June 2006

Although modern electronic means of transmitting the statistics of many major sports are now common, innovations in the statistics themselves are extremely rare. Baseball is virtually the only sport where statistics are frequently being discovered. This column details five new statistics invented by the author:

  • Isolated Power
  • 2×2 Rate Distribution
  • 2×2 Volume Distribution
  • Pitcher Measure
  • Volume Pitcher Measure

The first of these creations, Isolated Power, is the simplest. Although this statistic is not very strong for actual analysis of how good a player is, it can be very helpful for comparing different types of players. The formula is:

1B + 2 x 2B + 3 x 3B + 4 x HR = TB = (SLG x AB)=IPow

H                                  H              H

(Note: an index of statistical abbreviations can be found at the end of this column.)

The typical IPow now is about 1.62, and surprisingly, due to the designated hitter, is slightly higher in the National League. Isolated Power is also useful for analyzing differences between eras. For example, in the baseball dark ages of 1880, there were only 1.28 bases per hit, a ridiculously low number. Also, IPow usually responds quite well to pitcher dominance, as the following chart of National League isolated powers and ERA’s shows:

Year 1967 1968 1969
ERA 3.38 2.99 3.60
IPow x 2.25 3.285 3.15 3.325

In fact, ERA and IPow x 2.25 have a Pearson correlation of .939, with -1 being no correlation and 1 being perfect correlation. IPow, though deceptively simple, can thus be very useful.

The second of these discoveries is 2×2 Rate Distribution. This statistic attempts to measure overall hitting prowess with double weight to both percentage hitting and slugging. The formula is:

SQRT (AVG x OBP x SLG2)=2×2 Rate

Some career 2×2 Rates:

Babe Ruth:         .277

Ted Williams:    .258

Ty Cobb:            .203

Mickey Mantle: .197

Willie Mays:      .190

One nice thing about this statistic is that it’s easy to adjust, because you can calculate adjusted AVG’s, OBP’s, and SLG’s, and plug them in the formula. This statistic is also the means for calculating Mean Differential (MDif), which is found by computing the player’s 2×2 Rate and then subtracting the league average.
For a volume interpretation of this statistic that reflects how many times a player has gone to bat,  we can use 2×2 Volume Distribution. It is found by the following formula:

(MDif x PA)/20=2×2 Volume

At this point, it is very helpful to use MDif and not 2×2 Rate. Why? If you do this with adjusted 2×2 Rate to find the MDif, you automatically get a built-in comparison to the average player, at 0. This is especially helpful in evaluating careers, since to find a career 2×2 Volume, you simply add all the career 2×2’s together.

Although these 2×2 methods do not factor in base running, stealing, and fielding, and give no way whatsoever to rate pitchers, they are an easy and accurate way to compare hitting. Since these statistics are calculated by multiplication, they also reward players who are more balanced which is an additional benefit.

Now let’s explore a new method for evaluating hurlers called Pitcher Measure. The formula is:

[(WP/TWP) x (LG ERA - ERA) x (K/BB)]/40=Pitcher Measure=PM

WP is in fact a poor statistic, but when it is divided by the team winning percentage, it is a simple and fairly accurate measure. Nobody doubts that ERA is a definitive measure of pitching excellence, and so it obviously merits inclusion. The adjustment to the league has two benefits. The first is that this automatically gives a statistic in which an average performance is 0. Also, this is an adjustment of ERA so regular adjustment is not needed. K/BB may look strange but is just an assessment of control. An average PM is obviously 0, but for a pitcher slightly above the mean .03 would be typical. A Cy Young Award candidate would be about .2. Also, it’s useful to note that this statistic is in fact quite comparable to 2×2 Rate.

The alteration of this statistic to volume type gives us Volume Pitcher Measure, or:

PM/5=VPM

In transforming this stat to volume form, note that we don’t have to make any alteration like we did above in finding 2×2 Volume. Since PM automatically adjusts to the mean, i.e., an average performance is 0, above average is >0, etc., there is no reason to have to make an adjustment to the mean like in 2×2 Distribution. Again, to find the career VPM, just add up all the seasonal values.

In conclusion,

Statistical Index

1B: Singles.

2B: Doubles.

3B: Triples.

AB: At-bats.

AVG: Batting average, H/AB.

BB: Walks.

ER: Earned runs, runs allowed without errors.

ERA: (ERx9)/IP

H: Hits.

K: Strikeouts.

L: Losses.

LG ERA: League ERA.

OBP: On base percentage, (H+BB)/(AB+BB)

PA: Plate appearances, AB+BB

SLG: Slugging percentage, TB/AB

TB: Total bases, 1B + 2 x 2B + 3 x 3B + 4 x HR.

TWP: Team winning percentage.

W: Wins.

WP: For a pitcher, W/L.