In his 1914 book, How to Play Baseball: A Manual for Boys, legendary New York Giants manager John
McGraw wrote,
"In scientific batting, a man should learn to 'hit behind the runner,' as Big Leaguers call it. By this I mean that if there is a runner on first base, the batter
should try to hit toward right field. It is easy to explain the reason. If he smashes the ball at the shortstop or third baseman, he will
probably hit into a double play, forcing the runner at second base; but if he drives it to right field, the runner should reach third base, and, even if he
hits to the first baseman, the chances are much better for the runner reaching second than if he hits to the shortstop or third base. With a man on first, even if the batter
makes a clean single to left field, the runner will probably get no further than second base."
McGraw's words are as true today as they were in 1914. On opening day in 2001, for instance, the Minnesota Twins benefited from
implementing a bit of McGraw's insight in their game against the Detroit Tigers. Twins center fielder Torii
Hunter came to the plate in the second inning with teammate David Ortiz on first base and one out on the board. Hunter proceeded
to drive a single into right field, thus enabling Ortiz to advance an extra base to third. As Tigers right fielder Roger Cedeno
tried to make a play on Ortiz at third, the enterprising Hunter advanced to second base. The next batter, Jacque Jones, then
grounded out to second, thereby enabling Ortiz to score.
The Twins would eventually win the game, 3-2.
Several days later, on April 20th, a similar situation arose in a game between the Tampa Bay Devil Rays and the Baltimore
Orioles. Greg Vaughn came to the plate in the first inning, with one out and teammate Gerald Williams on first. Vaughn
was also able to hit a single in this situation--but unlike Hunter, his single went to left field instead of
right. Williams tried to stretch an extra base out of the single anyway but was thrown out at third by Orioles left
fielder Delino DeShields. Back at first base, the not-so-enterprising Vaughn failed to advance to second on the
play. When the next batter, Fred McGriff, grounded out to second, the inning was over.
The Devil Rays would go on to lose this game to the Orioles, 6-3.
In these two cases, the difference between hitting to right field and hitting to left turned out to be
drastic. Hunter's single not only enabled the runner to advance to third but also enabled him to take an extra base
on the throw from the outfield. In this case, Hunter's single put two men in scoring position with only one out; each
player (the batter and the runner) was two bases closer to home than they had been before the play began. Vaughn's
single, on the other hand, did nothing to improve the Devil Rays' situation; once the dust had settled, the Devil Rays still only had one man on first, but
there were now two outs on the board. The fact that both of these singles were followed by ground outs to second underscores
the difference between them--in one case, the ground out drove in a run, while in the other, the ground out ended the inning.
Traditional baseball statistics would nonetheless count both Hunter's and Vaughn's plate appearances exactly the same--they would both be singles, no more and no less. There would be nothing in the newspaper box scores the next day to indicate that one of these singles had helped the team go on to score a run (which eventually decided the game), while the other had only helped hasten the end of the inning. The difference between the two plays would not even show up in the end-of-the-year season statistics for both teams--and would, in fact, be lost for the rest of eternity, forever unknown to statisticians and baseball fans alike.
The system of baseball statistics which I am about to propose captures all of the significant differences between plays which (like this one) traditional statistics miss. It fills in the gaps between first and home, as well as the beginning of an inning and its end; it makes clear how one single might differ from another; it turns the wise observations of baseball's past into the quantifiable statistical realities of the present.
This statistical system can do all of these things because it simply recognizes that every significant action in the course of a baseball game results in either an offensive player advancing a base or a defensive player tallying an out on the board. Sometimes both of these things can happen on the same play; in the example above, for instance, Gerald Williams both advanced to second and was thrown out at third on Greg Vaughn's single. For the purposes of this system, however, the important thing is that every time a player advances a base, the system attributes a "base produced" to the player who enabled him to reach that base; likewise, every time a player is put out, the system attributes an "out produced" to the player whose actions made that out happen.
Traditional statistics do keep track of such "bases" and "outs produced" in a limited--but inexplicit--fashion. "Total bases," for instance, counts all the bases a batter produces for himself on base hits—one for singles, two for doubles, three for triples and four for home runs. Stolen bases also keeps track of bases players produce for themselves as baserunners. One might even add stolen and total bases together to get a partial view of how many bases a player has produced for himself throughout the course of a game, season or career. Doing this is, in fact, exactly how I first hit upon the idea of a stat called "bases produced"—and thereby began to understand just how much important information was missing from traditional baseball statistics.
Traditional statistics do not, for starters, count all of the bases a player produces for himself as a baserunner. In the first example above, Torii Hunter advanced from first to second on a throw to third base; though the result of this play is exactly the same as a steal of second, traditional statistics ignore it completely. In this statistical system, however, advancing a base in this way counts just as much as a steal of second would—i.e., exactly one base produced.
Traditional statistics also do not count the number of bases a batter enables his teammates to reach. Torii Hunter's single to right field, for example, enabled David Ortiz to reach two bases: second and third. Hunter had, in effect, "produced" both of these bases for his teammate. Vaughn's single to left field, on the other hand, only enabled Gerald Williams to safely advance as far as second base—it only effectively produced one base for his teammate. Traditional statistics have no means of accounting for this difference; the only (indirect) measure it gives us of the bases players produce for teammates is Runs Batted In, which combines the number of times a batter enables either himself or his teammates to reach home. There are no equivalent numbers for second or third base.
Traditional statistics also have no means of accounting for certain types of outs in baseball; for instance, the fact that Gerald Williams was thrown out at third in the example above would go unnoticed in a baseball box score, since it neither counts as a failed at-bat nor as an instance of being "caught stealing." Yet it carries the same weight as either of these plays; they all result in one more out being put up on the board.
There are so many ways for players to produce outs in baseball that we are better off, for the time being, concentrating on the comparatively fewer number of ways in which they may produce bases. Specifically, offensive players can only produce bases in one of three basic ways:
(1) As batters. These are "Batting Bases Produced" (BBP); in this system they include all the bases a batter reaches safely on base hits (i.e., total bases) as well as walks and times hit by pitch.
(2) As baserunners. These are Running Bases Produced (RBP); they include (most familiarly) stolen bases as well as bases advanced to on fielder's indifference or plays at another base.
(3) For teammates. These are Team Bases Produced (TBP); they include all the bases a batter enables a teammate to advance to by getting a base hit, drawing a walk, getting hit by a pitch, grounding out or flying out. RBIs--minus home runs--is a traditional stat that measures the number of times a player produces home base for his teammates.
There is one other way in which bases may be produced for offensive players:
(4) By the defense. These are Error Bases Produced (EBP); they include all the bases a defensive player mistakenly produces for the opposition on either fielding or battery errors.
It is one of the subtle beauties of the game that there are as many ways of producing bases as there are bases in base ball.
Bases produced of types one through three form a natural class in that they are bases that an offensive player produces for his own team (whether for himself or a teammate). An offensive player's total number of "bases produced" (BP), then, equals his batting bases produced plus his running bases produced plus his team bases produced. This total includes every positive contribution an offensive player makes to his team's effort to score runs.
(5) BP = BBP + RBP + TBP
Adding only "batting" and "running" bases produced together, however, yields only those bases which a player has produced for himself. Of these bases, batting bases produced are unique in that they represent the only way an offensive player can earn his way to first base. The special status of first base is, therefore, the one caveat to the earlier observation about there being as many ways to produce bases as there are bases in baseball. It is only possible to produce second, third and home by any of the four means of base production; in order to produce first, a player either has to earn his way there as a batter, or have the defense award it to him on an error. It turns out that you not only "can't steal first," but that you can't have a teammate help you get there, either!
The fact that first base is special in this way provides one insight into why bases produced may not have been an integral part of the statistical understanding of the game from the very beginning. If the production of all subsequent bases depends on a player's ability to produce first, then one may (perversely) deem it more important to produce first than it is to produce second base, third base or even home. Among batting bases produced, base hits may seem more important than walks or times hit by pitch, since putting the ball in play gives not only the batter but also any baserunners a chance to advance more than one base. Such fruitful side benefits might even lead one to believe that a batter's only goal in stepping up to the plate is to get base hits. In such a world, the appropriate measure of an offensive player's worth ought to be his batting average--the number of times he successfully earns a base hit divided by the number of times he has an opportunity to do so.
Those who invented baseball statistics back in the middle of the nineteenth century seem to have taken this approach towards understanding the game. The only official statistics of baseball's first professional league, for instance--the 1870's "National Association"--were at-bats, base hits, runs scored and batting average. Over the years, statisticians have chipped away at the misguided simplicity of these categories in order to gain a better insight into what baseball players are trying to do when they step up to the plate. Official at-bats, for instance, now exclude a number of situations in which a batter helps his team without getting base hits: walks, times hit by pitch, sacrifice hits and sacrifice flies, to name a few. The eventual development of the concept of "sacrifices"--along with the arrival of "runs batted in" sometime in the early twentieth century--show that statisticians have come to recognize that a batter's job involves helping his teammates as well as helping himself. Stolen bases--the status quo's only significant baserunning statistic--also provide a narrow glimpse into the offensive world beyond the batting box.
Despite these and more recent inventions such as On-Base Percentage and "OPS" (On-Base Percentage plus Slugging Percentage), the full extent to which an offensive player can help his team beyond merely getting base hits remains unrecognized in the world of modern baseball stats. Neither OPS nor On-Base Percentage (nor Batting Average, nor Slugging Percentage, etc.) can capture the fact that part of a batter's job is to help teammates advance along the basepaths; nor can these statistics account for those bases an offensive player produces as a baserunner, well after he has left the batter's box. These statistics still consider an offensive player to be primarily a batter; they misconstrue an offensive player's most salient role as his only significant one and therefore fail to capture exactly what such players are trying to do.
The only way to overcome this fundamental flaw in traditional baseball statistics is to reconceive of the role of offensive players in baseball: offensive players are not batters, they are base producers. Batting--as was briefly mentioned before--only plays a crucial role in baseball in that it is the only way an offensive player can produce first base for himself. To capture this special status of first base, then, this system simply counts the number of times a player produces each base separately. A player's total number of bases produced can therefore also be broken down as in (6) below:
(6) BP = First Base Produced (BP1) + Second Base Produced (BP2) + Third Base Produced (BP3) + Home Base Produced (BP4)
Each of the subtotals in (1)-(3) can be broken down in much the same way:
(7) BBP = BBP1 + BBP2 + BBP3 + BBP4
(8) RBP = RBP2 + RBP3 + RBP4
(9) TBP = TBP2 + TBP3 + TBP4
...the catch being, of course, that there is no way to produce first as a runner or for a teammate.
From this point the system begins to break down into more familiar numbers. Batters can produce first base in any of the ways traditional statistics credit them with having successfully made their way "on base"--
(10) BBP1 = Base Hits + Total Walks + Times Hit by Pitch
It is impossible, however, to produce second, third or home on a walk or being hit by a pitch. Hence--
(11) BBP2 = Doubles + Triples + Home Runs
(BBP2 is traditionally known as "Extra Base Hits.")
(12) BBP3 = Triples + Home Runs
(13) BBP4 = Home Runs
Running Bases Produced only consist of either stolen bases or "bases gained"—bases that players advance to on fielder indifference or on plays at another base (e.g., Torii Hunter's advancing to second on the play at third amounts to one "Base Gained" ).
(14) RBP = Stolen Bases (BS) + Bases Gained (BG)
(15) RBP2 = BS2 + BG2
(16) RBP3 = BS3 + BG3
(17) RBP4 = BS4 + BG4
The mathematics become slightly more complex with Team Bases Produced, unfortunately. (3) states that Team Bases Produced include "all the bases a batter enables a teammate to advance to by getting a base hit, drawing a walk, getting hit by a pitch, grounding out or flying out,"--but not all of these various actions can produce each of the individual bases for a teammate.
One type of "Team Bases Produced" which can result in the production of any base for a teammate is "Forced Bases Produced," which are, in a sense, the prototypical "Team Bases Produced." If the batter puts the ball in play with a runner on first, that runner is forced to advance to second. Should he make it that far, the batter earns one "Forced Base Produced," which can be specifically pigeonholed as a "Second Forced Base Produced" (FBP2). If that same batter had hit a home run, he would have forced the runner to advance to second, third and home--1 FBP2, 1 FBP3 and 1 FBP4 to go along with the four batting bases he produced for himself.
Batters can also produce team bases without strictly forcing their teammates ahead to the next base. Such Team Bases Produced are (unimaginatively) called "Unforced Bases Produced;" a good example would be where a batter hits a single with a runner on second but no one on first. If that runner can advance from second to third on that single, the batter earns one "Unforced Base Produced." In this specific instance, the "Unforced Base Produced" would have been third (i.e., "UBP3"); hopefully it is clear that UBP4 are also possible but that UBP2 are not.
Another type of Team Bases Produced which can only possibly apply to third base and home are "Bases Advanced Produced." The inspiration for this statistic initially came from baseball's bygone years and the original conception of what it meant to "steal a base". Specifically, the rule changes listed in the MacMillan Baseball Encyclopedia (6th ed.) include this one for 1886: "Stolen base credited to the runner for each base advanced by his own volition (i.e., if the runner advances from first to third on a single, he is credited with a stolen base)." Though statisticians would no longer consider a player to have stolen a base when he advances from first to third on a single, that player has advanced a base which is equally as important to scoring a run as any he might have advanced to through a steal. The ability to do this depends on a number of different factors, one of which (as John McGraw knew) was the batter's ability to hit the ball to right field. Such extra bases advanced do not count, therefore, as stolen bases in this system, but rather as "Bases Advanced Produced" by the batter. The fact that these bases represent bases reached in excess of the number reached by the batter means that it is impossible for a batter to produce any BAP2 for a runner, but it is possible to produce BAP4--for instance, by driving in a runner from second on a single.
The last type of Team Bases Produced may, however, apply to any base, as it counts only those bases a batter produces for teammates on fly outs. These are "Bases Tagged Produced" (BTP).
The separate base totals for a player's "Team Bases Produced" therefore break down into each of these four TBP sub-categories.
(18) TBP2 = FBP2 + BTP2
(19) TBP3 = FBP3 + UBP3 + BAP3 + BTP3
(20) TBP4 = FBP4 + UBP4 + BAP4 + BTP4