For those joining us in medias res, previously we discussed the fundamentals of run estimation (and really, the essence of baseball analysis). If you haven’t read it yet, I’d suggest doing so before going any further.
Well, they say that those who don’t understand history are doomed to repeat it. So let’s take a brief look at the history of run estimation. You could probably write a book simply on this topic, but for now I think a rather broad overview will suffice.
As with any such survey, some nuance will be missed and some things will be excluded. My goal, rather than giving a blowbyblow history of who invented what run estimator when, is to get a feel for the context of our current run estimators. So if your favorite obscure run estimator is excluded, I apologize in advance. And if understanding runs is the key to understanding baseball, then to understand the history of run estimation, we need to put it in the context of the history of baseball itself.
Origin of the sport
Of course, with any history of this sort, the big trouble is deciding where (or is it when?) to start. Call me crazy, but let’s go ahead and start with… Jane Austen. (No, really.) In one of her early novels, Northanger Abbey, Austen makes this curious reference:
"It was not very wonderful that Catherine, who had nothing heroic about her, should prefer cricket, baseball, riding on horseback, and running about the country at the age of fourteen, to books."
This was all the way back in 1797, well before the supposed invention of the sport in Cooperstown. In Britain at the time, there were two chief stickandball sports—cricket, of course, and rounders, or “baseball.” The two both probably derive from an earlier game, known as stoolball, and both are probably more similar to each other than either resembles baseball as we know it.
But in at least one key fact, rounders greatly resembles modern baseball, in sharp contrast to cricket—cricket only has two bases, whereas rounders has four. And when people came to the Americas from England, they brought these stickandball games with them and adapted them (if you were curious, the transition of rounders to something we would recognize as baseball probably occurred with the socalled Knickerbocker rules).
So how did America end up with a national pastime descended from what was essentially the British version of dodgeball—a sport largely reserved to children—rather than the more popular game of cricket? In fact, in the mid19^{th }century, both of them were popular sports. But America was busily transitioning from a largely rural, agrarian lifestyle to a more modern, urban lifestyle, dominated by factory and office work.
You see, in an agrarian society, you can neatly split the year in two parts—the working season, and the resting season. You plant in spring, work through the summer, harvest in fall. Once you’ve finished harvesting and storing crops for the winter, you have large amounts of leisure time available to you. (This distinction is neatly preserved in the modern school year—children were put in school during the fall and winter, once the crops were in—and once planting season came around again, children were put to work.)
In contrast, an office or factory worker did not have nearly as much leisure time as a farm worker—at least, not all at once. Unlike a farm, a factory doesn’t have to wait on the seasons. And so leisure activities that could neatly fit into a few hours between when one’s shift ends and when the sun sets became more and more popular—such as baseball.
Invention of the box score
And so baseball won— but there are still some strong influences from cricket left over that persist into today. Very few of them influence how the game is played, mind you—they all almost show up in how the game is observed and recorded. For, you see, Henry Chadwick was a cricket player. He was also the most influential sports journalist… probably of all time. I’ve written in the past about Chadwick’s influence on the game today. And one of the things he did (far from the only thing he did, but the one most relevant to our current line of inquiry) is create the box score.
And he did so by adapting what he was familiar with—the box score for cricket. For our purposes here, there are some key differences between cricket and baseball that Chadwick didn’t seem to account for properly, if at all:

Chadwick seemed to misunderstand the role of walks in baseball. The closest analogue in cricket is the “wide,” a ball so high or so far off that the “striker” (cricket’s equivalent of a batter) has no chance of reaching it. In cricket these count as “extras,” which are akin to baseball’s battery errors, wild pitches, and passed balls. (And in fact at one point he proposed counting the walk as a battery error.) Notably, extras were not counted for individual strikers in cricket. By accounting for walks in much the same fashion, you wholly ignore both the skill it takes for a batter to “work a walk” by not swinging at pitches outside the zone and the effect a walk has on a team’s ability to score runs. Chadwick’s favored offensive metric, batting average, excluded walks entirely, as though the batter never stepped to the plate.
 In cricket, the same batter always both scores and drives in every run. There are only two bases, and the "nonstriker" has to switch places with the striker for every run that is taken (which can happen any number of times on any hit), but there is no advancing other runners (either bases or runs) like in baseball.
And so you’re left with this very stark distinction between “hit” and “out,” with no further differentiation. (Or, the “total bases” logic that only looks at bases attained by the batter, and not bases he advances the runner.) And walks are largely ignored. There was the occasional person who would come along and challenge this—F.C. Lane was one of the most notable—but for the most part, this is how baseball was measured over the course of its history.
The vertical invasion of the barbarians
Then came the sabermetricians. A lot of innovation happened in the early days, too much to touch on fully here. But there are some key discoveries that persist to this day—and some dead ends whose effects are still felt from time to time.
Runs Created
I don’t think I need to introduce Bill James here—I can do little to improve upon what’s been written about his place in the history of baseball analysis, and he doesn’t need my help in raising awareness. What’s interesting about James to me—I mean, aside from the obvious things—is how utterly prolific he was. I honestly can’t think of a topic in sabermetrics where he hasn’t left a mark somewhere. Here, however, we’ll restrict ourselves to one of his best known contributions—Runs Created.
We can express the basic structure of Runs Created as:
A*B/C
Where A is number of baserunners, B is an “advancement factor,” and C is opportunities. Alternately, you can think of A as the number of baserunners, and the B/C term as the percentage of baserunners who score.
The original form of Runs created, given that construction, was:
Or, phrased differently:
But as mentioned before, James is amazingly prolific. There are probably 30 variant formulas along the same lines—but all of them follow the essential A*B/C relationship. It should be noted that Runs Created in this form is a dynamic formula for estimating team runs—so what you get if you input, say, Barry Bonds’ batting line is an estimate for how many runs a team of nine Barry Bondses would have scored in that number of plate appearances. Runs Created also puts everything in terms of absolute runs—in other words, if you put an average team’s batting line into Runs Created, you’ll get the same number of observed runs scored as you do Runs Created (or at least, pretty close to it, depending on the environment used to “tune” the version of Runs Created used).
Linear Weights
Another early approach to run estimation was linear weights. There were two key early implementations, seemingly discovered independently of each other. Pete Palmer proposed his formula for Batting Runs, based upon the results of a simulation (which was further based upon playbyplay accounts of World Series games):
.46*1B + .80*2B + 1.02*3B + 1.40*HR + .33*(BB+HBP) + .20*SB – .35*CS .25*(AB–H) – .50*(H+BB+HBPLOBR–CS)
There are three terms that account specifically for the value of an out—caught stealing, batting outs, and an approximation of other outs on base. In contrast with Runs Created, Batting Runs gives us runs above (or below) average. And it does so in a linear fashion – in other words, it tells us what the value of a single (for instance) would be to an average team. If you plug in Barry Bonds' batting line, it will tell you how many additional runs an otherwise average team would score if they replaced an average hitter with Bonds for that number of opportunities.
The other early linear weights formula of note was Paul Johnson’s Estimated Runs Produced:
(2 * (TB + BB + HBP) + H + SB – (.605 * (AB – H + CS + GIDP))) * .16
We can rewrite that formula, to present it similarly to Batting Runs, like so:
0.48 * 1B + 0.80 * 2B + 1.12*3B + 1.44 * HR + .32* (BB+HBP) + .16 * SB – .0968 * (AB – H + CS + GIDP)
In most respects this produces a formula practically indistinguishable from Palmer’s Batting Runs, with the exception of the value of outs. While both are linear formulas, what ERP gives us is (like Runs Created) absolute runs, not runs above average. Past that distinction, though, they’re two ways of arriving at practically the same answer. This distinction (or really, lack thereof) seemed to have been lost on James, incidentally, who was famously dismissive of Batting Runs, even while giving Estimated Runs Produced its first moment in the limelight.
It, like linear weights, is a Pete Palmer creation. Unlike linear weights, though, it was not explicitly thought out like a run estimator. That said, I figured I would mention it here for the sake of completeness, since it is often used in lieu of one.
Note the similarity with the basic form of Runs Created—instead of multiplying OBP and SLG together, they are simply added. While an improvement upon batting average, in that it considers walks and takes some consideration of extrabase hits, it is still based upon the logic of “total bases,” which are really only totaled for the batter, not any of the runners on ahead of him. It seems to have caught on to a greater extent than its more robust contemporaries, despite lacking much of their finesse, because of the relative ease of computation (assuming, of course, that OBP and SLG are already computed for you).
And of course, Palmer introduced a close relative, OPS+, also known as Adjusted OPS or Pro+. Many people seem to assume that the formula is a player’s OPS divided by the league OPS. It’s actually:
A little more complicated and less direct than what the name implies. And also a bit better as a run estimator, as it brings the units of OBP and SLG into sync—the difference between a 700 and an 800 OPS in terms of run scoring depend on how many points of OBP and how many points of SLG contribute to the difference.
Bases Per Something
If anyone ever tells you they’ve discovered a new offensive stat, bet that some variation of this is what they’ve stumbled across. The two most common flavors are:
and
Call them “bases per out” and “bases per plate appearance,” because that’s what they are, essentially. Some variation on the two themes have gone under any number of names, such as BaseOut Percentage, Total Average, Base Production Average, TOPR… the list goes on for a while. It’s somewhat easier to calculate than even OPS. It uses readily available stats. Both of those things collude to make it perennially “discovered” and announced breathlessly.
The other thing that keeps people discovering it is that nobody pays much attention to any of these announcements. It simply isn’t as good as OPS in some rather obvious ways—it’s the only metric I know of that has ever really overrated the walk in such dramatic fashion. And at the same time, it is based upon the logic of total bases that is at the root of some of OPS’ more notable flaws.
Notes and asides
This is going to spill over into a second article, thus increasing the length of the series to at least four pieces. Expect to pick up next time with the start of the Internet era of baseball analysis—people who remember rec.sports.baseball on USENET are in for a real treat, I should think. Those looking for more information on the origins of baseball would do well to read Retrosheet’s Protoball Chronology.
Special thanks to Craig Burley, who attempted as best he could to give me a better understanding of the sport of cricket.