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May 14, 2003
by Nate Silver
Your favorite player hit .360 last season. If you know nothing else, what can you expect him to hit this season? This isn't meant to be a trick question; let's assume the guy had at least 500 at bats in the previous season. Gates Brown and Shane Spencer need not apply. What's your best guess? .350? .340? Not likely. The evidence is overwhelming. Let's look at all hitters since WWII who hit .350 or better in at least 500 at bats; the only other requirement is that they had at least 250 at bats in the year following.
May 8, 2003
by Jonah Keri and Nate Silver
Toldyaso.
It doesn't matter whether your game is roto, Strat, Scoresheet, or fantasy NASCAR: Drafting for value is the right way to go. Cute little strategies might help to break a tie, and a mastery of bidding psychology can matter at the margins, but sound player evaluation is the name of the game. Between the PECOTA projections and the Will Carroll Walking Injury Database, we felt that Team BP was in an in ideal situation to leverage our edge in information into success in Tout Wars. The results so far have been affirming: in spite of some disappointing individual performances, we're in first place by a healthy margin.
It's too soon, of course, to come to any conclusions about how the standings will end up--hell, it's early enough in the season that Carl Everett hasn't even been suspended yet. Still, there are a few take-home lessons from the season thus far, as embodied by some of our more successful acquisitions and strategies.
May 7, 2003
by Nate Silver
The baseball season has reached its adolescence. Oh sure, there are the still the occasional temper tantrums, the delusions of grandeur, the fashion faux pas. But the season has been around for long enough that we can't totally dismiss it, even when it mouths off without reason or, convinced of its own invincibility, it pushes its limits a bit too far.
The PECOTA system wasn't originally designed to update its forecasts in real time, but through some creative mathematics we can adapt it to that purpose. In particular, we can evaluate its projections by means of a something called a binomial distribution (geek alert: if you're uninterested in the math here, the proper sequence of keystrokes is Alt+E+F+"Blalock"). The binomial distribution is a way to test the probability that a particular outcome will result in a particular number of trials when we know the underlying probability of an event. For example, the probability of a "true" .300 hitter getting six or more hits in a sequence of 15 at bats is around 27.8 percent. (The binomial distribution's cousin, the Poisson distribution, has a cooler name but is less mathematically robust).
A couple of important objections are going to be raised here. First, the binomial distribution is designed to test outcomes in cases in which there are mutually exclusive definitions of success and failure--for example, "hit" and "out," or "Emmy Nomination" and "WB Network." The measures of offensive performance that we tend to favor don't readily meet that criterion. Second, the binomial distribution assumes that we know the intrinsic probability of an event occurring, as we would with a dice roll or coin flip. But we never really know what a baseball player's underlying ability is--we're left to make a best guess based on his results, presumably coming closer to the mark as the sample size increases.
The first problem has an intriguing, if mathematically sketchy solution in the form of Equivalent Average, which is scaled to take on roughly the same distribution as batting average, even though it accounts for all major components of offensive performance. So, we could test the probability of a "true" .300 EqA hitter putting up an EqA of .400 in 15 plate appearances by assuming that this is equivalent to six successes (40%) in 15 trials. Since I haven't heard any objections, let's roll with it.
April 30, 2003
by Nate Silver
You've been hanging 'round these parts long enough. You've heard the party line, once or twice or 20 times: Higher payrolls don't result in higher ticket prices. Correlation is not causation. Salaries don't shift demand curves. It's Economics 101. Simple, textbook stuff.
The problem with this line of argument--the problem with a lot of economically-based arguments--is that it's easy to let the theory get ahead of the data. Well, I should state that more precisely: It's easy to let an oversimplified theory get ahead of the data. A lot of what you learn in Economics 102, and Economics 201, and graduate-level classes that I was too busy drinking Boone's Farm to take advantage of, is that much of the theory you master in an intro-level class is based on a particular set of assumptions that can prove to be quite robust in certain cases, and utterly misleading in others.
A lot of people shun economics for this very reason--we've all had coffee shop conversations with the scruffy, Skynard-mangling philosophy major who is fond of spewing out faux-profundities about the irrationality of human nature. He's missing the point, of course, but so too is the Ayn Rand-spouting prepster from down the residence hall who conflates assumptions with hard rules.
In either case, a little bit of knowledge is a dangerous thing. Economics, though it sometimes harbors pretensions to the contrary, is above all else a behavioral science, and an empirical science. If the theory doesn't match the data--well, it's not the data's fault. This is especially important to keep in mind when evaluating something like ticket prices to baseball games, a commodity that is unusual in many ways. As we've stressed frequently, ticket prices ought to be almost wholly determined by demand-side behavior--the marginal cost of allowing another butt in the seats is negligible. But baseball tickets are unusual in other ways, too: They're very much a luxury good, and their prices are determined by a finite number of decision-makers who may be subject to conflicts of interest. It's certainly worth evaluating the available data to see whether we can put our money where our mouth is.
April 23, 2003
by Nate Silver
Silicone. Margarine. O'Doul's. Why fool around with watered-down imitations when you've got the real thing ready and available?
Rightly or wrongly, a lot of attention has been focused on pitch counts in the past several years. That's partly because of the efforts of people like Rob Neyer, Keith Woolner, and Will Carroll, not to mention those coaches, executives and agents who understand the importance of protecting their golden-armed investments. Pitch counts have become easy to take for granted because pitch count data is more readily available now than it ever was in the past. These days, just about any self-respecting box score lists pitch counts alongside the rest of a pitcher's line, a far cry from the dirty newsprint days of yore, when pitch count references were about as common as mentions of Reality TV or the Information Superhighway.
But what about when you don't have pitch count information available? Like, say, you're at a ballgame, and wondering whether Dusty Baker should send Kerry Wood out for another inning? Or you're perusing through minor league stats? Or you're looking at old boxes on Retrosheet, which wonderful as they might be (this, folks, was the first game I ever attended), don't contain any information on pitch counts?
Well, it turns out that it's not that difficult to make a reasonable guess at pitch counts based on other information that's much easier to come by. Looking at a complete set of data from the 2001 and 2002 seasons as provided by Keith Woolner, I ran a simple linear regression of pitches thrown against various other characteristics of a pitcher's stat line. Here was the formula that I came up with:
April 16, 2003
by Nate Silver
In last week's 6-4-3, Gary Huckabay wrote about the fact that our perceptions are more often colored by the way information is presented than by the substance of the information itself. There are plenty of examples of this, drawn both from the ballpark and the world at large. Get your hands on most any media guide, and you're sure to see the familiar rotisserie categories--batting average, home runs, RBI--presented prominently in bold face. Now, a typical media guide runs about 400 pages, and there's plenty of information to go around, ranging from the trivial (Mike Lincoln's career ERA at Busch Stadium is 14.29) to the frivolous (Joe Borowski's wife is named Tatum). Thus, should it really be that much of a surprise to find out that in the thick of that pulp forest, the people who rely on media guides to grab information on the fly--like beat writers pushing on a deadline and radio announcers trying to keep a cadence--gravitate toward those bits of knowledge that are literally staring them boldly in the face?
April 9, 2003
by Nate Silver
What's the best pitcher in the world worth?
Let's imagine for a moment that Pedro was right now putting his 2004 services up on the open market. Of course, that's not what he's doing--but indulge me for a moment.
April 2, 2003
by Nate Silver
Nate Silver examines PECOTA's five-year forecasts. Guess who PECOTA picks as baseball's MVP over the next five years. You'll be surprised.
March 26, 2003
by Nate Silver
The nerdiest part of our preseason blitzkrieg, this is the second of two articles describing the final standings in each league as compiled based on our PECOTA forecasts.
March 21, 2003
by Nate Silver
After using PECOTA-generated roto values at the recent Tout Wars National League draft, Nate Silver runs the numbers to produce values for the AL. Hint: as in the NL, pay the premium for studs. And do everything you can to get Pedro.
by Nate Silver
Fresh off PECOTA's maiden voyage into rotoland, Nate Silver publishes the PECOTA-generated roto values used by the BP team at the recent Tout Wars National League draft. Hint: pay the premium for studs.
by Jonah Keri and Nate Silver
What happens when Nate Silver's PECOTA system joins forces with Jonah Keri's boundless energy and Will Carroll's injury encyclopedia? You get a killer roto team...maybe. Read on to see how BP fared at this year's Tout Wars National League draft.
March 19, 2003
by Nate Silver
The PECOTA system acknowledges that there is a wide range of variance intrinsic to any set of forecasts. What's more, there's no reason to expect that this variance will be unrelated to the team that a player toils for. On the contrary, there are myriad anecdotal examples of entire teams who routinely fall toward the top or the bottom of their forecast range. Under Dusty Baker, the Giants have consistently gotten more production than would reasonably be expected from a set of thirtysomethings. Under Leo Mazzone, the Braves have consistently turned waiver wire fodder into good or even great bullpen arms.
Indeed, it's possible to conjure up an argument like that for just about every team, and some of the time, you won't even be BSing. Translating player projections into team forecasts is an exercise that caters mostly to the left side of the brain; you're sure to see some more creative solutions in the coming days as we publish the BP author forecasts, crazed opium dreams like the Cubs taking the pennant. I have myself deviated from the HAL 9000 version in quite a number of cases. Nevertheless, we've never had anything quite like PECOTA before, and it's worth seeing what it has to say.
March 12, 2003
by Nate Silver
Moving a top-notch reliever into the starting rotation is neither a new nor a particularly unusual idea. The Indians and Orioles experimented with moving Hoyt Wilhelm into a starting role in 1958, which culminated in a nationally televised no-hitter. Bill Lee and Wilbur Wood began their major league careers as relievers; Goose Gossage received a one-year trial as a starter; Rick Aguilera logged 89 career starts. Derek Lowe, of course, made a successful conversion last year, which may have helped assuage any misgivings on the parts of Bowden and Garagiola.
What's interesting about this year's guinea pigs is that Graves and Kim are radically different pitchers. Both were born in the Far East and allow very few home runs; that's where the similarities end. Graves, statistically speaking, is a finesse pitcher--perhaps the most successful finesse closer since the beloved Dan Quisenberry. Kim is a fire-and-brimstone submariner, striking out a quarter of the batters he faces, sometimes at the cost of allowing others too many free passes.
March 5, 2003
by Nate Silver
Do day games really set the Cubs up for failure? To answer the question, I consulted Retrosheet game logs for each game played from 1997 to 2001 (Retrosheet doesn't have the 2002 data ready just yet). The first series of numbers I ran looked at every team except for the Cubs, with data broken down between day and night games, as well as various permutations on what the team's schedule had been like on the previous day (afternoon game on the road, and so forth). In the table below, I've provided the home team's winning percentage based on each condition.
February 26, 2003
by Nate Silver and Will Carroll
Between a careful analysis of what data is available, the creative use of proxy variables in estimating injuries throughout time, and the application of some principles of sports medicine, we are at least in a position to make some educated guesses about the nature of pitcher injuries. Our particular focus in this article will be the progression of pitcher injury rates by age.
by Nate Silver and Will Carroll
Pitching is an unnatural act that invites injury. The stress it places on the
bones of the shoulder, arm, and back is immense. The strain it places on the 36
muscles that attach to the humerus, clavicle, and scapula is remarkable. It is
widely accepted by sports medicine practitioners that every pitch causes at
least some amount of damage to the system.
February 21, 2003
by Nate Silver
There is enough evidence to perform at least an exploratory empirical analysis of what types of skills are best accentuated by Coors Field.
February 11, 2003
by Nate Silver
As pitchers and catchers report to sunny climes this week--soon to be joined by hitters, beer vendors, and spring breakers--much will be made of the battle for the five slots in the New York Yankees' starting rotation.
February 6, 2003
by Nate Silver
No, the most contentious sports battles of February are fought not in football rinks or hockey stadiums, but in hotel conference rooms in Tampa and Phoenix, where owners and agents will square off against one another all month long in a series of arbitration hearings that will be fully nasty enough to recall the high period of the Gorgeous Ladies of Wrestling circuit, except without quite as much hair-pulling.
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