Fans of the game of baseball, its writers and broadcasters, its players and managers, executives...all rely on the sport's various and wonderful statistics to enhance their enjoyment of the game.

Three of the main tools used to evaluate hitters are batting average, on-base percentage, and slugging percentage.

Of these, on-base percentage is in vogue in the decade of the 1990's as far evaluating the relative merits of ballplayers...as well as where those ballplayers are best suited to bat in the starting lineup.

The now widely-accepted view is that high on-base percentage guys should populate the top half of the batting order...because those very players will come to bat most often in a given baseball game, and thus add value their respective teams.

In "Batting Orders...and Statistics (Part One)", another statistic was introduced.

The statistic?

We'll call it "Scoring Average".

Scoring Average is analogous to on-base percentage...in that while a player's on-base percentage is a measure of his ability to reach base safely (including walks), a player's Scoring Average is a measure of how often he crosses home plate, once he gets on base.

Stated differently, Scoring Average can be thought of as follows:

Every time a hitter reaches base by a hit or a walk (but not a home run...that's not reaching base!)...what fraction of the time does he score?

A given player's Scoring Average (SA) is, therefore, a measure of the ease with which a player, once he reaches base, can be pushed around the bases, by some combination of his teammates' achievements and the opposition's miscues.

All factors equal (which they never are), speedy players should have higher Scoring Averages than slow-footed players...and good baserunners should have higher Scoring Averages than poor baserunners.

And it seems logical that, in a given lineup, third place hitters should have higher Scoring Averages than fourth place hitters...

Which leads us to Mark McGwire, and McGwire's spot in the Cardinals 1998 and 1999 batting orders: third.

In Batting Orders...and Statistics (Part One), former Cardinal Brian Jordan explained why he did not enjoy hitting clean-up as a Cardinal, behind Mark McGwire.

Jordan believes that Mac's lack of speed should preclude the single-season home run king from a top-of-the-lineup spot in the batting order.

And in the same article, Cardinals manager Tony La Russa, who acknowledged that McGwire "clogs the bases", explained why he believes that McGwire-in-the-three-hole is the best batting order for the Cardinals.

Paraphrasing, La Russa's reasoning can be reduced to the following--"Why mess with a line-up in which your #3 hitter has hit 135 homers in two years?"

But also found in "Batting Orders...and Statistics (Part One)" were statistics, which, at some level, suggested that La Russa's insistence that McGwire batting third flies in the face of baseball tradition.

In 1998 and 1999, Mark McGwire hit a total of 135 home runs (70 and 65, respectively).

During those same two seasons, Mac scored 248 runs (130 and 118, respectively).

In other words, McGwire drove himself in 135 times, and scored as a result of a teammate's effort (or an opponent's misplay) a total of 113 times.

Also, in 1998 and 1999, McGwire reached base (i.e. first, second, or third base) via a single, double, triple or walk a total of 457 times.

Meaning that, while batting third in 1998 and 1999, and excluding home runs, McGwire scored 113 runs while reaching base 457 times...a "scoring average" of 0.25.

Therefore, in 1998 and 1999, when Mark McGwire reached base via a hit or walk (but not a home run), he eventually scored about 25% of the time (1 time in 4).

[EDITOR'S NOTE: To calculate scoring average...subtract home runs from runs...and divide that total by hits + walks - home runs; [(R - HR) / (H + W - HR)]. This analysis ignores occasions in which batters reach base via a fielder's error, fielder's choice, or a hit by pitch...among others.]

"Scoring Averages" for other batting-third sluggers in 1998 include those for Sammy Sosa (0.33) and Ken Griffey Jr. (0.33).

Sosa and Griffey, McGwire's slugging contemporaries, therefore scored approximately one run every three times that they reached base in 1998...again excluding home runs.

But Mark McGwire, while batting third in the Cardinals line-up in 1998 and 1999, circled the bases only 25% of the time that he reached base...excluding home runs.

At least on the surface, these comparisons provide some evidence for Brian Jordan's assertion that Mark McGwire's spot in the batting order should be clean-up...or lower.

Indeed, Big Mac's career Scoring Average is 0.25...identical to his percentage during the last two seasons.

Statistically speaking, which baseball player comes to mind as most similar to Mark McGwire?

Says here that Harmon Killebrew fills that bill.

For one thing, Killebrew played most of his big league games at 1B...as does McGwire.

And, with 19 career stolen bases, Killebrew averaged one steal per season in a 22 year major league career..totals similar to Mac's 11 steals in 15 seasons.

Of course, there's the matter of home runs.

Courtesy of STATS, Inc, the career statistics for Harmon Killebrew and Mark McGwire are reproduced below.

      
HARMON KILLEBREW
 YR TEAM LG    G    AB    R    H   2B  3B  HR  RBI   BB   AVG   OBP   SLG
1954 Was AL    9    13    1    4    1   0   0    3    2  .308  .400  .385
1955 Was AL   38    80   12   16    1   0   4    7    9  .200  .281  .362
1956 Was AL   44    99   10   22    2   0   5   13   10  .222  .291  .394
1957 Was AL    9    31    4    9    2   0   2    5    2  .290  .333  .548
1958 Was AL   13    31    2    6    0   0   0    2    0  .194  .212  .194
1959 Was AL  153   546   98  132   20   2  42  105   90  .242  .354  .516
1960 Was AL  124   442   84  122   19   1  31   80   71  .276  .375  .534
1961 Min AL  150   541   94  156   20   7  46  122  107  .288  .405  .606
1962 Min AL  155   552   85  134   21   1  48  126  106  .243  .366  .545
1963 Min AL  142   515   88  133   18   0  45   96   72  .258  .349  .555
1964 Min AL  158   577   95  156   11   1  49  111   93  .270  .377  .548
1965 Min AL  113   401   78  108   16   1  25   75   72  .269  .384  .501
1966 Min AL  162   569   89  160   27   1  39  110  103  .281  .391  .538
1967 Min AL  163   547  105  147   24   1  44  113  131  .269  .408  .558
1968 Min AL  100   295   40   62    7   2  17   40   70  .210  .361  .420
1969 Min AL  162   555  106  153   20   2  49  140  145  .276  .427  .584
1970 Min AL  157   527   96  143   20   1  41  113  128  .271  .411  .546
1971 Min AL  147   500   61  127   19   1  28  119  114  .254  .386  .464
1972 Min AL  139   433   53  100   13   2  26   74   94  .231  .367  .450
1973 Min AL   69   248   29   60    9   1   5   32   41  .242  .352  .347
1974 Min AL  122   333   28   74    7   0  13   54   45  .222  .312  .360
1975 KC  AL  106   312   25   62   13   0  14   44   54  .199  .317  .375
TOTALS      2435  8147 1283 2086  290  24 573 1584 1559  .256  .376  .509
      

MARK McGWIRE
 YR TEAM LG    G    AB    R    H   2B  3B  HR  RBI   BB   AVG   OBP   SLG
1986 Oak AL   18    53   10   10    1   0   3    9    4  .189  .259  .377
1987 Oak AL  151   557   97  161   28   4  49  118   71  .289  .370  .618
1988 Oak AL  155   550   87  143   22   1  32   99   76  .260  .352  .478
1989 Oak AL  143   490   74  113   17   0  33   95   83  .231  .339  .467
1990 Oak AL  156   523   87  123   16   0  39  108  110  .235  .370  .489
1991 Oak AL  154   483   62   97   22   0  22   75   93  .201  .330  .383
1992 Oak AL  139   467   87  125   22   0  42  104   90  .268  .385  .585
1993 Oak AL   27    84   16   28    6   0   9   24   21  .333  .467  .726
1994 Oak AL   47   135   26   34    3   0   9   25   37  .252  .413  .474
1995 Oak AL  104   317   75   87   13   0  39   90   88  .274  .441  .685
1996 Oak AL  130   423  104  132   21   0  52  113  116  .312  .467  .730
1997 2TM     156   540   86  148   27   0  58  123  101  .274  .393  .646
     Oak AL  105   366   48  104   24   0  34   81   58  .284  .383  .628
     StL NL   51   174   38   44    3   0  24   42   43  .253  .411  .684
1998 StL NL  155   509  130  152   21   0  70  147  162  .299  .470  .752
1999 StL NL  153   521  118  145   21   1  65  147  133  .278  .424  .697
TOTALS      1688  5652 1059 1498  240   6 522 1277 1185  .265  .394  .587

Significantly, Killebrew's career Scoring Average is 0.23...a value very close to Mac's lifetime Scoring Average of 0.25.

And the slow-footed Harmon Killebrew, for much of his career, hit fourth in the Minnesota Twins lineup.

In fact, it's hard to envision "The Killer" as a number-three guy, isn't it?

Scoring Averages for other sluggers are easily determined from readily available statistical compilations...and single-season Scoring Averages (SA) for several home run hitters who batted fourth (or lower in the order) during the listed years are shown below.

Analysis of the statistics for the hitters listed above reveals a remarkable consistency in the Scoring Averages for stereotypical sluggers that lack foot speed. After reaching base, Johnny Bench (1970) and the rest of the players listed above circle the bases about a quarter of the time.

Note that Hank Aaron, in 1971, was at the tail-end of his career...and his once-great speed was not in evidence then.

Not all clean-up hitters, though, have Scoring Averages that translate into one run for every four times on base.

For example, Scoring Averages for Lou Gehrig (in 1937), Hank Greenberg (1938), Jimmie Foxx (1932), Mickey Mantle (1961), Reggie Jackson (1973), Hank Aaron (1957), and Sal Bando (1969) are 0.35, 0.36, 0.34, 0.33, 0.33, 0.35, and 0.30, respectively.

And Brian Jordan, hitting clean-up as a Cardinal in 1998, and as an Atlanta Brave in 1999, posted Scoring Averages of 0.39 and 0.40, respectively.

What distinguishes this latter group of players (Gehrig et al) from those listed in the clean-up hitters list?

Gehrig, Greenberg, and Foxx et al could run a bit.

For example, Gehrig recorded 17 steals in 1931, Greenberg had nine steals in 1934, Foxx had 13 stolen bases in 1936, and even Bando had 20 stolen bases as a 32-year-old third baseman in 1976.

The speed possessed by Mantle, Jackson, Aaron (in his prime), and Jordan is obvious to most readers.

But this story is really about Mark McGwire, and his position (third) in Cardinal manager Tony La Russa's lineup.

The relevant Scoring Average stats for Mark McGwire, batting third for the St. Louis Cardinals in 1998 and 1999, are shown below:

Single-season Scoring Averages for several other home run-hitting third-place hitters are listed below:

Analysis of the statistics for third-place hitters listed above reveals a remarkable consistency in the Scoring Averages for stereotypical power hitters that possess some speed...in that...after reaching base, the third-place hitters circle the bases about a third of the time...or greater.

The vagaries of the Scoring Average statistic, in terms of its dependence on the quality of the hitters that follow a given player in the lineup, are demonstrated by the Joe DiMaggio 0.46 SA that the Yankee Clipper posted in 1937.

The fact that perhaps the greatest clean-up hitter of all time, Lou Gehrig, posted phenomenal power and RBI numbers that year added luster to DiMaggio's scoring average.

But DiMaggio, in addition to possessing good baserunning skills, had good speed, too (although his stolen base totals were low). Babe Ruth, in his monstrous '27 season...also batted third in front of Gehrig...but "only" managed a 0.36 SA.

Historically speaking, then, analysis of Mark McGwire's Scoring Averages in 1998 and 1999 (0.24 and 0.25 while batting third as a Cardinal) and 1987 (0.26 while batting clean-up as an Oakland A) suggests that his "proper" spot in a batting order is as a number four hitter, and not as a #3 guy.

But times change in baseball.

Perhaps Tony La Russa is on to something.

That's because, in 1999, Sammy Sosa and Chipper Jones, both hitting third in their respective lineups, posted Scoring Averages of 0.25 and 0.27, respectively.

Poor Brian Jordan.

He cleans up after McGwire in 1998 (starting 91 games as the Cardinals clean-up hitter) and posts a Scoring Average of 0.39.

Then he complains about his spot in the order...and leaves St. Louis for Atlanta.

Then Andres Galarraga is stricken with cancer.

So in 1999, Jordan bats fourth behind Chipper Jones, and his Scoring Average improves to 0.40!

And then there's Ray Lankford, for whom 1999 was an off year.

Lankford's '99 Scoring Average...batting fourth behind Mac?

0.38.

And Fernando Tatis, who, in 1999, had a breakout year in which he scored 104 runs, clubbed 34 homers, had 160 hits, and walked 82 times...batting fifth or lower most of the time?

Tatis' 1999 Scoring Average was 0.34.

Which brings us back to Cardinals manager Tony La Russa and his daily decision to make out a lineup card that features Mark McGwire in the #3 hole.

La Russa believes that if Mac hits fourth, in a lineup without sufficient protection, that "no one would ever pitch to Mark", that his power production would drop substantially, and that the Cardinals offense would suffer as a result.

Which leads to several unanswerable questions.

Would Mark McGwire have hit 70 homers in 1998 if he had batted fourth?

Or, would Mark McGwire have hit, say, 65 homers in 1998 if he had batted fourth?

Or, would Mark McGwire hit "only" 50 homers in 1998 if he had batted fourth?

Exactly how many homers would Mark McGwire have hit in 1998 if he had batted fourth?

Would he have broken Maris' record?

But, more importantly from La Russa's perspective, a manager who, in the opinion of many, craves winning as much as most humans crave oxygen, would the Cardinals have won more games with Mac hitting behind Lankford and Jordan in 1998...and behind Lankford and Tatis, in 1999?

And what will the Cardinals batting order look like in 2000?