Base Advance Average
Base-Advance Average
Gary M. Hardegree
Department of Philosophy
University of Massachusetts
Amherst, MA 01003
1.
Introduction
In what follows, I propose a new performance measure ("stat") for baseball, which I call base-
advance average, which I compare with conventional stats, including batting average, on-base
percentage, slugging percentage, and OPS.
My comparisons are based on play-by-play records of all the regular season games currently
available at Retrosheet, which total 74,255 games, and include the years 1960-1992 and 2000-2004
(alas, the years 1993-1999 are still unavailable to the public).
In order to facilitate the comparison, I further propose a simple way to evaluate stats called win-
tracking rate. As it turns out, among the conventional stats, the best is OPS, which tracks wins at a rate
of 84%, and the worst is hits, which tracks wins at a rate of 71%. But the conventional stats are all
eclipsed by base-advance average, which tracks wins at a rate of 95%.
Along the way, by way of illustration, I evaluate various players and teams with respect to base-
advance average. The evaluation of teams leads to further statistical comparisons. Here, the results are
equally decisive in favor of base-advance average. For example, over the period 2000-2004, base-
advance average for-and-against predicts wins just as well as runs for-and-against. This is because, over
this period, base-advance average correlates with runs at a "rate" of .988!
2.
Evaluating Stats
Baseball comes with a vast array of performance measures ("stats"), some of which are
enshrined, such as batting-average and earned-run-average, and others of which are less prestigious, but
which are nevertheless useful in managing and appreciating the game.
Stats are used to evaluate and compare players and teams, but how do we evaluate and compare
stats? For this purpose, I propose that we measure all stats against the collective purpose of the team,
which (presumably) is winning. In particular, in order to evaluate various stats, I propose a very simple
measure, which I call win-tracking rate, which is defined as follows.
Let S be a stat. Then the win-tracking-rate (WTR) of S is, by definition, the frequency at
which the winning team out-performs the losing team with respect to S.
For example, the win-tracking-rate of hits is how frequently the winning team out-hits the losing team.1
Besides being fundamentally easy to understand, win-tracking-rate can be applied indifferently
to count-stats, such as hits, and rate-stats, such as batting average.2
1 Note that, by the win-tracking criterion, the best stat of all is, of course, runs. The winning team out-performs the losing
team 100% of the time with respect to runs, by definition. Unfortunately, runs is not a very good stat for evaluating
individual players because scoring runs generally involves teamwork. Accordingly, baseball analysts seek other stats that
apply meaningfully to individual players but manage to track runs and hence wins.
2 A count-stat is one that results from totaling a kind of events – e.g., hits – whereas a rate-stat is one that results from
dividing one total by another – e.g., batting average – which is total hits divided by total at-bats.
Hardegree, Base-Advance Average
page 2 of 9
3.
The Data
The data I examine come from play-by-play records of all the regular-season games currently
available from Retrosheet, 3 which include the years 1960-1992 and 2000-2004, and comprise 74,225
games. The following table summarizes the findings for selected conventional stats.4
stat
WTR
maximum
minimum
variance
OPS
84.0%
85.0%
81.5%
0.99%
weighted batting average5
81.7%
83.7%
78.6%
1.60%
slugging percentage
80.8%
83.1%
78.9%
1.07%
on-base percentage
79.8%
82.3%
76.6%
1.79%
total bases + times on base
79.7%
81.0%
76.0%
1.47%
batting average
78.6%
80.8%
76.0%
1.41%
total bases
75.0%
78.8%
73.9%
1.33%
times on base
74.5%
76.9%
70.9%
2.01%
hits
70.5%
73.2%
67.8%
1.90%
As one can see in the above chart, the winner is OPS, and the loser is hits. Over the course of
74,225 games, the winning team out-performed the losing team 84% of the time with respect to OPS,
whereas the winning team out-hit the losing team only 71% of the time. That it tracks winning the best
among conventional stats supports its increased attention over the last few years.
Nevertheless, there remains considerable room for improvement.
4.
A New Way to Measure Offensive Performance
By way of improving upon the above results, in what follows, I propose a new way of measuring
offensive performance. The new measure is not constructed from existing measures, but is rather
created from scratch from play-by-play data. Of course, this means that the proposed stat cannot be
calculated from the usual baseball summaries (e.g., box-scores). Nevertheless, it can be readily
calculated from widely available play-by-play accounts of games, and it can be calculated on the spot by
anyone who keeps score during the game.6
1.
The Basic Idea – Advancing Base Runners
It has often been said that the goal of the offense in baseball is to get men on base, move them
along, and get them home.7 We can simplify this account by treating every offensive player as a base-
runner, in which case we can say that the goal of the offense is to advance base-runners ultimately home.
3 Baseball researchers are all profoundly grateful to Retrosheet and its many dedicated volunteers over the years, who have
made this data available, and whose only requirement in return is that we include the following official disclaimer.
The information used here was obtained free of charge from and is copyrighted by Retrosheet. Interested parties
may contact Retrosheet at 20 Sunset Rd., Newark, DE 19711.
4 In this chart, WTR is win-tracking rate, whereas maximum, minimum, and variance refer to year-to-year results. For
example, in its best year, OPS tracked wins at a rate of 85.0%, and in its worst year OPS tracked wins at a rate of 81.5%.
5 Weighted batting average is similar to slugging percentage, except that it includes walks and it also weights the various
events according to well-known ideas according to how much each is worth. The weights I employ, which come from Albert
and Bennett, Curveball, are as follows. Walk – .36; Single – .52; Double – .67; Triple – 1.18; Homerun – 1.50.
6 That is, provided one includes a few more details in the account. See Section 4.3.
7 Bear in mind that, in this context, a "man" may very well be a woman or a child. For the sake of simplifying my
description, and grammar, I simply pretend that all baseball players are men.
Hardegree, Base-Advance Average
page 3 of 9
Accordingly, the success of an offensive player is measured by how many base-runners he
advances how far.8 The unit of measurement is base-runners-bases-advanced, or more simply bases-
advanced, or even more simply bases. For example, if the batter moves a runner from first-base to
second-base, he is credited with one base; and if he moves a runner from first-base to third-base, he is
credited with two bases; etc. In the meantime, if the batter advances himself to first-base, he is credited
with one base, and if he advances himself to second-base, he is credited with two bases, etc. A player is
also credited with a base-advance for each base he steals.
Note that the exact manner in which the base-advances are achieved is irrelevant to score-
keeping. For example, with the bases empty, reaching first-base is scored as one base, irrespective of
whether it achieved via a hit, walk, or error. Similarly, a lead-off walk followed by a stolen base is
tallied as two bases, which is the same as a lead-off double. By the same token, a lead-off batter who
hits but not safely is credited with zero bases, just as if he had struck out.
One can also achieve negative bases-advanced, which happens when base-runners are erased. In
particular, erasing a base-runner on first / second / third is scored as −1 / −2 / −3 bases, respectively. For
example, suppose the lead-off batter reaches first on a single, but is subsequently caught stealing. The
first event counts as +1, and the second event counts as −1, so that the net result is 0. An extreme
example involves a batter hitting into a triple-play (say 5-4-3). Since the man on second is erased, this
counts as −2, and since the man on first is erased, this counts as −1, so the net result is −3. Other
examples involve force-outs and fielder's choices. For example, a force-out at second-base produces a
net result of 0, since the batter reaches first (+1), but the man on first is out (−1).9
2.
Base-Advance Average
The next obvious question is what denominator do we use to produce a base-advance average?
One's initial inclination is to divide bases-advanced by plate-appearances, but this does not properly
count opportunities, which can be greater or smaller, and which can be converted or squandered. For
example, it is generally agreed that striking out with the bases loaded is considerably worse than striking
out with the bases empty; yet both involve zero bases-advanced over one plate-appearance (0-for-1).
In order to take these important differences into account, I propose a considerably more useful
denominator, called base-advance opportunities, or simply opportunities. For each plate appearance, for
each base-runner (including the batter), there is a maximum number of bases that the base-runner can be
advanced; for example, the batter can be advanced a maximum of 4 bases, and a man on first can be
advanced a maximum of 3 bases. The number of opportunities is then the total of all of these individual
maxima. So, for example, if the bases are empty there are 4 opportunities, whereas if the bases are
loaded there are 10 (4+3+2+1) opportunities.
8 Since beginning my investigations, I have learned that this measure was proposed over 90 years ago. In Alan Schwarz's
fabulous book The Numbers Game , he reports on page 37 that, in a letter to Baseball Magazine in 1913, a fan J.H. Hamel
proposes measuring base-advances in exactly this manner. Also, I recently learned that, for the past few years, Steve Winters
has promoted this idea on his extensive website http://www.basesproduced.com/. There are differences in our approaches. I
count base-losses as negative base-advances, whereas Winters counts them separately, and Hamel does not mention them.
Furthermore, in the matter of constructing an associated base-advance average, Hamel proposes using plate-appearances as
the denominator, and Winters proposes using base-runners (including the batter) as the denominator, whereas I propose base-
advance opportunities as the denominator (see Section 4.2).
9 As with many stats, such as hits versus errors and wild pitches versus passed balls, score-keeping requires interpretation.
For example, suppose a runner is sent home by the third-base coach, but is thrown out at home. Who do we charge the −3
bases to? The batter? The base-runner? The third-base coach? The team? In live score-keeping, this will be a matter of on-
the-spot evaluation, since we have the play right in front of us. For example, in Game 3 of the 2004 World Series, the
audience witnessed a colossal base-running error, which clearly should be charged to the base-runner. On the other hand, in
retrospective score-keeping, we do not have this luxury; we only have the before-states and the after-states. For retrospective
score-keeping, I propose that we charge −3 bases to the batter, treating such a play as similar to a fielder's choice. This is not
entirely fair to the batter, but the batter gets breaks on other plays in which he is credited for base-advances that perhaps
should be credited to the swiftness of a base-runner ahead of him.
Hardegree, Base-Advance Average
page 4 of 9
Base-advance average is computed by dividing the total bases-advanced by the total number of
base-advance opportunities.10 So, a strike-out with the bases empty counts as 0-for-4, whereas a strike -
out with the bases loaded counts as 0-for-10. On the other hand, a walk with the bases empty counts as
1-for-4, whereas a walk with the bases loaded counts 4-for-10, and a grand-slam counts as 10-for-10.
3.
A Sample Inning
By way of a illustration, I present the following sample half-inning, which recreates the top of
the third inning of the fourth game of the 2004 World Series, between the Boston Red Sox and the St.
Louis Cardinals.
base-runner
base
bases
player
play
advances
advance
adv'ed
0
1
2
3
opp's
Cabrera
F7
0
0
4
Ramirez
1b 7
1
1
4
Ortiz
2b 9
2
2
4
7
Varitek
FC 4-2
1
1
−3
−1
7
Mueller
BB
1
1
0
2
8
Nixon
2b 8
2
2
2
1
7
10
Bellhorn
BB
1
0
0
1
7
Lowe
K
0
0
0
0
0
10
Total
14
57
Fundamental to score-keeping are the base-runner advance entries, which are highlighted. For example,
Varitek bats with men on second and third, so the number of base-advance opportunities for him is 7.
He grounds into a fielder's choice, which moves him to first (+1), and moves the man on second to third
(+1), but erases the man on third (−3), and which accordingly tallies as −1 for 7. All told, the inning
produces 14 base-advances over 57 opportunities, for a base-advance average of .245.11
5.
How Good a Stat is Base-Advance Average?
Irrespective of its intuitive appeal, the "cash value" of a stat is how well it tracks winning. Here,
our findings demonstrate that total bases-advanced is a very good stat, and base-advance average is an
excellent stat, which may be seen in the following summary table.
stat
WTR
maximum
minimum
variance
base-advance average
95.5%
96.4%
94.7%
0.16%
total bases-advanced
88.5%
90.0%
86.3%
0.68%
What is remarkable, I believe, is that no t only does base-advance-average track winning at an
astonishing rate of 95.5% over the course of 74,225 games, it also does so with a rock-steady
consistency from year to year, as indicated by the exceptionally small variance.
10 Note carefully that non-batting plays (e.g., stolen bases) add to the total number of bases advanced, but do not add to the
total number of opportunities. Accordingly, a lead-off walk followed by a stolen base nets the player +2 base-advances over
4 opportunities. The calculations produce occasional oddities; for example, if a pinch-runner steals a base, he is credited with
+1 base over 0 opportunities for a base-advance average of "infinity". The latter, of course, is similar to those occasions in
which an unfortunate pitcher gives up runs but records no outs, and whose ERA is accordingly infinite.
11 The fraction .245 is not very good as a batting average, let alone a slugging average, but it is a very good number for base-
advance average, whose average value from 2000 to 2004 was 150. See Section 6.
Hardegree, Base-Advance Average
page 5 of 9
6.
How do the Players Stack Up?
The following table presents the base-advance-average champions for the available years, as well
as the league averages for those years.12
-
advance
-
advance
ses
ses
se
late
year
player
p
appearances
ba
advanced as
a batter
ba
advanced as
a runner
base
opportunities
ba
average
league
average
1960 Williams
Ted
390
455
5
2256
203.9
140.9
1961 Mantle
Mickey
646
758
22
3543
220.2
143.8
1962 Mantle
Mickey
502
613
19
2839
222.6
142.7
1963 Aaron
Hank
654
653
38
3518
196.4
133.7
1964 Mantle
Mickey
567
615
10
3170
197.2
136.7
1965 Mays
Willie
638
649
26
3445
195.9
133.1
1966 Allen
Dick
599
636
8
3307
194.7
133.6
1967 Yastrzemski Carl
679
735
25
3662
207.5
130.2
1968 Yastrzemski Carl
664
616
39
3623
180.8
126.8
1969 McCovey
Willie
583
684
10
3319
209.1
136.4
1970 McCovey
Willie
638
758
10
3714
206.8
144.3
1971 Aaron
Hank
546
598
5
3011
200.3
136.1
1972 Williams
Billy
650
717
13
3533
206.6
132.1
1973 Stargell
Willie
609
657
14
3307
202.9
139.3
1974 Morgan
Joe
641
632
66
3580
195.0
138.2
1975 Morgan
Joe
639
701
72
3636
212.6
140.9
1976 Morgan
Joe
599
708
65
3397
227.6
136.6
1977 Carew
Rod
694
746
27
3765
205.3
145.1
1978 Parker
Dave
642
676
38
3417
209.0
140.1
1979 Lynn
Fred
622
682
10
3335
207.5
145.6
1980 Brett
George
515
629
20
2849
227.8
140.0
1981 Schmidt
Mike
434
495
17
2456
208.5
135.2
1982 McRae
Hal
676
704
5
3727
190.2
139.7
1983 Murphy
Dale
687
663
38
3705
189.2
140.0
1984 Davis
Alvin
678
695
8
3740
188.0
139.6
1985 Brett
George
665
678
15
3497
198.2
143.9
1986 Davis
Eric
487
440
91
2613
203.2
146.0
1987 Davis
Eric
562
577
66
3059
210.2
149.5
1988 Canseco
Jose
705
705
40
3837
194.2
140.0
1989 Clark
Will
675
701
24
3631
199.7
140.2
1990 Bonds
Barry
621
610
42
3350
194.6
142.0
1991 Bonds
Barry
634
657
45
3626
193.6
141.3
1992 Bonds
Barry
612
653
38
3382
204.3
140.9
2000 Helton
Todd
697
903
13
3971
230.7
155.6
2001 Bonds
Barry
664
864
13
3604
243.3
150.6
2002 Bonds
Barry
612
783
17
3331
240.2
148.2
2003 Bonds
Barry
550
670
17
3062
224.4
149.9
2004 Bonds
Barry
617
835
21
3449
248.2
151.3
12 Note that the units for base-advance average we employ are bases per thousand opportunities. So, for example, in 1960
Ted Williams produced 203.9 bases per t housand opportunities.
Hardegree, Base-Advance Average
page 6 of 9
On the other hand, the following are the top ten cumulative performances for each decade except the 90's
(for which we only have three years of data).
-
advance
-
advance
ses advanced
ses advanced
late
decade
player
p
appearances
ba
as a batter
ba
as a runner
base
opportunities
base
average
60-69
Mantle
Mickey
4499
4495
94
24619
186.4
Robinson
Frank
6172
6091
205
33950
185.4
Mays
Willie
6181
5979
198
33652
183.6
Aaron
Hank
6175
5960
241
33895
182.9
McCovey
Willie
4961
4875
90
27279
182.0
Killebrew
Harmon
6000
5858
80
32663
181.8
Allen
Dick
3664
3452
72
19932
176.8
Kaline
Al
5450
5037
172
29909
174.2
Cash
Norm
5688
5365
117
31594
173.5
Yastrzemski Carl
5942
5444
164
32561
172.2
70-79
Morgan
Joe
6273
5784
556
34060
186.1
Stargell
Willie
5083
5069
70
27971
183.7
Lynn
Fred
3035
2968
50
16636
181.4
Parker
Dave
3607
3417
113
19459
181.4
Williams
Billy
4189
3997
91
23103
176.9
Jackson
Reggie
5913
5513
180
32528
175.0
Rice
Jim
3456
3259
71
19053
174.8
Schmidt
Mike
4506
4117
154
24654
173.2
Aaron
Hank
3363
3203
49
18811
172.9
Carew
Rod
5916
5287
288
32272
172.8
80-89
Brett
George
5381
5148
150
29454
179.9
Strawberry
Darryl
3928
3746
164
21897
178.6
Henderson
Rickey
6206
4818
762
31571
176.7
Mattingly
Don
4423
4223
83
24490
175.8
Schmidt
Mike
5556
5294
90
30648
175.7
Gibson
Kirk
4557
4037
240
24814
172.4
Raines Sr
Tim
5621
4294
629
28663
171.8
Murray
Eddie
6437
6052
135
36058
171.6
Hrbek
Kent
4767
4441
87
26390
171.6
Guerrero
Pedro
4858
4423
120
26565
171.0
00-04
Bonds
Barry
3050
3828
87
16732
234.0
Helton
Todd
3448
3935
81
19157
209.6
Pujols
Albert
2728
2967
43
15180
198.3
Giambi
Jason
3036
3310
60
17021
198.0
Ramirez
Manny
3012
3304
43
16915
197.9
Berkman
Lance
3142
3389
63
17596
196.2
Walker
Larry
2406
2481
62
13046
194.9
Edmonds
Jim
2970
3149
64
16546
194.2
Rodriguez
Alex
3542
3618
125
19484
192.1
Delgado
Carlos
3299
3470
53
18387
191.6
Hardegree, Base-Advance Average
page 7 of 9
7.
How do the Teams Stack Up?
The following table presents the cumulative team-data for 2000-2004, including wins and runs,
and is sorted by wins.13
FOR
AGAINST
wins
runs
BAA
ba
ob%
slg%
OPS wins
runs
BAA
ba
ob%
slg%
OPS
Yankees
488
4346
158.2
272
350
459
809
320
3748
146.9
263
319
415
734
Athletics
483
4192
153.9
261
337
434
772
326
3497
142.1
256
321
399
720
Braves
482
3957
151.8
267
333
438
772
327
3330
139.2
254
317
395
712
Cardinals
475
4219
156.4
273
342
452
795
335
3558
144.0
258
324
425
749
Giants
473
4112
154.3
266
342
445
786
336
3519
142.0
258
325
406
731
Mariners
456
4141
154.0
276
346
429
775
354
3566
141.9
253
319
410
729
Red Sox
453
4333
157.2
282
352
470
823
356
3732
147.7
255
319
408
727
Dodgers
442
3604
143.6
263
326
425
751
368
3356
139.9
247
316
398
714
Twins
430
3868
150.7
272
335
441
776
379
3831
147.8
270
324
437
761
White Sox
428
4288
156.6
270
335
456
791
382
3978
150.4
265
332
433
764
Astros
428
4142
154.1
264
335
435
770
382
3783
148.2
262
329
434
763
Angels
425
3978
151.5
271
333
425
758
385
3720
146.5
261
328
423
751
D'backs
410
3761
147.4
263
330
424
755
400
3689
145.7
255
319
416
735
Marlins
408
3641
145.8
268
333
431
764
401
3696
146.5
260
332
420
752
Indians
403
4143
154.0
266
334
434
768
407
4109
153.3
270
340
433
772
Phillies
403
3795
149.1
258
333
426
759
406
3751
147.9
259
327
431
758
Cubs
397
3760
147.8
263
328
443
772
413
3712
146.3
252
325
410
735
Blue Jays
394
4054
152.6
264
331
430
761
415
4138
154.4
276
342
445
787
Mets
388
3465
142.0
258
322
402
724
420
3639
146.4
260
326
419
745
Rangers
376
4267
156.0
269
334
457
792
434
4587
161.8
284
356
472
828
Reds
375
3713
146.3
255
324
419
743
436
4182
155.7
273
340
459
798
Padres
372
3649
144.2
261
329
408
737
438
3978
151.4
266
332
442
773
Rockies
370
4355
159.4
276
341
455
796
440
4516
161.7
283
354
479
832
Expos
368
3489
142.7
257
321
408
729
442
3917
150.7
270
335
439
773
Orioles
354
3733
146.3
264
326
419
745
457
4165
154.5
270
342
440
782
Pirates
350
3524
142.7
258
323
407
730
458
4021
152.4
271
341
433
774
Royals
345
3901
149.4
266
326
422
749
465
4451
160.0
282
350
469
818
Brewers
332
3455
141.7
261
327
422
748
478
4083
153.9
268
342
442
784
Devil Rays
319
3507
143.3
257
318
404
722
488
4341
158.0
272
345
454
800
Tigers
315
3540
143.2
258
318
416
733
494
4339
158.3
283
344
460
804
8.
Correlation Results
With the above data in hand, we are immediately led to ask how the various stats correlate with
wins. First of all, one should not expect any offensive measure to correlate too closely with wins, since
winning depends upon both offense and defense. This is born out by the following correlation values.14
runs
BAA
ba
ob%
slg%
OPS
correlation with wins
.502
.523
.381
.606
.467
.539
On the other hand, one should expect winning to correlate with differential offensive production, which
is born out by the following much stronger correlation values.15
13 Here BAA is base-advance-average, ba is batting average, ob% is on-base-percentage, slg% is slugging percentage.
14 The correlation measure I employ is R2, which best delineates strong from weak correlation.
15 For example, differential-runs is simply runs-for minus runs-against.
Hardegree, Base-Advance Average
page 8 of 9
differential
runs
BAA
ba
ob%
slg%
OPS
correlation with wins
.958
.956
.667
.850
.807
.861
What is quite surprising is that base-advance average performs almost as well as runs. The latter stat, of
course, is linked by definition to winning. Nevertheless, runs is only very slightly better than base-
advance average in predicting the number of wins a team achieves over the five year period under
consideration.
The reason that base-advance average does as well as runs is that they are very strongly
correlated with each other, which is presented in the following table of correlation values.16
BAA
ba
ob%
slg%
OPS
correlation with runs
.988
.739
.823
.831
.874
With a correlation (R2) of .874, OPS is definitely a very good stat, but with a correlation of .988,
base-advance average is "ridiculous" (as they might say on ESPN's Sports Center). This point is further
emphasized when we examine the associated linear-regression scatter-plots for base-advance average
and OPS, which are given as follows.
runs versus base-advance average
4600
4500
4400
4300
4200
4100
4000
runs 3900
3800
3700
3600
3500
3400
3300
138
140
142
144
146
148
150
152
154
156
158
160
162
base-advance average
16 Technically, one should use runs per game, or runs per out, or some other rate-stat. But, on the whole, the teams played the
same number of games, so I simply use runs. Also, note that the correlation values involve 60 points, rather than 30, since
they include both runs-for and runs-against for each of the 30 teams.
Hardegree, Base-Advance Average
page 9 of 9
runs versus OPS
4600
4500
4400
4300
4200
4100
4000
runs 3900
3800
3700
3600
3500
3400
3300
710
720
730
740
750
760
770
780
790
800
810
820
830
OPS
9.
Conclusion
When Bill James began his pioneering efforts to shed light on baseball using baseball statistics,
he complained that much of the needed data was unjustly withheld from the general public. By way of
correcting the latter problem, he proposed the formation of Project Scoresheet, which put baseball data
collection in the hands of the people, and which eventually gave rise to Retrosheet.
The present work is one of the many beneficiaries of these efforts. Using play-by-play data
available from Retrosheet, I have compared a proposed stat – base-advance average – with numerous
conventional stats, in regard to how well they model win-production and run-production.
In particular, whereas the best available conventional stat – OPS – has a win-tracking rate of
84%, base-advance average has a win-tracking rate of 95%, which constitutes a dramatic
improvement. 17
Questions remain concerning missing play-by-play data – for games prior to 1960, and for games
between 1993 and 1999. From a purely statistical point of view, the existing data set of 74,255 games is
vastly more than sufficient to make our point. On the other hand, from a historical point of view, the
play-by-play data from the missing games are sorely missed. We can examine box scores to ascertain
the conventional stats for Babe Ruth, or Lou Gehrig, or Ty Cobb, but we need the play-by-play data to
ascertain their base-advance averages, which we would love to know.
Likewise, we have a tantalizing glimpse of Ted Williams' career based on his farewell year,
1960, when he was the base-advance average champion, with a base-advance average of .204, which is
comparable to our contemporary slugging goliaths. We would love to know Ted Williams' base-
advance average during his prime years.
17 For example, a stat with a win-tracking rate of 84% makes over three times as many prediction/tracking errors as a stat
with a win-tracking rate of 95%.
