Foundations of Batting Analysis – Part 2: Real and Indisputable Facts

In Part 1 (, we examined how the hit became the first estimate of batting effectiveness in 1867 leading to the creation of the modern batting average in 1871. In Part 2, we’ll look more closely at what the hit actually measures and the inherent flaws in its estimation.

Over the century-and-a-half since Henry Chadwick wrote “The True Test of Batting,” it has been a given that if the batter makes contact with the ball, he has only shown “effectiveness” when that contact results in a clean hit – anything else is a failure. At first glance, this may seem somewhat reasonable. The batter is being credited for making contact with the ball in such a way that it is impossible for the defense to make an out, an action that must be indicative of his skill. If the batter makes an out, or reaches base due to a defensive error that should have resulted in an out, it was due to his ineffectiveness – he failed the “test of skill.”

This is an oversimplified view of batting.

By claiming that a hit is entirely due to the success of the batter and that an out, or reach on error, is due to his failure, we make fallacious assumptions about the nature of the game. Consider all of the factors involved in a play when a batter swings away. The catcher calls for a specific pitch with varying goals in mind depending on the batter, the state of the plate appearance, and the game state. The pitcher tries to pitch the ball in a way that will accomplish the goals of the catcher.[i] The batter attempts to make contact with the ball, potentially with the intent to hit the ball into the air or on the ground, or in a specific direction. The fielders aim to use the ball to reduce the ability of the batting team to score runs, either by putting out baserunners or limiting their ability to advance bases. The baserunners react to the contact and try to safely advance on the bases without being put out. All the while, the dirt, the grass, the air, the crowd, and everything else that can have some unmeasurable effect on the outcome of the play, are acting in the background. It is misleading to suggest that when contact between the bat and ball results in a hit, it must be due to “effective batting.”

Let’s look at some examples. Here is a Stephen Drew pop up from the World Series last year:

Here is a Michael Taylor line drive from 2011:

The contact made by Taylor was certainly superior to that made by Drew, reflecting more batting effectiveness in general, but due to fielding effectiveness—and luck—Taylor’s ball resulted in an out while Drew’s resulted in a hit.

Here are three balls launched into the outfield:

In each case, the batter struck the ball in a way that could potentially benefit his team, but varying levels of performance by the fielders resulted in three different scoring outcomes: a reach on error, a hit, and an out, respectively.

Here are a pair of a groundballs:

Results so dramatically affected by luck and randomness reflect little on the part of the batter, and yet we act as if Endy Chavez was effective and Kyle Seager was ineffective.

Home runs may be considered the ultimate success of a batter, but even they may not occur simply due to batting effectiveness. Consider these three:

Does a home run reflect more batting effectiveness when it lands in front of the centerfielder, when it’s hit farther than humanly possible,[ii] or when it doesn’t technically get over the wall?

The hit, at its core, is an estimate of value. Every time the ball is put into play in fair territory, some amount of value is generated for the batter’s team. When an out is made, the team has less of an opportunity to score runs: negative value. When an out is not made, the team has a greater opportunity to score runs: positive value. Hits estimate this value by being counted when an out is not made and when certain other aspects of the play conform to accepted standards of batting effectiveness, i.e. the 11 subsections of Rule 10.05 of the Official Baseball Rules that define what are and are not base hits, as well as the eight subsections of Rule 10.12.(a) that define when to charge an error against a fielder.

Rule 10.05 includes the phrase “scorer’s judgment” four times, and seven of the 11 parts of the rule involve some form of opinion on the part of the scorer to determine whether or not to award a hit. All eight subsections of Rule 10.12.(a) that define when to charge an error against a fielder are entirely subjective. Not only is the hit as an estimate of batting effectiveness muddled by the forces in the game that are outside of the batter’s control, but the decision whether to award a hit or an error can be based on subjective opinion. Imagine you’re the official scorer; are these hits or errors?

If you agreed with the official scorer on the last play, that Ortiz reached on a defensive error, you were “wrong” according to MLB, which overturned the call and awarded Ortiz a hit retroactively (something I doubt would have occurred if Darvish had completed the no-hitter). Despite Chadwick’s claim in 1867 that “there can be no mistake about the question of a batsman’s making his first base…whether by effective batting, or by errors in the field,” uncertainty in how to designate the outcome of a play is all too common, and not a modern phenomenon.

In an article in the 6 April 1916 issue of the Sporting News, John H. Gruber explains that before scoring methods became standardized in 1880, the definition of a hit could vary wildly from scorer to scorer.

“It was evidently taken for granted that everybody knew a base hit when he saw one made…a group of ‘tight’ and another of ‘open’ scorers came into existence.

‘Tight’ were those who recognized only ‘clean’ hits, when the ball was not touched by a fielder either on the ground or in the air. Should the fielder get even the tip of his fingers on the ball, though compelled to jump into the air, no hit was registered; instead an error was charged.

The ‘open’ contingent was more liberal. To it belonged the more experienced scorers who used their judgment in deciding between a hit and an error, and always in favor of the batter. They gave the batter a hit and insisted that he was entitled to a hit if he sent a ‘hot’ ball to the short-stop or the third baseman and the ball be only partly stopped and not in time to throw it to a bag.

Some of them even advocated the ‘right field base hit,’ which at present is scored a sacrifice fly. ‘For instance,’ they said, ‘a man is on third base and the batsman, in order to insure the scoring of the run by the player on third base, hits a ball to right field in such a way that, while it insures his being put out himself, sends the base runner on third home, and scores a run. This is a play which illustrates ”playing for the side” pretty strikingly, and it seems to us that such a hit should properly come under the category of base hits.’”

While official scorers have since become more consistent in how they score a game, there will never be a time when hits will not involve a “scorer’s judgment” on some level. As Isaac Ray wrote in the North American Review in 1856, building statistics based on opinion or “shrewd conjecture” leads to “no real advance in knowledge”:

“The common fallacy that, imperfect as they are, they still constitute an approximation of the truth, and therefore are not to be despised, is founded upon a total misconception of the proper objects of statistical inquiry, as well as of the first rules of philosophical induction. Facts—real and indisputable facts—may serve as a basis for general conclusions, and the more we have of them the better; but an accumulation of errors can never lead to the development of truth. Of course we do not deny that, in a mere matter of quantity, the errors on one side generally balance the errors on the other, and thus the value of the result is not materially affected. What we object to is the attempt to give a statistical form to things more or less doubtful and subjective.”

Hits, these “approximations of the truth,” have been used as the basic measurement of success for batters for the entire history of the professional game. However, in the 1950s, Branch Rickey, the general manager of the Los Angeles Dodgers, and Allan Roth, his statistical man-behind-the-curtain, acknowledged that a batter could provide value to his team outside of just swinging the bat. On August 2, 1954, Life magazine printed an article titled “Goodby to Some Old Baseball Ideas” in which Rickey wrote on methods used to estimate batting effectiveness:

“…batting average is only a partial means of determining a man’s effectiveness on offense. It neglects a major factor, the base on balls, which is reflected only negatively in the batting average (by not counting it as a time at bat). Actually walks are extremely important…the ability to get on base, or On Base Average, is both vital and measurable.”

While the concept didn’t propagate widely at first, by 1984 on base average (OBA) had become one of three averages, along with batting average (BA) and slugging average (SLG), calculated by the official statisticians for the National and American Leagues. These averages are currently calculated as follows:

BA = Hits/At-Bats = H/AB

OBA = (Hits + Walks + Times Hit by Pitcher) / (At-Bats + Walks + Times Hit by Pitcher + Sacrifice Flies) = (H + BB + HBP) / (AB + BB + HBP + SF)

SLG = Total Bases on Hits / At-Bats = TB/AB

The addition of on base average as an official statistic was due in large part to Pete Palmer who began recording the average for the American League in 1979. Before he began tracking these figures, Palmer wrote an article published in the Baseball Research Journal in 1973 titled, “On Base Average for Players,” in which he examined the OBA of players throughout the history of the game. To open the article, he wrote:

“There are two main objectives for the hitter. The first is to not make an out and the second is to hit for distance. Long-ball hitting is normally measured by slugging average. Not making an out can be expressed in terms of on base average…”

While on base average has proven popular with modern sabermetricians, it does not actually express the rate at which a batter does not make an out, as claimed by Palmer. Rather, it reflects the rate at which a batter does not make an out when showing accepted forms of batting effectiveness; it is a modern take on batting average. The suggestion is that when a batter reaches base due to a walk or being hit by a pitch he has shown effectiveness, but when he reaches on interference, obstruction, or an error he has not.

Here are a few instances of batters reaching base without swinging.

What effectiveness did the batter show in the first three plays that he failed to show in the final play?

In the same way that there are a litany of forces in play when a batter tries to make contact with the ball, reaching base due to non-swinging events requires more than just batting effectiveness. Reaching on catcher’s interference may not require any skill on the part of the batter, but there are countless examples of batters being walked or hit by a pitch that similarly reflect no batting skill. A batter may be intentionally walked because they are greatly skilled and the pitcher, catcher, or manager fears what the batter may be able to do if he makes contact, but in the actual plate appearance itself, that rationalization is inconsequential. If we’re going to estimate the effectiveness of a batter in a plate appearance, only what occurs during the plate appearance is relevant.

Inconsistency in when we decide to reward batters for reaching base has limited our ability to accurately reflect the value produced by batters. We intentionally exclude certain results and condemn others as failures despite the batter’s team benefiting from the outcomes of these plays. Instead of restricting ourselves to counting only the value produced when the batter has shown accepted forms of effectiveness, we should aim to accurately reflect the total value that is produced due to a batter’s plate appearance. We can then judge how much of the value we think was due to effective batting and how much due to outside forces, but we need to at least set the baseline for the total value that was produced.

To accomplish this goal, I’d like to repurpose the language Palmer used to begin “On Base Averages for Players”:

There are two main objectives for the batter. The first is to not make an out and the second is to advance as many bases as possible.

“Hitters” aim to “hit for distance” as it will improve their likelihood of advancing on the bases. “Batters” aim to do whatever it takes to advance on the bases. Hitting for distance may be the best way to accomplish this, in general, but batters will happily advance on an error caused by an errant throw from the shortstop, or a muffed popup in shallow right field, or a monster flyball to centerfield.

Unlike past methods that estimate batting effectiveness, there will be no exceptions or exclusions in how we reflect a batter’s rate at accomplishing these objectives. Our only limitation will be that we will restrict ourselves to those events that occur due to the action of the plate appearance. By this I mean that baserunning and fielding actions that occur following the initial result of the plate appearance are not to be considered. For instance, events like a runner advancing due to the ball being thrown to a different base, or a secondary fielding error that allows runners to advance, are to be ignored.

The basic measurement of success in this system is the reach (Re), which is credited to a batter any time he reaches first base without causing an out.[iii] A batter could receive credit for a reach in a myriad of ways: on a clean hit,[iv] a defensive error, a walk, a hit by pitch, interference, obstruction, a strikeout with a wild pitch, passed ball, or error, or even a failed fielder’s choice. The only essential element is that the batter reached first base without causing an out. The inclusion of the failed fielder’s choice may seem counterintuitive, as there is an implication that the fielder could have made an out if he had thrown the ball to first base, but “could” is opinion rearing its ugly head and this statistic is free of such bias.

The basic average resulting from this counting statistic is effective On Base Average (eOBA), which reflects the rate at which a batter reaches first base without causing an out per plate appearance.

eOBA = Reaches / Plate Appearances = Re/PA

Note that unlike the traditional on base average, all plate appearances are counted, not just at-bats, walks, times hit by the pitcher, and sacrifice flies. MLB may be of the opinion that batters shouldn’t be punished when they “play for the side” by making a sacrifice bunt, but that opinion is irrelevant for eOBA; the batter caused an out, nothing else matters.[v]

eOBA measures the rate at which batters accomplish their first main objective: not causing an out. To measure the second objective, advancing as many bases as possible, we’ll define the second basic measurement of success as total bases reached (TBR), which reflects the number of bases to which a batter advances due to a reach.[vi] So, a walk, a single, and catcher’s interference, among other things, are worth one TBR; a two-base error and a double are worth two TBR; etc.

The average resulting from TBR is effective Total Bases Average (eTBA), which reflects the average number of bases to which a batter advances per plate appearance.

eTBA = Total Bases Reached / Plate Appearances = TBR/PA

We now have ways to measure the rate at which a batter does not cause an out and how far they advance on average in a plate appearance. While these are the two main objectives for batters, it can be informative to know similar rates for when a batter attempts to make contact with the ball.

To build such averages, we need to first define a statistic that counts the number of attempts by a batter to make contact, as no such term currently exists. At-bats come close, but they have been altered to exclude certain contact events, namely sacrifices. For our purposes, it is irrelevant why a batter attempted to make contact, whether to sacrifice himself or otherwise, only that he did so. We’ll define an attempt-at-contact (AC) as any plate appearance in which the batter strikes out or puts the ball into play. The basic unit to measure success when attempting to make contact is the reach-on-contact (C), for which a batter receives credit when he reaches first base by making contact without causing an out. A strikeout where the batter reaches first base on a wild pitch, passed ball, or error counts as a reach but it does not count as a reach-on-contact, as the batter did not reach base safely by making contact.

The basic average resulting from this counting statistic is effective Batting Average (eBA), which reflects the rate at which a batter reaches first base by making contact without causing an out per attempt-at-contact.

eBA = Reaches-on-Contact / Attempts-at-Contact = C/AC

Finally, we’ll define total bases reached-on-contact (TBC) as the number of bases to which a batter advances due to a reach-on-contact. The average resulting from this is effective Slugging Average (eSLG), which reflects the average number of bases to which a batter advances per attempt-at-contact.

eSLG = Total Bases Reached-on-Contact / Attempts-at-Contact = TBC/AC

The two binary effective averages—eOBA and eBA—are the most basic tools we can build to describe the value produced by batters. They answer a very simple question: was an out caused due to the action in the plate appearance. There are no assumptions made about whose effectiveness caused an out to be made or not made, we only note that it occurred during a batter’s plate appearance; these are “real and indisputable facts.”

The value of these statistics lies not only in their reflection of whether a batter accomplishes his first main objective, but also in their linguistic simplicity. Miguel Cabrera led qualified batters with a .442 OBA in 2013. This means that he reached base while showing batting effectiveness (i.e. through a hit, walk, or hit by pitch) in 44.2 percent of the opportunities he had to show batting effectiveness (i.e. an at-bat, a walk, a hit by pitch, or a sacrifice fly). That’s a bit of a mouthful, and somewhat convoluted. Conversely, Mike Trout led all qualified batters with a .445 eOBA in 2013, meaning he reached base without causing an out in 44.5 percent of his plate appearances. There are no exceptions that need to be acknowledged for plate appearances or times safely reaching base that aren’t counted; it’s simple and to the point.

The two weighted effective averages—eTBA and eSLG—depend on the scorer to determine which base the batter reached due to the action of the plate appearance, and thus reflect a slight level of estimation. As we want to differentiate between actions caused by a plate appearance and those caused by subsequent baserunning and fielding, it’s necessary for the scorer to make these estimations. This process at least comes with fewer difficulties, in general, than those that can arise when scoring a hit or an error. No matter what we do, official scorers will always be a necessary evil in the game of baseball.

While I won’t get into any real analysis with these statistics yet, accounting for all results can certainly have a noticeable effect on how we may perceive the value of some players. For example, an average batter last season had an OBA of .318 with an eOBA of .325. Norichika Aoki was well above average with a .356 OBA last season, but by accounting for the 16 times he reached base “inefficiently,” he produced an even more impressive .375 eOBA. While he was ranked 37th among qualified batters in OBA, in the company of players like Marco Scutaro and Jacoby Ellsbury, he was 27th among qualified batters in eOBA, between Buster Posey and Jason Kipnis; a significant jump.

In the past, we have only cared about how many total bases a batter reached when he puts the ball into play, which is a disservice to those batters who are able to reach base at a high rate without swinging. Joey Votto had an eSLG of .504 last season – 26th overall among qualified batters. However, his eTBA, which accounts for the 139 total bases he reached when not making contact, was .599 – 7th among qualified batters.

This is certainly not the first time that such a method of tracking value production has been proposed, but it never seems to gain any traction. The earliest such proposal may have come in the Cincinnati Daily Enquirer on 14 August 1876, when O.P. Caylor suggested that there was a strong probability that “a different mode of scoring will be adopted by the [National] League next year”:

“Instead of the base-hit column will be the first base column, in which will be credited the times a player reached first base in each game, whether by an error, called balls, or a safe hit. The intention is to thereby encourage not only safe hitting, but also good first-base running, which has of late sadly declined. Players are too apt, under the present system of averages, to work only for base hits, and if they see they have not made one, they show an indifference about reaching first base in advance of the ball. The new system will make each member of a club play for the club, and not for his individual average.”

Of course, this new mode was not adopted. However, the National League did count walks as hits for a single season in 1887; an experiment that was widely despised and abandoned following the end of the season.

It has been 147 years since Henry Chadwick introduced the hit and began the process of estimating batting effectiveness. Maybe it’s time we accept the limitations of these estimations and start crediting batters for “reaching first base in advance of the ball” and advancing as far as possible, no matter how they do so.


[i] Whether it’s the catcher, pitcher, or manager who ultimately decides on what pitch is to be thrown is somewhat irrelevant. The goal of the pitching battery is to execute pitches that offer the greatest chance to help the pitching team, whether that’s by trying to strike out the batter, trying to induce weak or inferior contact, or trying to avoid the potential for any contact whatsoever.

[ii] Technically, it only had a true distance of 443 feet—not terribly deep in the grand pantheon of home runs—but the illusion works for me on many levels.

[iii] The fundamental principle of this system, that a reach is credited when an out doesn’t occur due to the action of the plate appearance, means that some plays that end in outs are still counted as reaches. In this way, we don’t incorrectly subtract value that was lost due to fielding and baserunning following the initial event. For instance, if a batter hits the ball cleanly into right field and safely reaches first base, but the right fielder throws out a baserunner advancing from first to third, the batter would still receive credit for a reach. Similarly, if a batter safely reaches first base but is thrown out trying to advance to second base, for consistency, this is considered a baserunning mistake and Is still treated as a reach of first base.

[iv] There is one type of hit that is not counted as a reach. When a batted ball hits a baserunner, the batter receives credit for a hit while an out is recorded, presumably because it is considered an event that reflects batting effectiveness. In this system, that event is treated as an out due to the action of the plate appearance—a failure to safely reach base.

[v] Sacrifice hits may be strategically valuable events, as the value of the sacrifice could be worth more than the average expected value that the batter would create if swinging away, but they are still negative events when compared to those that don’t end in an out—a somewhat obvious point, I hope. The average sacrifice hit is significantly more valuable than the average out, which we will show more clearly in Part III, but for consistency in building these basic averages, it’s only logical to count them as what they are: outs.

[vi] There are occasionally plays where a batter hits a groundball that causes a fielder to make a bad throw to first, in which the batter is credited with a single and then an advance to second on the throwing error. As the fielding play is part of the action of the plate appearance—it occurs directly in response to the ball being put into play—the batter would be credited with two TBR for these types of events.


I’ve included links to spreadsheets containing the leaders, among qualified batters, for each effective average, as well the batters with the largest difference between their effective and traditional averages, for comparison. Additionally, the same statistics have been generated for each team along with the league-wide averages.

2013 – Effective Averages for Qualified Players

2013 – Largest Difference Between Effective and Traditional Averages for Qualified Players

2013 – Effective Averages for Teams and Leagues

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2 years 1 month ago

This is great. Interested in where this series leads.