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Baseball team and player performance examined realistically and accurately.

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Stat Definitions


“A definition is the enclosing a wilderness of idea within a wall of words.”

– The Note-Books of Samuel Butler,
Samuel Butler

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The Standard Baseball Measures

Several of the calculated measures are standard in baseball and—presumably—already familiar to you. For batters, “PA” is simply total Plate Appearances—the total of At-Bats, Walks, Hit-By-Pitch, Sacrifice Flys and Sacrifice Bunts, and the rare but distinct Catcher’s Interference. The “BA” is the familiar Batting Average, the “SA” is the familiar Slugging Average, and the “OBA” is the familiar On-Base Average (sometimes rendered elsewhere as “OBP” or “OB%”).

For pitchers, “IP” and “ERA” are obvious; “K/W”—the strikeout-to-walk ratio—will also be familiar to many. We include the K/W ratio because it is often thought to be a barometer of pitching ability (an idea we find to be about half-true).

(Actually, it is now realized that a better measure is relative difference rather than ratio: strikeouts minus walks divided by plate appearances — (K-BB)/PA — but the K/W ratio is more familiar to most people and serves almost as well.)

By now, “BABIP” (Batting Average on Balls in Play) is become another “standard” measure. It is just what its name says: the hits obtained on all balls put in play—that is, all balls that are theoretically fieldable (that’s at-bats less strikeouts and home runs plus sac flies; Sacrifice Bunrsa are excluded.)

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Some Non-Standard Baseball Measures

Miscellaneous Useful Stats

The “HA” is an Owlcroft stat—the “Hitting Average”. It is similar to the BA, but the basis is all plate appearances, not just at-bats. It thus expresses the batter’s actual likelihood of getting a hit in a particular appearance, which the Batting Average (one of the least useful of conventional stats) does not. It’s not an integral part of our analyses, but it’s a nice little metric for actual hitting (players with the same number of hits in the same number of plate appearances will always have the same HA, but their BAs can differ substantially depending on how often each walks).

The “PF” is the Power Factor; it is total bases divided by hits, or—put another way— the average number of bases per hit by the batter. This number is related to but quite distinct from so-called “Isolated Power” (SA - BA), because it is unrelated to how many hits or extra bases a batter or team gets: it is concerned only with the ratio of total bases to hits, which makes it the only available realistic measure of actual power. A better with a terrible BA can still have huge raw power, and this metric shows raw power (or lack of it); though speed is nominally in the mix, it has almost no effect, because home runs dominate the PF. Power Factors run in well-established ranges: from 1.15 to 1.25 is the now-rare true “Judy” or “banjo” or “slap” hitter—the man who just gently pokes the ball over the infielders for a single, only very occasionally getting a double and almost never a home run. From 1.30 to 1.35 is the usual non-power-hitter value. From 1.5 up, we are dealing with power hitters, though the low end of that range is nowadays debased by the SillyBall, the juiced baseball (values from 1.35 to 1.50 are somewhat unusual, and are often slow runners who are getting singles where an even average runner would get doubles.) A value of 2.0 or above is rare even in a single season (though, again, now much less so than not so long ago), and for a career was once (in the sunny days before the juicing) seen only once in a decade or so; even nowadays, it remains unusual.

The “BBA”, the BB Average (sometimes rendered as “BB%”), is simply the average rate at which the man takes walks (walks per plate appearance); likewise, the “KA” is simply the average rate at which the man strikes out (strikeouts per plate appearance).

The “TBA” is the “Total-Base Average”: total bases per plate appearance. It stands to the Slugging Average as the Hitting Average does to the Batting Average, and is correspondingly very much more meaningful than the SA. (Obviously, it is not truly an “average” because it can exceed 1.000, but that is a handy term for it, paralleling “On-Base Average”.)

A perhaps useful way to relate these measures to a baseball game you see before your eyes is this:

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The TOP: Total Offensive Productivity

To the extent that a man’s total value to a team as a batter can be expressed in a single number (most analysts accept that it can) the TOP is Owlcroft’s rendition of such a number.

Simply put, the TOP is the number of runs that would be scored in a full, normal-length season by a baseball line-up of nine men each an exact clone of the man being rated. There is an extended discussion of the TOP and baseball-analysis theory in general elsewhere on this site.

Key here is that the TOP is not a relative and thus subjective measure: it is an absolute measure, meaning that it has a demonstrable real-world application and possesses what scientists call “falsifiability”—in other words, its correctness can be tested and proved or disproved. It has been tested, thoroughly, and has not been falsified.

( If you’re a sportscaster, that’s “very key”.)

There is a corresponding measure for pitchers, the TPP, “Total Pitching Productivity”, and a derived close relative, the “Quality of Pitching”; we discuss those on a separate page here.

One can thus, in principle, combine the TOPs of the men on an actual baseball team and make presumably useful and reasonably accurate predictions of how many runs that team will score. And indeed, subject to some qualification and technicalities, one can in fact as well as principle. The chief technicality is that one cannot simply add up the men’s TOPs, even pro-rated for play time, because the TOP is a multiplicative measure and “the average of the means is not, in general, equal to the mean of the averages”.

Illustration of that mathematical remark:
  7 x 9 = 63
  5 x 5 = 25
  ----------
  6 x 7 = 42
The average of the products, 63 and 25, is 44. But the product of the averages, 6 and 7, is 42, which is obviously not equal to 44.

The proper technique is to separately average the men’s on-base values and their “RBI factor” values—each pro-rated by percentage of team play time—then multiply those separately averaged values. (There is a quick-and-dirty method that simply averages the pro-rated TOPs, then multiplies by a rule-of-thumb fudge factor to get an approximate estimated team TOP.)

The tools’ limitations as a means of projecting the final October standings on the morning of opening day are chiefly associated with one variable: playing time. Men get injured or traded, managers get good or bad inspirations, and so on. One cannot get rich by going to a baseball sports book with these techniques, because one cannot project—even approximately—who, by season’s end, will actually have played how much where. We are scientists, not thaumaturges. But one can use the principles to “engineer” a team that should win a specified number of games (if the horses can be had).

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This page was last modified on Tuesday, 29 September 2020, at 4:56 am Pacific Time.