The Disappearance of .400 Hitting

I've been reading this Stephen Jay Gould book, Full House, which is all about how various things in the world that we usually describe as "trends" are in actuality better understood as side effects of changes in statistical variation. One of the two main examples he uses throughout the book is the disappearance of batting averages over .400 over the last century. This "trend" does not represent a decline in hitting ability over time, but rather a narrowing of variation in hitting ability.

As the excellence of play in professional baseball has increased over the years, the difference in ability between the best and worst batters and the best and worst fielders has become smaller. In addition, MLB management has occasionally tweaked the rules to keep the mean batting average essentially constant from season to season. Also, the fact that .000 represents a hard lower limit (you can't have a negative batting average) means that the distribution of averages will skew right. As a consequence of these three factors, the right-hand tail of the batting average distribution curve has been brought in closer: whereas a century or so ago, the handful of batters out on the end of that curve were hitting above .400, that narrower curve now puts them significantly below .400. Here's some graphs showing how the curve has changed shape over the years:



So I've pretty much been thinking of all sorts of trends that may or may not be understood better with this sort of model. One that came to mind this morning was the stock market. It is sort of a general rule that market indexes and averages march ever upward. There are corrections and recessions and stuff, but the overall trend seems to be one of continuous increase. Does this represent a miracle of capitalism, that all firms will tend to gain in value over time, or is it merely a side effect of a widening variation among firms?

I didn't look for historical data—I know that the mean value of publicly traded firms has increased, so all I'm really interested in is the shape of the distribution of firms' values at a single point in time—but I was able to find the current values of all the US corporations listed on the NASDAQ. Here's the histogram showing how many firms are valued in each range (Y-axis is number of companies, X-axis is value in millions of dollars as of market close on 8/31):



It's the same kind of right-skewed curve as with batting averages, which makes sense: $0 represents another hard lower limit on firm value, because a company can't have negative worth without disappearing from the market. Gould talked about the idea of a "drunkard's walk": if a drunk leaves a bar, and is staggering back and forth on a sidewalk between the bar on one side a ditch on the other, then even if he staggers completely randomly (even chance of staggering towards the wall or towards the ditch) then he will still always end up in the ditch.

In the same way, it could be completely random whether a given company increases or decreases in value each day: some firms will move to the right in the distribution curve, some will move left, but the left limit will never drop below zero, and some very few (Microsoft) will inch the right limit further out. There needs be no general tendency for company values to increase, just variation increasing in the only direction it can over time.

Of course, that doesn't mean that the value of a company is random. Just that the shape of the curve could be explained by randomness. To actually demonstrate that it's all random you'd need to track individual firms over time. And in fact I would expect there to actually be tendency to increase in value as a result of the steadily increasing labor pool. But it is interesting that the growing mean value of corporations is not indicative of anything greater than an increase in variability.

Mets @ Phillies

What a ridiculous game. Four hours of emotional roller-coastery. So sad to see David Wright have such a great game and have it all slip through their fingers, but I guess that's part of what it means to play on a team. Sometimes one player's transcendent play can make up the difference, and sometimes it can't. And credit to the Phillies, they played excellent baseball up until their bullpen fell apart in the eighth. The Mets took their best shot, but in the end they did not step up as a team. A tough loss.

Mets @ Phillies

It's the bottom of the sixth now as I watch some baseball on TV. I do enjoy watching Jamie Moyer pitch (nullus).

Speaking of nullus, on this installment of "Baseball is Gay," someone earlier was talking about Merkle's Boner, and just now Keith Hernandez told us about how much he loves The Rose with Bette Midler.

Update: Specifically, he was talking about when he was in high school and went to see The Rose at the Ziegfeld theater because they had the best sound system.

I haven't been watching baseball!

Looking at my blog posts, it appears that it's been eleven days since I've even caught a game on TV! I have been txting up a storm when I remember that a game is on, but there's just been so many social things going on, and in such good weather, that I haven't sat down to enjoy a broadcast in almost two weeks. I think hanging out with real people in real life has got to trump watching imaginary people play a game on television, so no regrets.

Maybe I will try to view the Mets/Phillies game this evening, perhaps after visiting the gym or going for a post-work bike ride (I'm supposed to be training for a century ride that's coming up). And it looks like I will at least get to see the Cyclones host the Yankees in a day game on Labor Day. The NY-Penn season is almost over! I wonder if playoff tickets will be gettable...it looks like Staten Island is going to take the Wild Card.

Checking Scores via Text

Last night I was having dinner at friend Dorothy's house. Her and Robert had cooked up some amazing medallions of pork in a Tuscan style (I think), served with a salad of asparagus (both colors!), anchovy, and poached egg. It was so awesome.

Anyway, because I am a ridiculous boor, at
one pointseveral points I checked the score of the Mets game, using a service I found out about a couple weeks ago where you text "score Mets" to GOOGL and they text back the current box score a few seconds later. I reported the score to all those who were interested (nobody) and Robert asked how I'd checked it. Robert works for MLB and Dorothy for Google, so I told him that Dorothy was eating his lunch.

So he told me to try texting "Mets" (no "score" required! Think of the time I'll save!) to MLB-GO. I tried it, and damn! It was so much better! Not only do they give you the box score, but you get the names of the pitcher and batter and the current count. And the response fits in a single text message, whereas Google always seems to send me two-page responses.

So there's my plug. It's for a free product of a monopoly, so I don't think my endorsement matters one way or the other. Oh, and my poor Mets fell to the dastardly Padres.

Pitching (nullus)

Last night Peter and I had a small bite to eat at the sports bar around the block from my house. Peter had a copy of the latest Times' "Play" magazine, which is like a sports insert they do on Sundays. But it had this cool little article on pitching where Mike Mussina laid out how he pitches in different situations, which pitches he throws and how they work, and how the strike zone has been affected by computer-aided umpire evaluation. The online version is not nearly as cool, because the really neat part of it were the illustrations of the strike zone, where the pitches were thrown in the different batter examples, and the different grips for pitches. Worth checking out, especially if you have the hard copy lying around.

Mets @ Nationals

The game is still ongoing. Indeed, it is even at a dramatic point where it is the bottom of the seventh with one out and the tying run at bat (is that how you say it? Dude on base is not the tying run). So I guess this qualifies as "live" blogging, except that instead of talking about what is actually happening in the game—because that information is available on television and radio and the internet—I am going to talk about the broadcasters. Again.

Okay, now the tying runs are on base.

Alright, broadcasters. Are they allowed to drink on Saturdies or something? They seem unusually punchy. I didn't catch how it started, but there have been like nonstop cracks about Gary Cohen's alma mater being Columbia. I guess it's a hippie baiting thing. He was probably an actual Marxist at that time, so I guess it's fair.

And then there was this conversation about what the best kind of stirrups are. "Hey, bet you like those stirrups?" "Those are the ugliest stirrups! We always hated those." I love how often they "dish" on uniforms. Baseball, so gay.

And then there was this part where for some reason (playing in DC?) they showed an Abraham Lincoln bobblehead (I heart USA), and one of them was like "wow, he looks grumpy" or something along those lines. Which, granted, not extremely clever observation. But homeboy's response was: "well, you would have looked like that if you'd been president at that time. Really tough presidency!" Uh, yeah. I guess the worst time to be president is, by definition, the time when the president is being assassinated.

The tying runs were left stranded!

I don't know, maybe I'm misreading the Lincoln thing. The comment only really makes sense as being humorously understated, but it still seemed off. Anyway, those stirrups, don't get me started. And I love the way this guy swings!

Little League World Series

I'm watching Saudia Arabia and Canada on ESPN right now. No pedo. The just had a funny bit where they caught Canada's first-base coach telling the runner on first that, with the bases loaded and two out, he should "run on anything except an infield fly." D'oh.

Williamsport seems like a good place for baseball fans, with the LLWS and a Phillies affiliate in the NY-Penn League.

Mets @ Nationals

I watched the Mets play on my TV. Some friends went to the Yankees game to see them play Detroit, so in between innings I'd switch over to that to see if I could catch a glimpse of them. I haven't so far, but the game was rain delayed so it's still ongoing, and maybe I'll luck out. Sadly, the Tiges are not faring as well as my Mets did down in Washington. One more inning, guys, you can do it!

Update: They didn't do it, sadly. Not sure what happened, they just seemed to collapse in the later innings. The effects of that flu, perhaps? But afterwards I did go to karaoke and dedicate a Pearl Jam song to the M's, who pulled out a win as a result. All in all, a victorious day.

Mets @ Pirates

I watched the first six or seven innings at home, then met up with some of the gang for Brunch Club: Nights and saw the last bit there. My dear New York Mets were I think a run or two behind for most of the game, but they were always putting guys in scoring position, so it was just a matter of time. Well executed.

I was surprised to see El Duque's visible irritation with his play. I guess I haven't seen him run into trouble like that before, and I would have guessed he'd remain stony-faced about it, as part of his whole thing is how intimidating and aloof he seems.

PNC Park looks really cool. Too bad the pinball championships that are held in Pittsburgh don't happen until after regular season play.

Mets vs. Braves

I guess I forgot to post about the game I watched on TV yesterday afternoon. Do I really need to post about each game I watch or listen to? I do. But yeah, my Mets were defeated, I was so sad. Current mood: so sad.

Mets vs. Braves and Women Sports Fans

What a game, right? I actually missed the top of the sixth in the transition from living room to the sports bar around the corner, so I don't even know how they got their three runs over on what seemed to be a tight Mets defense throughout. Or until the ninth, anyway. Still, awesome game. No homo on this, but does it count as small ball when the winning run is a homer? Whatever it's called, it's fun baseball to watch.

Unrelated, but a blog post that was somewhat tangentially baseball-related prompted a user comment linking to an older discussion on a (booooo) Yankees fan blog that is more or less about what sexist boors Yankees fans are. No surprise there.

Anyway, I read this several days ago, and aside from thinking that I probably know more women baseball fans than men (and that Peter and I are more likely to discuss the history of uniforms than statistics), I didn't give it much thought. But when I woke up this morning, the phrase the Bronx Banter guy used to characterize the sexist conversation happening around him—"[l]et's make fun of women because they don't have a clue when it comes to sports"—came back to me. What a hilarious thought! And my favorite defense (offered by multiple commenters in the original blog post) is that, well, for at least some sports, most of the knowledgeable fans really are men, so what's sexist about saying so? Even more hilarious!

Grant that the premise is true: women, in general, don't know or care anything about baseball. Well, we could say the same thing about, say, Dungeons and Dragons, or prog rock. Sure, there are dozens of women who play tabletop RPGs or listen to King Crimson, but they are scattered across the population and therefore sparsely represented. These pursuits are hugely male-dominated. But what would we say about a 14th-level paladin who sought to "make fun of women because they don't have a clue when it comes to" rolling for initiative? We would quite rightly identify the speaker as an insufferable dork, a hopeless geek who probably has a chip on his shoulder from not getting laid.

Not only that, but if we perceive that kind of attitude as widespread in the worlds of tabletop gaming, then that perception functions as an indictment of the entire hobby, and women's lack of participation is completely justified, a rational reaction to an environment hostile to women. It's like making fun of black people for not playing golf: this kind of inequity can not only not be made light of, it must actively be lamented, lest the male prog rock aficionado or white golfer immediately be suspected of getting into a hobby because of who it excludes.

But anyway, I don't grant the premise, as men don't at all appear to be overrepresented in the population of sports fans, but merely in the population of people who can only talk about or form relationships over sports. I.e., the population of geeks. Which, yeah, we've had a lock on since probably while most of the cavepeople were out bringing down a mammoth, these two cavedudes were out looking for specimens, making fun of women who didn't know the first thing about stone collecting.

Update: I forgot to mention something I noticed at the bar as I checked out the scores across the rest of baseball. First, watching the Yankees get whooped as my Mets came back to win was a treat. But then Seattle also won while Detroit lost, putting the M's ahead in the AL wild card race. So all my teams won and all my anti-teams lost. Awesome.

Glavine

Managed to catch some of the game at a restaurant. My friends ordered food, but I took my sustenance from nonstop baseball action with a side of sweet, sweet victory. Cool!

Mets @ Cubs

Great game. I was really looking forward to this, just from reading about the pitching matchup, and I wasn't disappointed. Zambrano was erratic but fun to watch, and El Duque was great. All around, both defenses seemed to play pretty tight for most of the game. The cracks that started showing in the eighth opened right up in the final inning, and for a minute it seemed like every pitch was another Mets hit. The Cubs seemed like they might be starting a rally in the bottom of the inning, with some sloppy fielding on the part of the Mets, until a double play took the wind out of their sails. A really satisfying and dramatic 6-2 victory for my dear New York Mets.

Unprecedented

Here at work, in my living room, I had the Yankees game on while I was waiting for first pitch in Milwaukee. Haha, the hated Yankees, down eight in the top of the second! And they were bringing on ex- and sub-[M]ariner Mike Myers for one batter! And then they tied it up in the bottom of the second! What!

As the inning came to a close, one of the announcers confirmed that coming back in the second inning after trailing 8-0 was unprecedented in MLB history. Andrew and I were talking about this on Sunday while debating the relative merits of baseball and soccer. Even as I made the argument that something extremely rare or even unprecedented happened in the course of almost every baseball game—and hence, baseball is interesting—I realized that, while true, it was sort of a foolish point.

Baseball is a game of discrete events: there's no timer, you always bat or pitch from the same place, and run from one of three places. This is fundamentally unlike basketball, soccer, or football, which are mostly games of continuous times and distances. Great quarterbacks complete lots of yards of passes, whereas great batters bat in lots of runs. I think this is one aspect of baseball that makes it so uniquely ripe for statistical summary and analysis (another is the sheer amount of gameplay in a season, which provides such a great sample size for statistical measurement).

This essential discreteness is also the reason for the number of unusual events in the game. Or rather, the reason said events are recognized when they happen. To use the sport of the original discussion in an example, a certain sequence of passes in a soccer game, with the participating players in certain places and striking the ball in certain ways, may be highly unusual, or even unprecedented, but spectators are unlikely to identify it as such because there is no system for recording that kind of sequence in an abstract way for later reference.

There is no analogue in most sports for the baseball scoresheet, a succinct account of every important thing that happened in the game. You can report the number of goals scored, the time spent by each team in possession of the ball, and the substitutions made and cards given, but this doesn't convey a complete picture of the game as it was played. Baseball box scores don't either, of course, not completely, but they come a damn sight closer. A detailed pitch-by-pitch scorecard portrays a baseball game nearly as well as a move-by-move written record does a chess match.

The key events of a baseball game can be abstracted, which means they can be recorded, which means they can be remembered. In the end, I don't think it's an unqualified strength of the sport: "chesslike" is not an objectively desirable quality in an athletic competition. But it does distinguish baseball from anything else, and I for one do take pleasure in seeing the unusual happen in nearly every game.

Update: Easley just hit a two-run inside-the-parker. Don't see that every day.

Baseball Buddy

Waiting for friends in the city last night, I decided to look for a place to eat that was showing baseball but wasn't too crowded. I had sort of resigned myself to a bar-n-grill type establishment, so I sort of lucked out when I stumbled across a sort of a hippie fusion place. They were out of the ostrich curry, but the catfish tacos proved a fine choice.

The Yankees were on, and I was sort of annoyingly asking the bartender to change it to the Mets game, forgetting that of course A-Rod was shooting for number 300. But the bartender, himself a Yankees fan, was very accommodating and changed it back and forth throughout the evening. The only other person interested in either game was this guy sitting next to me, who was very friendly. He was also a Yankees fan, and talked a bit of anti-Mets trash, but with both New York teams winning, nobody was really upset. He was from Belize, told me he was a sports fan, an alcoholic, and a marijuana dealer, and he showed me pictures of his 7-day-old daughter on his ESPN-branded phone.

Anyway, no real point to this story. I guess I've had plenty of similar conversations with total strangers...you're hanging out alone and you just start talking to someone about something. Sports is just another hook on which to hang a temporary hat of friendship. Which is fine. And the Mets won.