Keeping the Line Moving—Total Bases Advanced or Relinquished: a Measure of Offensive Production, by Fred Krumbein

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Thursday, 2019 November 28th

issue 1

As long as the game has been played, baseball students, observers, professionals, and fans have compiled and studied stats in order to measure, among other things, the offensive production of teams, of individual players, and of strategies, deployments, techniques, and approaches for optimizing their play.

One ancient baseball adage holds “keeping the line moving” as a way to describe the basic process of trying to score runs. In that vein, we will here take a look at TBAR/PA (total bases advanced or relinquished per plate appearance)—the statistic that measures, for each plate appearance, both to how many bases a runner or runners are advanced and also how many bases are relinquished that a runner or runners have previously reached.

All the bases that are gotten to or are given up are counted, regardless of whether the runners are moved up to a base or removed from a base due to the actions of the offense or of the defense. Because of this, a team’s overall TBAR for each completed half inning will always be a multiple of four and will, naturally, be equal to four times the number of runs scored in that half inning.

Therefore the team’s overall TBAR for each game will also be equal to four times the number of runs scored in the game—usually. An exception can take place when the game ends without the inning being completed. This happens when a runner is SOB, still on base. SOB is distinct from LOB, left on base, and this is because (by our understanding of Major League Baseball’s published rules) LOB refers to batters who are “left on base” when the half inning ends (when the third out is made). These exceptions of course occur in the case when the home team scores its winning run after the eighth inning (a “walk-off”) and there are runners “still on base” behind the winning runner; the third out is never made, and the inning is never completed even though the game ends.

In tallying this statistic of total bases advanced or relinquished per plate appearance, the general rule of thumb being followed is that results that are scored as being due to the actions of the batter are attributed to the batter’s plate appearance. All other results are attributed to the plate appearances of each of the runners who had already reached base.

Following are some illustrative simple examples, real-world cases from this year, and a few extreme examples, along with comparison to and contrast with other offensive stats.

The batter hits a home run (a grand slam). That batter’s plate appearance is attributed with 10 bases advanced: for advancing the runner at third base to home (+1), the runner at second to home (+2), the runner at first to home (+3), and the batter to home (+4).

The batter gets a base on balls (a walk). That batter’s plate appearance is attributed with four bases advanced: for advancing the runner at third base to home (+1), the runner at second to third (+1), the runner at first to second (+1), and the batter to first (+1).

The batter makes an out, ending that half inning. That batter’s plate appearance is attributed with minus six bases advanced: for relinquishing the runner at third base (-3), the runner at second (-2), and the runner at first (-1).

The runner at third base makes an out by getting picked off, ending that half inning. That runner’s plate appearance is attributed with minus six bases advanced: for relinquishing the runner at third base (-3), the runner at second (-2), and the runner at first (-1). This is in addition to the attribution already tallied for that runner’s plate appearance. If, for instance, the runner had reached base by hitting a single and by then being advanced to third by other batters, the total bases advanced for that runner’s plate appearance would be minus five (+1 - 6). If, for instance, the runner had reached base by hitting a triple, the total bases advanced for that runner’s plate appearance would be minus three (+3 - 6).

Here we examine the offense and TBAR/PAs of the ascendant team in each of the big leagues, as they faced off against each other in this year’s World Series:

Moving the Runners in the ’19 World Series

Next we take an even closer look at the runs production and TBAR/PAs during a part of the 2019 season of a transitioning team:

The ’19 Giants—a Team in Transition

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In this example, the third batter of this half inning hits into a fielder’s choice, in which the batter reaches first base and the defense gets the runners at third and second out. This third batter’s plate appearance is attributed with minus four bases advanced: for relinquishing the runner at third base (-3) and the runner at second (-2), and for advancing the batter to first (+1).

With two outs now, the runner at first base is advanced to third during the plate appearances of the fourth and fifth batters, who are now runners at second and first. So the third batter’s TBAR is still minus four, with the bases loaded.

The runner at third base then makes an out by getting picked off, ending that half inning. That runner’s plate appearance is attributed with minus six bases advanced: for relinquishing the runner at third base (-3), the runner at second (-2), and the runner at first (-1). This is in addition to the attribution of minus four already tallied for that runner’s plate appearance. So this third batter’s final TBAR for this one plate appearance is -10 (-4 - 6).

In this example, the fourth batter of this half inning gets a single that clears the bases (each of the runners on base scores a run). That batter’s plate appearance is attributed with seven bases advanced: for advancing the runner at third base to home (+1), the runner at second to home (+2), the runner at first to home (+3), and the batter to first (+1).

The fifth batter hits into a fielder’s choice, in which the batter reaches first base but the fourth batter reaches second on a throwing error. Because the results (the fifth batter having reached first and the fourth batter having reached second) are not scored as being due to the actions of this batter, this fifth batter’s plate appearance is attributed with zero bases advanced.

There are now runners on second and first. Three bases advanced must be accounted for. The runner on first has already been attributed to the fourth batter’s plate appearance; the fifth batter has in essence simply replaced the fourth batter at that base (this is how it is accounted for in a fielder’s choice, whether the runner who had been on the base is gotten out or not). Therefore the fourth batter’s plate appearance is attributed with two more bases advanced: for advancing to second on the defensive error (+7 + 2). One way to look at it is that this fourth batter is supposed to have been out, and therefore not on any base at all; the runner can be thought of as having advanced to second from nowhere, just as if having advanced from the plate. So the fourth batter’s TBAR is now nine, and this runner is on second base.

The sixth batter hits into a fielder’s choice, in which the batter reaches first base but the fourth batter reaches third on a throwing error. This sixth batter’s plate appearance is attributed with zero bases advanced.

The fourth batter’s plate appearance is attributed with three more bases advanced: for advancing to third on the defensive error (+9 + 3). So the fourth batter’s TBAR is now 12, and this runner is on third base.

The seventh batter hits into a fielder’s choice, in which the batter reaches first base but the fourth batter scores a run on a throwing error. This seventh batter’s plate appearance is attributed with zero bases advanced.

The fourth batter’s plate appearance is attributed with four more bases advanced: for advancing to home on the defensive error (+12 + 4). So this fourth batter’s final TBAR for this one plate appearance is +16.

These three scenarios are given as the context for the examples that follow, for comparison to and contrast with some other common offensive statistics:
In all three scenarios, the batter comes to the plate 70 times.
The batter gets nine walks and one hit-by-pitch, in addition to 60 at-bats.
The results in the at-bats are two home runs, a triple, four doubles, 11 singles, and 42 outs.

In the three scenarios, the batter gets 18 hits in 60 at-bats. That’s a batting average of .300. Getting on base 10 other times (the nine walks and the hit-by-pitch) along with the 18 hits adds up to reaching base 28 times in 70 plate appearances. That’s an on-base percentage of .400. The two home runs account for eight bases, the triple for three, the four doubles for eight, and the 11 singles for 11 more (+8 + 3 + 8 + 11), adding up to a total of 30 bases in the 60 at-bats. That’s a slugging percentage of .500.

So when leaving out of consideration any other possible runners and also leaving out of consideration any other defensive mistakes or other offensive ways to move the line, a batter with a .300/.400/.500 slash line could have a .571 TBAR/PA.

In the second scenario:
The bases are loaded with two outs all of the 42 times the batter makes an out.
The batter comes to the plate with no outs and no runners on base in any of the other 28 plate appearances.

The total of 40 bases advanced is tallied as +40. The total of six bases relinquished in each of the 42 outs is tallied as -6 x 42, which equals -252. That adds up to -212 (+40 - 252).

In the third scenario:
The batter comes to the plate with no outs and no runners on base all of the 42 times the batter makes an out.
The bases are loaded in all of the other 28 plate appearances.
In all of the 18 plate appearances in which the batter gets a hit, that hit clears the bases (each of the runners on base scores a run).

The 10 bases advanced in each of the two home runs (grand slams) is tallied as 10 x 2, which equals 20. The nine bases advanced in the triple is tallied as 9. The eight bases advanced in each of the four doubles is tallied as 8 x 4, which equals 32. The seven bases advanced in each of the 11 singles is tallied as 7 x 11, which equals 77. The four bases advanced in each of the 10 other times the batter reaches base (the nine walks and the hit-by-pitch) is tallied as 4 x 10, which equals 40. That adds up to 178 (+20 + 9 + 32 + 77 + 40).

So there can be a wide range of possible TBAR/PAs when tallying the results, because the runners on base will be taken into consideration. A batter with a .300/.400/.500 slash line could have a TBAR/PA as low as -3.029 or as high as 2.543.

And of course, there also might be other defensive mistakes or other offensive ways to move the line that might contribute to bases advanced. Therefore the range in possible TBAR/PAs could be even wider still.

The situations that batters are put in when coming to the plate, and runners when on the base paths, are intrinsic to their team’s opportunities, for contributing to failure or to success. (And remember, just keep on keepin’ the line movin’.)