[Dr. Giganto]

This site (baseballprospectus.com) is basically the home base (no pun intended) for progressive baseball thinkers and those with an interest in advanced statistical analysis. Although most of the material is on the nonn-free section of the site, they have a bunch of articles that serve as an introduction to what they do, and some of their beliefs. I figured I would post them here, and when I'll just post in this thread when I see cool stuff on there:

Baseball Prospectus Basics: Introduction


If you're not familiar with Baseball Prospectus, here's what we're all about: understanding the game better, and innovating in order to do it. Everyone at BP loves the game of baseball with a passion that most people just don't understand. We feel that this greatest of games is so compelling that we want to know everything about it. We always want to improve our understanding of the game; each player, each play, each pitch, each throw, each hit--what does it really mean? Those arguments that take place in bars about the relative merits of different players? We really want to know the definitive answer to those questions. But we don't want to kill the joy of the game while we're looking.

To help better understand what we're all about, we're launching a series of articles, entitled "Baseball Prospectus Basics." This series seeks to make our work more accessible to new readers, and to remind those familiar with our work of the underlying concepts. As Keith Woolner's recently published "Hilbert Questions" article noted, there is much work still to be done.

We want to be able to compare players on an apples-to-apples level. Most every baseball fan understands, at least on some level, that it's easier to hit .300 in Coors Field than Dodger Stadium. We calculate how much easier it is, and allow you to see the players' performances without the distortion of park and league effects. It's not a very complicated idea, but it can be kind of daunting at first. As part of the Baseball Prospectus Basics series, BP's Clay Davenport will take you through the steps we take to adjust for ballpark effects, as well as the effects of hitting and pitching in different eras of major league history.

There's more. What's wrong with traditional stats like wins? Are there better ways to look at a pitcher's performance? BP's Michael Wolverton will take a closer look. Why not use the Triple Crown stats we all grew up with to compare hitters to each other? Is there a better way? We'll look at Baseball Prospectus statistics such as Keith Woolner's Value Over Replacement Player to find out.

What can managers do to make better use of their bullpens? Is there a better way to evaluate defense? Does clutch hitting really exist? We're always asking these types of questions, and over the next few weeks, we'll look at possible answers with you.

To a great extent, Major League Baseball has been insulated from many of the competitive pressures that other businesses face every day. Modern management techniques have been slow to arrive in MLB front offices. The intense pressure that drove millions of businesses to invest and focus on improvement has been absent, or at least barely noticeable in baseball circles.

Not anymore. The information revolution has finally arrived in baseball. Teams are learning better, more efficient ways to build winning rosters. They're asking many of the questions we'll be asking in Baseball Prospectus Basics, plus many more. By questioning conventional wisdom and looking for new solutions, we hope you'll develop an even greater love and appreciation for the game of baseball. As the game progresses, your favorite team will acquire a player or make a move that may not be popular in many circles; meanwhile, you'll nod your head knowingly and smile.

Will the search for new answers damage the game? Will its poetry be lost in a blizzard of derived numbers? Not in the slightest. The game is going to be better than ever before. Because better players will be playing. As defense is evaluated more and more effectively, teams will value it more highly, and you'll see better defense on the field. Teams will pass on the rickety veteran with the brand name in favor of the unknown independent league slugger, and you'll see better hitting on the field. As we learn better ways to manage pitchers, teams will experience fewer injuries and greater success, and you'll see greater pitching on the field.
And that's the way it should be. Life's supposed to get better, not worse. We want the same for baseball.

[Dr. Giganto]

Baseball Prospectus Basics: Reshaping the Debate
by Joe Sheehan


"Stathead."
"Stat-drunk computer nerd."
"Rotisserie geek."

You can earn a lot of derision when you look at things in a new way, and the people who have applied statistical tools to evaluate baseball players and teams have heard the above epithets and more. The work of people such as Bill James, Craig Wright and Clay Davenport has often been dismissed as the mind-numbing analysis of people who need to put their slide rules away and get out and watch a game once in a while. Their efforts, which have been dubbed "statistical analysis," have expanded and improved the body of objective baseball knowledge, and their work is even beginning to penetrate the insular world of baseball front offices.

But the term "statistical analysis," as applied to baseball, isn't descriptive enough. Actuaries analyze statistics, and while the work pays well, it is pretty dry stuff. Life-expectancy tables and risk/benefit workups aren't going to get your average Red Sox fan excited, nor should they: baseball fans care about their teams, and the players on them, not a series of numbers.

But baseball statistics are not numbers generated for their own sake. Statistics are a record of performance of players and teams. Period. Benjamin Disraeli's oft-quoted line--"There are three types of lies: lies, damned lies, and statistics"--just doesn't apply.

Looking at statistics--looking at the record of player and team performance--helps analysts reach conclusions about players. So when Rany Jazayerli writes that
Jose Rosado is one of the 10 best starting pitchers in the American League, that's not an analysis of statistics, that's an analysis of performance. In the same way that a scout watches a player run and decides whether he's fast or slow, analysts look at a player's EQA and determine how good a year he had. That's performance analysis, a more descriptive term for the work we do.

The distinction is critical in moving this type of baseball analysis from an outsider view to the mainstream, so that in the front office of a major-league team it can be as acceptable to look at a player's on-base percentage as to look at a scout's opinion of his foot speed. Organizations need to credit a pitcher for his consistently good Triple-A performance in the same way that they mark him down for his below-average fastball.

Reshaping the debate between traditional baseball people and the analyst community will give a significant push to what is currently a creeping movement. If you look at the success of the New York Yankees of the late 1990s or the 1999 Oakland A's, it's clear that some teams have embraced one of the fundamental tenets of baseball analysis: the importance of on-base percentage in scoring runs. In fact, the A's have become the first organization to emphasize plate discipline in their player-development program.

We have seen the work of Wright and Rany Jazayerli on pitcher usage, particularly young-pitcher usage, start to make inroads within the game. Teams have become increasingly aware of the workloads they put on their best pitching prospects, recognizing relationships between workload and injury and workload and ineffectiveness. Given the significant investments that organizations make in their top talent, this is a prime area in which baseball analysis can make a financial impact as well as an on-field impact.

Performance analysis does not, and should not, exist in a vacuum. First of all, it is important to understand the context of statistics, and the Davenport Translations you see in this book are prima facie evidence of this. The line ".280/.350/.450" is about as informative as a George W. Bush campaign speech. At what level was this performance? How old is the player? In what park and what league does he play? What position?

And once you have all those answers, you still have only half the picture. Every player has a skill set, abilities that make him the player he is. Each player has certain strengths and weaknesses. Skills analysis--the province of scouts, managers and coaches--isn't made obsolete by performance analysis. It's enhanced by it.

Knowing that a 23-year-old right-hander has a live fastball, a middling curve and a change-up he can spot at will is essential. A pitcher's repertoire, a hitter's bat speed, a short-stop's arm...if you're going to develop a complete, accurate picture of any player, you must know these things. But you also want to know if the pitcher has an acceptable strikeout rate, because that's the best predictor of career length. You want to know if the player can drive the ball, as measured by his slugging percentage and isolated power. And if that shortstop is among the league leaders in assists and double plays, it's an excellent indication that he is great at using his arm to get outs. Isn't that what fans and general managers really want to know?

Performance analysis has limitations. Amateur baseball players, with aluminum bats, shorter schedules, and widely variable levels of competition, are best analyzed by their skills. Performance analysis of players in short-season leagues is also unreliable, both because of limited sample sizes and the adjustments that the players, usually new to professional baseball, are making. Given a choice between a scouting report and a Davenport Translation on an 18-year-old with 200 plate appearances in the Gulf Coast League, the scouting report will be a better tool.

Performance analysis paired with skills analysis is how successful teams are going to be built in the 21st century. Good organizations will accept that there's as much to be gained from looking seriously at a player's track record as there is from looking at the scouting reports on him. Successful teams will be built on principles that have developed from performance analysis. Ideas that were radical just 10 years ago will become conventional wisdom, as people like Billy Beane have success, and as other organizations imitate what made the A's successful.

Reshaping the debate continues a cycle that began with Branch Rickey's conclusions about on-base percentage and continued through Bill James's work in popularizing sabermetrics. It provides a means for the baseball mainstream to embrace the concepts of performance analysis while maintaining their established, valuable methods of skills analysis. Eventually there will be no debate, as both will be used routinely in evaluating talent and building baseball teams. A better brand of baseball for everyone will be the ultimate legacy of performance analysis.
Joe Sheehan is an author of Baseball Prospectus. You can contact Joe by clicking here or click here to see Joe's other articles.

[Dr. Giganto]

Baseball Prospectus Basics
Measuring Offense
by Dayn Perry


Before delving into those harrowing inhabitants of the Baseball Prospectus statistics page like VORP, RARP, EqA or any other acronym that sounds like a debutante sneezing or something uttered on Castle Wolfenstein circa 1986, it's worth asking: What's wrong with those comfy traditional offensive measures like RBI, batting average and runs scored?

This Baseball Prospectus Basics column is going to address that question and, ideally, demonstrate why the traditional cabal of offensive baseball statistics tell only a piece of the story. Later, someone smarter (but shockingly less handsome) than I will take you on a tour of the more advanced and instructive metrics like the aforementioned VORP, RARP and EqA. For now, though, we'll keep our focus on why we need those things in the first place.

Many of the stats you encounter in mainstream baseball circles are what we call "counting stats." That is, they count things: 23 homers, 107 RBI, six triples, etc. This may sound painfully obvious, but the more a hitter plays in a given season, the higher his counting stats are likely to be. Some counting stats, like RBI and runs scored, are highly team and batting-order dependent. A cleanup hitter logging 600 plate appearances in a potent lineup must work very hard not to rack up at least 100 RBI. Whereas a leadoff hitter on an otherwise weak offensive team won't crack the 100-RBI mark no matter how effective he is. If a superior player is surrounded by weak hitters, it's entirely possible that he'll cash in on a much greater percentage of his RBI opportunities and still have a lower RBI total than a lesser player in a stronger lineup.

The thing to understand about counting stats is that, absent supporting information, they're really only useful at the margins. That's to say, it's hard to rack up 140 RBI and somehow stink. Conversely, it's difficult to log a season's worth of plate appearances, total 40 RBI and somehow be any good.
The flip side of this is that it's entirely possible, especially in eras conducive to run scoring, to break the vaunted 100-RBI barrier and still be an ineffective player. It's debatable what the worst 100-RBI season is, but Ruben Sierra in 1993 may be hard to beat. More later on why he was a lousy player that season.

So, highly context-dependent counting stats like RBI and runs scored can be inflated or deflated by a panoply of factors that have nothing to do with that hitter's true abilities. One of the prevailing missions of sabermetrics is to evaluate the player in a vacuum: What's he doing independently of his teammates and environment? Using only RBI or runs scored to judge a player or to frame an argument at the tavern is a fool's errand.

Home runs, since they have almost nothing to do with a hitter's teammates, are more reliable than RBI, but they're still not an ideal metric. It's fully possible for a player with fewer home runs than another to be a far superior player. How's that? Again, it's context. Home runs (and singles, doubles, triples, etc.) aren't lineup- and teammate-dependent like RBI and runs scored, but, like any other unadjusted statistic, they are dependent upon the ballpark and, when comparing players across history, the era (more on park and league effects later in this series).

Another factor to consider when comparing hitters is the notion of positional scarcity. This is the idea that it's easier to find good hitters at the less demanding defensive positions than it is at those positions that require a great deal of skill with the glove. The less demanding positions are the corner slots: left field, right field, third base and first base. The more exacting positions are those up the middle: catcher, shortstop, second base and center field. Up-the-middle defenders handle more balls and cover more ground than corner players, or, in the case of the catcher, they have defensive duties distinct from those who man other positions.

So if a first baseman and a shortstop have identical offensive statistics and equal defensive abilities relative to their positions, who's the better player? The shortstop, because the offensive-productivity bar for shortstops is notably lower than it is for first baseman, since it's far easier to find a good-hitting first baseman than it is a good-hitting shortstop. Generally, from highest level of positional scarcity to least, the positions go shortstop, catcher, second baseman, center fielder, third baseman, right fielder, left fielder and first baseman. Those can vary from year to year, but most seasons up-the-middle defenders who can hit will always be rarer beasts than corner players who can hit. This is why Alex Rodriguez is such a special player: He hits like an All-Star first baseman, yet he plays the most challenging defensive position on the diamond, and does it well to boot. Again, many stats you'll find on this site are already adjusted to reflect the demands of the position.

And what of batting average? Well, it's a percentage stat and not a counting stat, so it has a somewhat different set of concerns and caveats. First, it's subject to sample-size errors. To provide an extreme example, a hitter who goes one for three on Opening Day and one who plays the entire season going 200 for 600 will both be hitting .333 when you check the box scores; however, it's the latter hitter whose .333 average is more legit. Why? Because it's been borne out over time, whereas the former hitter may be a banjo-hitting fringe player who had a lucky day. (As an aside, counting stats are also prone to a different kind of sample-size error. It's the dread "on pace to" statistical distraction. When some unlikely player is, say, leading the league in RBI after the first two weeks of the season, we'll hear how he's "on pace" to put up 380 RBI on the season or some such nonsense.) Basically, if a hitter is doing something that's completely out of step with the rest of his career, you should be skeptical and demand a larger sample before you buy into those reports that his stroke has been tweaked or how he's seeing the ball better since he started drinking liver smoothies. Sample size is a major principle to grasp, and you'll never look foolish by being roundly unmoved by what a player does in the first few weeks of the season.

That's not all that's wrong with batting average. As much as the .300 hitter is a lionized, what does that really tell us about a player? It tells us he got a hit of some kind in 30% of his at-bats. We have no idea what kinds of hits he got, and we have no idea how he fared in terms of reaching base by other means. We don't even know how many times he came to the plate.

When dealing with percentage statistics, having at least a rough idea of the number of plate appearances is essential. And as far as batting average goes, you can tell much more about a player if his average (AVG) is presented along with his on-base percentage (OBP) and slugging percentage (SLG).

OBP is how often a player reached base via hit, walk or hit by pitch; among traditional offensive statistics, it's the most important. The higher a player’s OBP, the less often he’s costing his team an out at the plate. Viewed another way, 1-OBP = out %. In other words, OBP subtracted from the number 1 will yield the percentage of how often a hitter comes up to bat and uses up one of his team’s 27 outs for that game. A player can play all season, rack up impressive counting stats and still be using up far too many outs.

SLG measures a player's power, albeit not perfectly. It places more value on extra-base hits than it does on singles, and what you're looking at when you see a hitter's SLG is the total bases he averages per at-bat. For example, a player with a .500 SLG averages one-half total base per at-bat.

You'll often see AVG, OBP and SLG presented in the following format: .300/.400/.500, where .300 is the player's AVG, .400 is the player's OBP and .500 is the player's SLG. Another statistic you can glean from this "holy trinity" is Isolated SLG, which is the player's SLG minus his AVG. This expresses how much "raw" power he's producing by focusing solely on his extra-base hits. So of the trinity, AVG, which by far the most popular and heavily relied upon, really provides you with the least important information. It's good info in the presence of OBP and SLG, but by itself it's almost as useless as RBI.

What's a good OBP and SLG? Well, as we've already mentioned, offensive statistical standards depend greatly upon a player's era, home ballpark and defensive position. Generally speaking, if a player today puts up a .360 OBP and .500 SLG, he's doing his job. If he's a shortstop in Dodger Stadium with these numbers (and with an ample number of plate appearances, of course), he's an MVP candidate; if he's a first baseman in Denver with these numbers, he's nothing special. Again, context is where the rubber hits the road. (We discuss OPS, the stat that adds OBP + SLG, later in this series.)

Remember our pal Ruben Sierra and his 101 RBI from 1993? Let's go back and look at him, knowing what we know now. Yeah, there's his 101 RBI. But that season his trinity numbers were .233/.288/.390. Those are ugly, and they get even uglier when you recall that he split his time between DH and the outfield corners. That means he had little defensive value, and, hence, his offensive standard was higher than that of most players. A .288 OBP and .390 SLG are patently unacceptable for a corner defender, no matter how many RBI he racks up.

So, in summary:

• Counting stats (RBI, HR, runs scored) aren't very informative because they're highly context dependent and don't account for how many outs a player is using up.
• Percentage stats are far better than counting stats, but only in the presence of a sizeable data sample (i.e., plate appearances).
• Percentage stats are only negligibly influenced by teammates and lineup slotting, but, like all traditional statistics, they are influenced by ballpark and historical era.
• Players at the corner positions generally produce better offensive numbers than those players at the more vital up-the-middle positions.
• AVG isn't really useful unless viewed in tandem with OBP, SLG and plate appearances.
• And the greatest of these is OBP because it can also tell you how often a player creates outs at the plate.

And that's that. Like I said, there's a whole other world of statistics out there besides the ones that have been foisted upon you since you bought your first set of Topps. Now that you know what's wrong with traditional offensive statistics, you're ready to arm yourselves with the tools of state-of-the-art baseball analysis.

[Dr. Giganto]

Baseball Prospectus Basics
Statistical Consistency
by James Click


February, in the baseball world, is the month of predictions. Every analyst, writer, web site, undefeatable computer program, guy with a beer, and book (some better than others) will spend the next month looking over the offseason wasteland and espousing conclusions. The method behind these processes varies more widely than Johnny Depp's acting roles; some are based purely on numbers, some purely on empirical data, some purely on names, and some purely on nothing. So what can you count on?
For one thing, you can count on me not offering you any spectacular predictions, guaranteed to be more accurate than anything on the market. If you want that, read up on BP's own PECOTA projection system. Instead, the aim will be to lay a basic groundwork for your expectations of the consistency of basic statistics from season to season. Surmising the volatility of various metrics, and their consistency from year-to-year, is the primary goal.


To accomplish this, I'm going to start with batting statistics, which are traditionally more stable than pitching statistics. To reduce outliers and the game's inherent degree of chance, only seasons in which a player accumulated at least 200 ABs will be used. All seasons from 1991 to 2003 were considered, looking particularly for consecutive seasons of sufficient sample size. This process yielded 3066 sample seasons from which to draw data.


The variety of statistics that can be tested is understandably large, but it's important to only use rate statistics such as AVG, OBP, and SLG because the large variance allowed in ABs and PAs. For the purposes of the study, 20 home runs in 300 AB is considered the same as 40 HR in 600 AB, but the difference between 20 and 40 actual home runs is irrelevant. To this end, AVG, OBP, SLG, BB% (Walk Rate, BB/PA), K% (Strikeout Rate), XBA% (Extra-Base Hit Percentage, XBA/H), HR% (Home Run Rate), and ISO (Isolated Power, SLG-AVG) were considered. Each is a rate statistic that reveals information about certain parts of a player's composition at the plate. Looking at the results both individually and in concert will yield some conclusions about year-to-year statistical consistency.



Metric R-Squared Standard Deviation
AVG 0.1761 0.031
OBP 0.3820 0.041
SLG 0.4171 0.080
BB % 0.5745 3.520
K % 0.6884 5.230
XBA % 0.4634 8.820
HR % 0.5751 1.730
ISO 0.5510 0.064
Before we get to the results, however, first let's do some house-cleaning. To the far-left we have our offensive metrics, followed by the R-Squared, as well as the Standard Deviation. For the uninitiated, R-Squared is another term for "coefficient of determination"--a measurement of correlation. The higher the R-Squared total, the greater the correlation, and thus, the more consistent the metric. Depending on how it's being used, an R-Squared of below 0.5000 is typically considered too low to justify any sort of predictive value. Standard deviation, meanwhile, is simply a measure of variance--the higher the number, the more volatile the metric.


With that being said, of these metrics, batting average has the least consistency, and thus the least predictive ability. Meanwhile, four metrics cleared the fabled 0.5000 line--Walk-Rate, K-Rate, and HR-Rate--all of which are defense-independent. This fact supports the idea that the hitters remain consistent from year-to-year, while much of the volatility of AVG and, to a lesser extent, OBP and SLG, can be attributed to the opposing defense. Removing the defense from the equation greatly increases the predictability of batting statistics, a fact that reinforces the idea that there is a significant amount of luck involved in AVG. This finding isn't really big news, but it's always nice to reconfirm something some of us might take for granted.


(As a brief aside, it's important to clarify what is meant by batting average being subject to great deal of "luck." This is not to say that all major league hitters are equal when it comes to AVG, and the differences evident between them are entirely random. Rather, players have a theoretical AVG-ability that varies from player-to-player, but the sample size of a season is too small to accurately reveal that every year. The high volatility of AVG from year-to-year--the statistical "noise," if you will--is sufficiently large enough to obscure the differences between many major league hitters of similar ability. The book Curve Ball, by Jim Albert and Jay Bennett, has some excellent discussion on this topic.)


When looking at pitchers, many of the same constraints were placed on the data as batters. The minimum playing time for pitchers was set at 50 IP in any given season. This yielded 2695 sample seasons from 1991-2003. Statistics considered were, again, entirely rate metrics: starting with the mainstream ERA and WHIP, and moving on to K/9 (Strikeouts per 9 IP), BB/9, H/9, HR/9, K/BB, and GB/FB. (Data for GB/FB was only available from 1999 on, yielding a much smaller sample size of 912 seasons.) Let's see how it turned out:


Metric R-Squared Standard Deviation
ERA 0.1091 1.20
WHIP 0.1410 0.20
K/9 0.5627 1.82
BB/9 0.3413 1.09
H/9 0.1745 1.45
HR/9 0.1273 0.41
K/BB 0.3610 1.00
GB/FB 0.5591 0.50
If you're a regular visitor to BP, the fact that ERA is, so far, worse than any other statistic at maintaining consistency from year-to-year should be of no surprise. Its volatility is approaching almost total randomness due to the variety of game events it attempts to take into account: the official scorer's decisions, defense, the sequence of events, and pitcher's actual ability, just to name a few. Interestingly, WHIP doesn't fair quite as well as expected when comparing it to H/9 and BB/9--two statistics that should map to it rather well since they take into account two of the three stats used in WHIP. Instead, by combining two inconsistent statistics, WHIP comes out worse overall. The only two metrics that seem to have any consistent value are K/9 and GB/FB--once again, statistics that do not involve the defense.

Considering the fact that much of the blame for the inconsistency of AVG, ERA, and other statistics has thus far been blamed on the defense, it would be unfair not to check and see how variable defense is. Measuring defense, though, is sticky business. It's best to read the results below with large grains of salt, constantly reminding yourself that defensive statistics don't always reflect the events on the field, and that defense is inherently a team activity. Adjusting for players switching positions over the course of the year also threw a wrench into the works.



The sample group was once again drawn from the same years, but the caveats included having to accumulate at least 100 innings at any one position. Further, if players accumulated over 100 innings at more than one position, those positions were only considered together if they were similar defensively. For instance, a player who played 200 innings in RF and 200 in LF had his total defensive line added together; likewise players who played 2B, SS, and 3B. Players moving around between 1B and the outfield were assigned on the stats from the position they played the most in the following season. (For example, if a player played 1000 innings at 1B in 2002 and split time between 1B and OF in 2001, only his 1B stats from 2001 were considered. Likewise with catchers and anyone named
Craig Biggio or
Chuck Knoblauch.) These conditions yielded a sample size of 5606 seasons.

The three statistics considered where again rate stats based on the (rather limited) defensive stats available. First is fielding percentage (FP, pronounced "Santangelo" if you like) which is Putouts (PO) plus Assists (A) over Total Chances (TC). Second is Total Chances per 9 Innings (TC/9), a measure that's almost the exact same stat as range factor, but with errors included. Finally, Defensive Efficiency (DE) was included because it more accurately reflects the team aspect of defense. Admittedly, this is a very small range of statistics to consider, but the current crop of available defensive statistics yields few options and instills limited confidence that the numbers are an accurate reflection of the events on the field (which, of course, is the whole point of stats).



Metric R-Squared Standard Deviation
FP 0.1183 0.030
TC/9 0.8056 2.580
DE 0.2767 0.011
While there is little hope for FP, TC/9 looks more impressive than any statistic sampled thus far. The only drawback to this is the fact that TC/9 doesn't reveal very much about the actual player involved. It's at least as dependent on the GB/FB and handedness of the pitcher or the quality of other defenders as it is on the ability of the player in question. Its year-to-year consistency does little more than reveal that balls put into play, for the most part, are distributed around the field in a consistent manner from season-to-season. The consistency of Defensive Efficiency falls towards the middle of the pack when compared with other metrics viewed so far, but its variance helps explain the high variance of H/9 and ERA, as expected. It does not, however, explain batting average, since league-wide DE stays very stable from year to year.
While the idea that defense-independent statistics are steadier than defense-dependent ones is not a new idea, it's worthwhile to clarify within those ranges which ones are the most constant. In the rather simple cases looked at here, the hierarchy would start with strikeouts, drop slightly to walks, then to home runs, and finally to anything involving balls in play. Obviously, there are ways to improve the year-to-year consistency--looking at more than the immediate previous season, adjusting for age, park, team, etc.--but for now, when various publications are predicting big things for this season based on last year's numbers, remember that things aren't quite as consistent as you might expect. That's why they play the games.

[Dr. Giganto]

Baseball Prospectus Basics
The Support-Neutral Stats

by Michael Wolverton

"...and the tough-luck loser in tonight's game is..."

We hear the above quote in dozens of post-game wrap-ups every year. A starting pitcher goes seven or eight innings and gives up only one or two runs, but his team's offense can't produce anything, so he gets stuck with an "L" next to his name in the box score. The fact that "tough-luck loser" is such a commonly invoked cliche suggests that it's widely recognized that the "L" isn't doing a very good job of measuring the starter's contribution, at least in those situations. But that still doesn't stop the W/L record from being possibly the most prominently used statistic to evaluate starting pitchers in major media baseball coverage.

The idea behind the pitcher's W/L record is flawed on its face. Wins are a team thing, after all, not a pitcher thing. If the offense fails to put runs on the board, or if the bullpen melts down in the late innings, the starter won't get the win no matter how well he pitches. Conversely, if the offense is having a great night (or if they're going up against the Rangers, which is pretty much the same thing), the starter doesn't have to do anything more than last five innings to get the W.

And it's not like the luck always evens out over the course of a season. Just ask any member of last year's Tigers rotation. Even over a long career, offense and bullpen support be a significant distortion to a pitcher's W/L record. Just ask Lew Burdette. Or Bob Friend.

The pitcher's role is pretty much limited to keeping as many runs off the board as possible. That may sound obvious, but it goes against the notion that "pitching to the score" is an important part of a pitcher's job. Plenty of people have looked for a significant ability to pitch to the score without finding it (most notably Greg Spira). And Bill James found that this year's ERA is a better predictor of next year's W/L record than this year's W/L record is.
Toward that end, there's been a gradual (very gradual) movement among baseball fans over the past 20 years to pay less attention to W/L record and more to ERA in pitching evaluation. And that's a good thing, since ERA is a good statistic. It's measuring more of what it's supposed to be measuring--the performance of the pitcher--and less of the performance of his teammates.

Still, as good a statistic as ERA is, it's not without its limitations. Some of those limitations are:

• It doesn't take into account the scoring environment--park, league, and era--in which the pitcher is performing. A 3.00 ERA in Coors Field in 2000 is radically different from a 3.00 ERA in Dodger Stadium in 1968.
• The rule for eliminating "unearned" runs is silly, and it only serves to remove an arbitrary subset of the runs the pitcher gave up.
• Since ERA is a rate stat, it doesn't incorporate playing time. It's easy enough to conclude that a 3.00 ERA over 180 innings is better than a 3.00 ERA over 120 innings. But how do we compare 180 innings of a 3.50 ERA to 120 innings of a 3.00 ERA?
• It includes the runners allowed in by the starter's bullpen successors. Really good bullpen support--i.e., stranding a lot of inherited runners--can chop a quarter or even a half a run off a starter's ERA. Really bad bullpen support can add about as much.
• It treats all runs as equal. More on this in a second.

To address these limitations, I developed the Support-Neutral Win-Loss (SNWL) record, which we've been tracking at Baseball Prospectus since the 1997 book. (Click here to see the final numbers for 2003.) The idea is to measure starting pitchers' performance on the familiar and understandable W/L scale, but without the distortions of run support and bullpen support that plague the traditional W/L record.

A starter's SNWL record is his expected (in the statistical sense) W/L record--how many games he would be expected to win and lose given his pitching performances, assuming he had a league average offense and bullpen behind him. An additional statistic, Support-Neutral Value Added (SNVA), measures the total number of extra games his team would be expected to win with his pitching performances instead of an average pitcher's.

The calculations are adjusted for park and league scoring level, they're based on runs allowed rather than earned runs, and they're based on the situation in which the starter leaves the game (before, not after, his relievers finish with the runners he turns over). So they're not subject to the problems with ERA we noted above. I won't go into the calculations in this article, but you can get all the gory details here.

One other benefit of the Support-Neutral numbers is that they look at each start's contribution to winning individually rather than a season's run total cumulatively, so a single disastrous outing can't have the disproportionate impact that it can have on a starter's ERA. Consider a simple example:
Start 1 Start 2 ---------- ---------Pitcher A 0 IP, 10 R 8 IP, 0 RPitcher B 4 IP, 5 R 4 IP, 5 RTheir ERAs are equal, but Pitcher A's starts are likely to lead to more wins than Pitcher B's. An average team has a good chance of going 0-2 behind Pitcher B's two starts, but that same team is almost guaranteed to win Pitcher A's second game. The Support-Neutral stats account for the fact that the 10 runs concentrated in Pitcher A's one start don't do the same amount of damage as the ten runs spread among Pitcher B's two starts. The above-linked article covers this in more detail.


Are the Support-Neutral stats the be-all and end-all in assessing pitching performance? Of course not. There are many different goals for pitching evaluation, and many different tools that are useful for achieving those goals. If you're doing short-term prediction, for example, you're certainly better off looking at the components of run scoring rather than a stat based on runs allowed itself. And we haven't even touched the nasty question of separating pitching from fielding.
But if you're looking at a pitcher's contribution toward winning, the Support-Neutral numbers have a lot going for them. They correct for the big distortions of the traditional W/L record, and the small distortions of ERA.

[Dr. Giganto]

Baseball Prospectus Basics
About EqA

by Clay Davenport

Dayn Perry explained why various statistics--like batting average (AVG) and runs batted in (RBI)--were not as reliable as you've always been told, and why we at Baseball Prospectus don't use them in our analysis terribly often. Today, we're going to look into one of the statistics we do use: Equivalent Average, or EqA.


In its rawest state, EqA is a simple combination of batting numbers, not so very different from OPS:
H + TB + 1.5*(BB + HBP) + SBEqA = ---------------------------- AB + BB + HBP + CS + SB/3Compared to OPS, it counts walks and HBP a little higher (at 1.5 instead of 1), it has stolen bases, and hits and extra bases are counted a little less (since they are divided by plate appearances, not just walks). What, then, makes EqA different from the other statistics? Simply put, it's more accurate, it's unbiased, and it models the scale of batting average, so it's easy for a new fan to understand.


Let us start with accuracy. Accuracy is traditionally measured in one of two ways--by correlation, and Root Mean Square Error (RMSE) against runs scored. Correlation is a statistical tool that measures how closely one set of numbers tracks a second set. It is measured from negative-one (-1) to positive-one (1); negative scores mean that when one number goes down, the other number tends to go up; positive scores mean that both sets rise and fall together. The closer you get to either end, the more perfect the relationship is, while a score close to zero means that knowing the first number tells you squat about the second number. You'll sometimes see people use r-squared instead, but that is essentially the same thing (mathematicians use "r" to stand for correlation). RMSE is just a fancy way to say how much you missed by, on average--it's a form of standard deviation. Statistics that have better correlation (closer to +1 or -1) usually have lower RMSEs as well.

Consider the following table of fairly traditional statistics.
Correl RMSEBatting Average .828 39.52On-base Percentage .866 34.16Slugging Percentage .890 31.56This shows how well the statistics have done for every team in history, from 1871 to 2003. In each case, I have compared the statistic relative to the league (team batting average divided by league batting average, for instance) to the relative run rate (team runs per plate appearance, divided by the league RPPA). Batting average has, truthfully, a very good correlation...it is just that on-base percentage is even better, and slugging percentage is better still. Combine the last two elements into OPS and the results get better still:

Correl RMSEOn-base plus slugging .922 25.54This is pretty much it for advanced methods, since they all represent only a rather small improvement over what OPS provides. Still, some improvement is better than none, that leads to a variety of stats that have been called "best" by one person or another, stats such as:

Metric Correl RMSEEquivalent Average .928 24.13BaseRuns .930 24.38eXtrapolated Runs (per PA) .920 24.83Runs Created (per PA) .928 24.96Total Average .926 25.33Here you see a big reason why we use EqA: because its ability to estimate runs scored from team and league data is unsurpassed. What the chart does not show is how these errors change over time. If you only looked at the years from 1971 to 2003, eXtrapolated Runs would have a virtually identical RMSE to EqA (20.98 for EqA, 21.06 for XR), while BaseRuns actually does a little better (20.77). However, if you look at the 30 years from 1871 to 1900, the same XR and BsR equations are getting more than 60% worse--their RMSEs shoot up to 34.16 and 33.41, respectively. EqA, in contrast, "only" loses about 50%, scoring a 31.69. EqA is less sensitive to the conditions of the times than many of the other metrics which have been "tuned" to fit recent performances, so it's especially good for historical performances.


(Aside for the technically interested: In all of the above, the formulas are limited to the same set of input statistics: at-bats, hits, doubles, triples, home runs, walks and hit-by-pitch, steals and caught-stealing. These are the basic forms; most of them, including EqA, have more advanced versions that count in things like sacrifices and intentional walks, and these can generally squeeze another run or so out of the RMSE. The RMSEs have been calculated using a best-fit relationship of estimated runs equals team plate appearances times league runs per plate appearance times (A times relative statistic plus B).)

All of this is intrinsic to the equation. The rest of what goes into EqA is what we, the users, force onto it. The first thing we force on--what nobody does for OPS, for instance--is to actually establish how to move between the rate statistic and the number of runs that come from it. Equivalent Runs is simply the number of runs that you get from a given EqA and plate appearances, and it goes up twice as fast as the EqA does. In formula form:
EqR = (2 * EqA/LgEqA - 1) * PA * (LgR / LgPA)Equivalent Runs is tied to the league average runs for two reasons. One, it serves to reinforce the idea that everything is relative--that you cannot say for certain whether any statistic is good or bad, unless you know the average value. Secondly, there is always information in the league total that is not part of the normal statistical line--things like reaching on errors, balks, wild pitches and...well, you get the idea. All of the statistics in the chart above had the same data available, and none of them are able to put that information to use as well as EqA.


The second thing we force onto the EqA/EqR figures goes to the second point I made, way back at the beginning: biases. The two primary biases are the league offensive level and the home park. When the league offense is high, players can put up astronomical totals--but since everything is relative, the numbers don't lead to as many wins as you think. It is the same with home parks: a hitter-friendly park, like any park in Colorado, lifts both sides up, so that once again you don't get the kind of winning results you would expect from the production.

Since winning and losing are what the game is all about, we have to adjust for this if we want to have a good, unbiased statistic. We already know how many EqR a player has; think of that as runs scored. We can easily calculate how many runs an average player would have produced, if he played in this league, with this home park, and made just as many outs as the player did. If you think of that as runs allowed, then you can use some form of the Pythagorean formula to estimate a winning percentage for that player.
The nice thing here is that, no matter what the batting conditions in the league may be, the winning percentage of the whole (and of an average player) will always be .500. We could rate the player's performance entirely by this number, except that virtually nobody has any comprehension of how good a .600 winning percentage is in player terms. Sure, it is better than average, but is it league-leading material? Top 10? For that reason, we re-map the winning percentage onto a familiar scale: batting average. For all its faults, anybody who is even a casual fan has a good feel for what is good, bad, or ordinary in a batting average. The final adjustment is entirely to make it easy to tell how good it is:
EQA (adjusted) = [ (winpct)/(1 - winpct) ] ^ 0.2 *.26By this formula, an average player will have a .260 Equivalent Average--always. Compare that to the all-time major-league batting average of .262. A .300 EqA (.672 WPCT) is almost exactly as common, historically, as a .300 batting average; a .400 EqA (.896 WPCT) represents the top-14 seasons in history. The .600 winning percentage I mentioned above would be reported as a .282 EqA--good, but not overly impressive. Easy to understand--the third stump in EqA's wicket.

Clay Davenport is an author of Baseball Prospectus. You can contact Clay by clicking here or click here to see Clay's other articles.