numbers.   Some of those other writers regarded me as a competitor, and tried to do what I was doing only better, and many of those were harshly critical of the work I had done, while others regarded me as the patron saint of the field, and wrote things about me that were excessively kind and excessively nice, although not always true.   But in either case, by 1987 there were a lot of other people doing similar work.

            Another thing that happened, beginning in 1979, was that I was hired by agents to work in salary negotiations, on behalf of players.   I didn’t make an awful lot of money doing that, but it is hard to believe how exhilarating it was for me.   What I do, basically, is to pick up a question, and try to find all of the evidence on either side of the question, but also, and more importantly, to try to find the evidence that ISN’T there.   In other words, I try to see the questions to which we DON’T have answers.   I try to see the elements of the debate on which there aren’t ANY statistics. 

            One side says this; the other side says that.   What are the facts?    One side says that clutch hitting exists; one side says that it doesn’t.   What are the facts?   One side says that a player’s platoon differential is an individual variable; another argument is that it is a condition of the game which applies to everybody.    What are the facts?  

            When you get into a salary arbitration case, what does the arbitrator want to know?    One side says that this player is worth $200,000 a year to his team; the other side says that it is more like $120,000.   What are the facts? 

            I lived in a world in which all of the smart guys, all of the professionals, were telling me every day that I didn’t know what I was talking about and that my work didn’t have value, but when we got into a salary arbitration, all of a sudden, everybody was trying to play MY game.   My view of the case was much more like the arbitrator’s view than anyone else’s was.   Everybody else was playing catchup.  

            I was a young man with no history of success, no real expectations of success, and this was thrilling to me, to be suddenly ahead of the curve.   But also, it had never occurred to me that this would happen before it did happen.   Salary arbitration in baseball was new at that time.   I had never really thought about what it would be like to be in a salary arbitration hearing, until I was hired to help the agent get ready for one.  

 

            I would like to try to explain a little bit better what it is that we do.   Think of it this way:   is an astronomer mostly interested in lenses, or in telescopes?  Is an auto mechanic mostly interested in wrenches?   Is a pharmacist mostly interested in pills, or in lotions?   Is a surgeon mostly interested in knives?

            Not exactly.   An astronomer has to be interested in telescopes because they are central to his profession, but he is not REALLY interested in telescopes; he is really interested in what you can see out in the skies by looking through telescopes.   An auto mechanic is interested in wrenches because he has to be, because they are necessary in his profession, but he is not REALLY interested in wrenches; he is interested in engines.   A pharmacist is interested in pills because he has to be, because he deals with them every day, but he is not REALLY interested in the pills; he is interested in what is IN the pills, and in how the medicines which are in the pills can help people or can kill them.    A surgeon is interested in cutting tools because he has to be, but he is not REALLY interested in cutting tools, he is really interested in the human body, and in fixing what has gone wrong inside the human body.  

            People refer to us as statistical analysts, and I understand the confusion about that, but it IS confusion.   We care about the statistics because we have to, but we do not analyze statistics, and we don’t really care anything about them; they are the pills and wrenches of our profession, just as they are the pills and wrenches of economics and of weather forecasting.    What we are analyzing is baseball.  

            One of the people who was interested in Sabermetrics before there was any such thing as sabermetrics was Dick Cramer.   At that time we were members of the Society for American baseball research, and absolutely the only publication that would publish articles about what we now call sabermetrics was the annual journal of the Society for American Baseball Research, whose editor was Bob Davids.   So Dick Cramer published an article about sabermetrics there in 1974, and in 1975 he submitted another one, and Bob Davids told him that he didn’t know if there was enough interest in this kind of material to publish an article about it every year.   The entire world of Sabermetrics had a de facto publication limitation of one article every two years.

            Well, I have watched in astonishment as the number of people interested in this area has grown from 3 to 5, from 5 to 10, from 10 to 20, from 20 to 100, from 100 to a thousand, from a thousand to a hundred thousand, and from a hundred thousand to millions.   There are now many articles about the analysis of baseball published every day of the year.   There are annual conventions of sports analysts, many of them, and some of them attended by thousands of young people.   Every professional sports team now employs people to follow the literature in this area, and to help them make decisions.  

            I understand NOW that this was sort of inevitable.   A lot of it is an inevitable consequence of the computer age, the computer revolution, and some of it is an inevitable consequence of the power of knowledge.

            One little anecdote about this, and then I’ll close and take questions.  From the time I was 15 years old, I always made projections of what players would hit next year.   When we got personal computers with spreadsheets in them that became a lot easier, so the projection systems became a lot more complicated very fast. 

            About 1985, my friend and business partner, John Dewan, suggested that we should publish the projections for next year.   I said, "John, we can’t publish those; they don’t mean anything.   It’s just a made-up system.   There’s no scientific validity to them."

            "That’s OK," said John, "We won’t TELL anybody that there is any scientific validity to the method.   We will just tell people to take them for whatever they think they are worth."

            I resisted doing that for a couple of years after that, but finally, about 1987, I agreed to publish the projections for hitters for the next season.    To the best of my knowledge, nothing like that had ever been published before.   It proved to be extremely popular with the readers, and within two years, several other people were publishing their own projections systems, and claiming that their projection systems were better than ours.   Now, 30 years later, every professional sports team in the United States or Europe uses some sort of projection system to make an educated guess about what kind of team they will have next year.

            And when you think about it. . .well, of course they do.   How can you have any idea of what kind of team you will have next year, if you don’t run projections?   How can you know what you can afford to pay each player, if you don’t run projections for each player and compare them to your budget?    In retrospect, it seems absurd to try to run a baseball team without constantly updated projections for each player.   Sort of like trying to drive a car with no maps. 

            But I didn’t foresee that AT ALL, from the other end.   I was just messing around, having some fun with the numbers, projecting what each player would hit next year to see how well I did.    That this was actually VALUABLE to somebody was a complete surprise.   I always expected to make a living doing this stuff, but I have been very surprised that I have made as good a living as I have.   I was surprised that I got to work in baseball, and I was surprised to be invited here today to speak to you.   But here I am, and, if you have any questions for me, I am at your service.  

 
 

COMMENTS (14 Comments, most recent shown first)

BenchWarmer
I was an early convert. Yes, I was young.

I remember a Sporting News column by Furman Bisher tearing into the work of Bill James.

I remember the owner of apba games, who had season tickets, arguing that the platoon differential didn’t exist.


4:01 PM May 6th
 
Arrojo
I bought the 1982 Baseball Abstract when I saw it in the bookstore and devoured it within a couple of days. Then I re-read it. I was 23 and attempted to try the same thing for hockey, but holding down a full-time job as an actuary, that project fizzled. I still have all the Abstracts ever published up in my attic.

Thank you for everything.
12:50 PM Apr 24th
 
matt_okeefe
My first Abstract was the 1985--I was 11, and my parents gave to me in my Easter basket.
8:47 AM Apr 24th
 
MarisFan61
Re DanaKing: "I'd always suspected there was more going on than what we were being told...."

Despite being a chronic habitual skeptical critic, I never suspected there was particularly more going on in the game of baseball than the conventional wisdom, before coming across the Abstracts.​
7:09 PM Apr 23rd
 
KaiserD2
Bill,

I will never forget discovering the 1982 Abstract at the Harvard Coop ( on a visit to Cambridge) and realizing that I was entering a new world. (I had also read Okrent's famous Sports Illustrated article on you.) And as you know, in later years I was able to review two of your books for major publications.

I would like to mention one sad aspect of the situation today, however. If you were in your early twenties today you might easily go to work for a major league team. But I don't think there's the slightest chance that you could have the same impact on the broader public. You wrote in an early Abstract that it was clear thta there was a market out there for intelligent books about sports. There was--but that market is MUCH smaller now. Even then, the boom in sports publishing worked out much more to the benefit of the Halberstams, Goodwins, and George Wills--celebrity authors who decided to do something about baseball--than it did to other serious students of the game. And now I have been informed by my agent that no major publisher will do a statistical baseball book, only biographies--because they aren't selling. McFarlane is bringing out Baseball Greatness..

The same thing has happened in my professional field of history. Everhone's sales are way down. You broke dramatic new ground on a well-known topic--baseball--but you also benefited from the literary culture that had grown up for a long time--and which has now largely faded away.

David Kaiser
8:42 AM Apr 23rd
 
DanaKing
I was 26 when Ballantine published the first mass-produced Abstract, but it hit me much the way you talk about younger kids. I'd always suspected there was more going on than what we were being told, and your methods and writing made your conclusions understandable and reasonable. What I enjoyed most about your work--and continue to--is your willingness to re-examine things. There aren't a lot of others in your field I pay much attention to, frankly because too many of them are Right, and any questions to the contrary are exposure of the questioner's ignorance. You seem to grasp that knowledge and understanding are constant progressions, as evidence by you walking back some of your early comments about chemistry and a willingness to acknowledge there are important things that maybe can't be measured directly. Thanks for all of this.
3:45 PM Apr 22nd
 
jeffburk
Bill, I bought and read my first copy of the Baseball Abstract in 1987 at age 15. I was heartbroken when you broke the wand just one year later, in 1988, although you rescued me with the Baseball Book a couple of years after that. There was no Internet for finding used copies of older books back then, and my parents were not going to drive me all over town to dig through stacks at second-hand bookstores. A dozen years later, thanks to the development of the Web, I finally found them all. If I were stuck on a desert island and could only have one book, I would take the softcover version of the first edition of the Historical Abstract. There is nowhere in the world I feel more at peace than sitting in a ballpark watching a game, and you were probably the biggest influence on what I see and think when I do that. Thanks for the fond memories, Bill.
1:26 AM Apr 22nd
 
hotstatrat
Bill - the popularity of your projections and others pretty well coincided with the popularity of fantasy baseball. I first heard of Rotisserie baseball in 1980, but fantasy baseball exploded over the next couple of decades. Based on my experience, projections and fantasy games spurred each other on.​
11:26 PM Apr 21st
 
bjames
Lou Brock in his career had a higher stolen base frequency and a higher stolen base percentage against right-handers than left-handers. It was actually Joe Morgan who said that. I didn't mention his name in part because this speech was in Cincinnati, but several people in the audience asked me if it was Morgan who had said that or remembered his saying it. Morgan also had a higher stolen base frequency rate against right-handers, but did have a higher stolen base percentage against left-handers.
4:35 PM Apr 21st
 
jimmybart
I believe it was Lou Brock who said it was easier for him to steal against lefties than righties. I see you did a study and found that to be false, but I wonder if Lou's numbers in this regard varied much from the norm?
4:14 PM Apr 21st
 
Gfletch
Terrific. You’ve told this stuff several times, but always find new ways to do so and thus bring new perspectives and ideas to your readers. Loved it.

I think an original thinker is like a native born anthropologist, living among the tribe but no longer really a part of it. First you are ostracized, but later gain followers. Still later, having continued to evolve, the followers will view your new ideas with dismay.

Bill James, heretic. That’s both the price you pay and the reward you earn for refusing to close your eyes. Thanks.

10:34 AM Apr 21st
 
MarisFan61
(dam, I can't type. Or can't multiply, not sure which it was.
It's not $470, but $270.)​
5:28 AM Apr 21st
 
MarisFan61
Great to see the texts of these speeches!

And y'know, in the process of publishing these, probably without your intending to do it, I think you're sort of starting your autobiography, in installments. Which is pretty cool, because you probably don't want to do an autobiography, but here it is anyway. :-)
Actually I guess you started it in the early Abstracts. As I'm sure you know, 1 or 2 guys have done 'biographies' of you that are based just on what they were able to extract from those Abstracts.

-----------------

In a way, those Baseball Digest articles paid better than you think!
$60 then was probably more like $470 now. According to a webpage that gives the multiples for dollar values for different years, the factor from 1975 to 2017 is a little over 4.5.
5:26 AM Apr 21st
 
 
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