Appendix
Tabletop Baseball Games
By Jim
Albert and Jay Bennett
This appendix provides background that is helpful to understanding the material in Chapter 1 of Curve Ball: Baseball, Statistics, and the Role of Chance in the Game. In particular, this appendix describes the All-Star Baseball, APBA, Strat-O-Matic, and Sports Illustrated tabletop baseball games for readers who are unfamiliar with these games.
Tabletop baseball games have a history about as long as professional baseball itself. Most of the early games were “generic” in nature, with each batter coming to the plate having the same chance of getting a hit. The games made no attempt to reflect the different skills of players, much less replicate the performances of actual professional players. It was not until well into the twentieth century that the games took on a statistical perspective.
The first game that attempted to simulate the play of Major League Baseball was Clifford Van Beek’s National Pastime, produced in 1931. Since then, tabletop games of ever-increasing sophistication and accuracy have attempted closer and closer simulations of the “real thing.”
The tabletop baseball games discussed in Chapter 1 have been among the most widely played. However, the games were selected as much for the different ways that the batter-pitcher interaction is modeled as for their popularity. As broad as these games have been in their appeal, tabletop baseball gamers are notorious for their parochialism in regard to their favorite games, so some readers may be unfamiliar with and even highly skeptical of the statistical underpinnings of one or more of these games. Nonetheless, we feel all of them are interesting from a statistician’s point of view, so this appendix provides a more lengthy and detailed description of each.
All-Star Baseball is the oldest game considered in Chapter 1. It was developed in 1941 by Ethan Allen, a professional ball player, but it is currently out of print. However, information and photographs of various versions of the game can be found at:
www.tabletop-sports.com/ReviewVault/reviews.asp?game=CadacoBaseball
In All-Star Baseball, the manager of each team is provided with a set of circular player disks that make up the team’s roster. Each disk provides the player’s name, defensive position, and batting ability. Figure 1-1 in Chapter 1 shows an illustration of a typical All-Star Baseball disk. There, the disk is like a pie chart, and each slice is identified with a particular play. The sizes of the various slices represent the batting ability of the player. For example, in Figure 1-1, the amazing home run ability of Babe Ruth is reflected in the relatively large home run pie slice (the slice numbered “1”).
When a player comes to bat, his disk is placed on a spinner, and the manager spins. When the spinner stops, it points to a numerically coded play result. To find the result, the manager looks the number up on a chart that indicates the play (e.g. single, walk, or strikeout).
All-Star Baseball is the simplest model of the tabletop games considered because the pitcher does not influence the outcome.
APBA (American Professional Baseball Association) Baseball is the oldest tabletop simulation baseball game still published today. The game was introduced in 1951 by its designer J. Richard Seitz. A brief biography of Seitz can be found at:
www.apbastadium.com/stadium/hall_of_fame/seitz.html
APBA Baseball has undergone several subsequent revisions. The system described here and analyzed in Chapter 1 is the basic version of the game. The Master version provides more detail, but is built on the same basic concepts. Each team has a set of 20 cards that make up the roster. Managers (players of the game) have the option to preserve the teams historically as presented in the rosters or to draft players in new fictitious teams. Each card gives the player’s name, defensive positions, and, if applicable, a letter rating his pitching ability. The batting ability is represented by a table on each card. Figure A-1 is an example of an APBA player card.
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Player Name |
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|
Positions |
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|
|
|
|
|
|
|
|
|
|
|
11 |
0- |
1 |
31 |
14- |
2 |
51 |
9- |
1 |
|
12 |
25- |
6 |
32 |
26- |
6 |
52 |
27- |
6 |
|
13 |
14- |
6 |
33 |
7- |
1 |
53 |
19- |
6 |
|
14 |
30- |
6 |
34 |
31- |
6 |
54 |
32- |
6 |
|
15 |
10- |
1 |
35 |
14- |
2 |
55 |
9- |
1 |
|
16 |
39- |
6 |
36 |
33- |
6 |
56 |
34- |
6 |
|
21 |
30- |
6 |
41 |
24- |
6 |
61 |
24- |
6 |
|
22 |
8- |
1 |
42 |
13- |
2 |
62 |
13- |
2 |
|
23 |
31- |
6 |
43 |
29- |
6 |
63 |
32- |
6 |
|
24 |
13- |
6 |
44 |
8- |
1 |
64 |
22- |
6 |
|
25 |
10- |
1 |
45 |
14- |
6 |
65 |
35- |
6 |
|
26 |
12- |
6 |
46 |
13- |
6 |
66 |
0- |
1 |
Figure A-1. Example of an APBA-type player card
When a player comes to bat, the manager rolls two six-sided dice, a large die and a small die. The large die provides the first play number and the small die the second number. So, if the small die result is 1 and the large die result is 5, the result is 51. The manager looks up 51 on the batter’s card and finds the play number listed immediately to the right of the dice number. If this play number had been #0 (produced by dice results of 11 and 66 in Figure A-1), the manager would roll the two dice again and use the third column (not the second column) to find the play number. Play results from #1 to #11 are generally hits while other results (except #14 for walks) are generally outs. Using the example card in Figure A-1, we see that a dice result of 51 produces a play result of #9. As we shall see shortly, the play resolution of a #9 result depends on the opposing pitcher’s rating.
Initially, the APBA game seems quite similar to the All-Star Baseball game aside from the use of dice instead of a spinner. However, there are several important differences between the two. First, All-Star Baseball uses a single chart for interpreting play numbers; APBA Baseball uses eight different charts, one for each base situation: bases empty, runner on first base, runner on second base, runners on first and second bases, runner on third base, runners on first and third bases, runners on second and third bases, and bases loaded. Second, unlike All-Star Baseball, ABPA play results are determined, in part, by the skill of the pitcher involved. Each of the eight ABPA charts is divided into columns which provide possible variations in the play result depending on the rating of the opposing pitcher. The six possible ratings of pitchers run from best to worst: A&B, A&C, A, B, C, and D (as described in greater detail in Chapter 1). In our example, if the bases are empty, the play result #9 produces a single against pitchers with a B or D rating and an out against all other pitchers.
Strat-O-Matic Baseball, designed by Hal Richman, was introduced in 1962. An interview with Richman can be read at:
www.sportplanet.com/som/int/richman01.htm
Strat-O-Matic Baseball was the first tabletop baseball game to capture pitching performance at the same level of detail as batting performance. Its basic pitcher/batter model lies at the heart of several subsequent tabletop baseball games, including Pursue the Pennant and Ball Park Baseball. Strat-O-Matic Baseball has a devoted following and survives to this day in both tabletop and computer forms. Like other tabletop baseball games, it has evolved into Advanced and Super-Advanced versions that are built on the same operating principles, while providing even more detailed simulations of baseball. The system described here and analyzed in Chapter 1 is the basic version of the game.
Each team has a set of 20 cards that make up the roster. Each card provides the player’s name and defensive positions. If the player is a pitcher, the card is divided into three columns labeled 4, 5, and 6; each column presents play results describing the pitcher’s ability in terms of the frequencies of these play results. Position player cards’ have a similar layout of three columns that are labeled 1, 2, and 3. Each column presents play results describing the player’s ability at bat. Figures A-2 and A-3 are examples of a batter’s card and a pitcher’s card.
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Player Name |
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Positions |
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1 |
2 |
3 |
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2-foulout |
2-lineout |
2-flyout |
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3-popout |
3-WALK |
3-groundout |
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4-lineout |
4-groundout |
4-HOMERUN |
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5-groundout |
5-WALK |
5-HOMERUN |
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6-groundout |
6-strikeout |
6-HOMERUN |
|
7-SINGLE |
7-flyout |
7-SINGLE |
|
8-SINGLE |
8-groundout |
8-DOUBLE |
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9-groundout |
9-flyout |
9-SINGLE |
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10-popout |
10-groundout |
10-SINGLE |
|
11-popout |
11-groundout |
11-groundout |
|
12-popout |
12-flyout |
12-TRIPLE |
Figure A-2. Example of Strat-O-Matic-type batter card
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Player Name |
||
|
Pitcher |
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4 |
5 |
6 |
|
2-HOME RUN |
2-HOME RUN |
2-flyout |
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3-FIRST BASEMAN X |
3-SHORTSTOP X |
3-RIGHT FIELDER X |
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4-CENTER FIELDER X |
4-SINGLE |
4-popout |
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5-popout |
5-flyout |
5-SINGLE |
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6-lineout |
6-flyout |
6-SINGLE |
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7-strikeout |
7-SECOND BASEMAN X |
7-WALK |
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8-flyout |
8-SHORTSTOP X |
8-popout |
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9-flyout |
9-groundout |
9-lineout |
|
10-THIRD BASEMAN X |
10-CATCHER X |
10-DOUBLE |
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11-PITCHER X |
11-strikeout |
11-LEFT FIELDER X |
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12-groundout |
12-WALK |
12-TRIPLE |
Figure A-3. Example of Strat-O-Matic-type pitcher card
When a player comes to bat, the manager rolls one white six-sided die and two red six-sided dice. The white die determines the column used to find the play result: Column 1, 2, or 3 on the batter’s card or Column 4, 5, or 6 on the pitcher’s card. The two red dice are summed to produce a number between 2 and 12 which indicates the row in the appropriate column. For example, if the white die showed 4, and the two red dice showed 5 and 1, the result of the play would be a lineout found next to the 6 (=5+1) under column 4 on the pitcher’s card in Figure A-3. However, if the red dice were the same but a 3 was on the white die, the result would be a home run, found next to the 6 (=5+1) under column 3 on the batter’s card in Figure A-2.
Several results on the pitcher’s card have an X next to the name of a fielding position. This means that the result of the play depends on the fielding rating of the defensive player at the position. A number from 1 to 20 is selected randomly by the batter and referenced against a defensive play chart which has different columns for each fielding rating. The better the fielding rating, the less of a chance of giving up a hit or an error. Thirty permutations of the three dice can produce an X result on the pitcher’s card in Figure A-2. Since three six-sided dice can produce 6 x 6 x 6 = 216 permutations, fielding influences 30/216 = 14% of all batting results.
Sports Illustrated Baseball was introduced in 1971. The game was designed by David S. Neft, who was a co-author of The Sports Encyclopedia: Baseball. It is likely that this game was an outgrowth of his work on the encyclopedia (or vice versa). In the late seventies, the Avalon Hill Game Company purchased the Sports Illustrated game line and published a modified version under the title Superstar Baseball.
In this game, each manager is provided with a chart describing his/her team’s roster of 25 players, both batters and pitchers. A reproduction of a portion of the all-time all-star Philadelphia Phillies chart can be seen at:
www.innova.net/~randycox/SSBATcht.htm.
Each player’s card lists 30 possible dice results numbered from 10 to 39. The dice used for Sports Illustrated Baseball are three six-sided dice, one black and two white, that are special to the game. When rolled, the black die is used to find the 10’s digit and the two white dice are summed to obtain the 1’s digit. In each plate appearance, the pitcher rolls first. The resulting number is checked against his pitching chart and can result in an out, a walk, hit batsman, a single, or the Batter Swings.
The first four results listed above end a plate appearance. A team’s fielding is represented on the pitcher’s chart in the Defense results section. The play results from 10 to 15 are directly affected by the fielding skills of the team as a whole. The greater the fielding skill, the more Outs that occur in the 10-15 range. For example, a team with a fielding rating of 30 would produce an Out when the pitcher rolls 11 or 12, while a team with a fielding rating of 50 would produce an Out when the pitcher rolls 11, 12, or 13. If the Defense result is not an Out based on the team’s fielding rating, the Batter Swings. The worst defense will produce an Out when 10 is rolled while the best defense will produce an Out when 11, 12, 14, or 15 is rolled.
Figure A-4 shows the chart of a Hall of Fame caliber pitcher. The dice for the game will produce an Out result for this pitcher 26 percent of the time and a walk about 6 percent of the time. Depending on the quality of the team’s defense, an Out will occur an extra 1 percent to 9 percent of the time. So, a “Batter Swings” play can result from 59 percent to 67 percent of the dice rolls depending on the fielding rating of the defensive team.
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Pitcher Chart |
|||||
|
10 |
Defense |
20 |
Batter Swings |
30 |
Batter Swings |
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11 |
Defense |
21 |
Batter Swings |
31 |
Batter Swings |
|
12 |
Defense |
22 |
Batter Swings |
32 |
Batter Swings |
|
13 |
Defense |
23 |
Out |
33 |
Batter Swings |
|
14 |
Defense |
24 |
Batter Swings |
34 |
Out |
|
15 |
Defense |
25 |
Walk |
35 |
Out |
|
16 |
Out |
26 |
Batter Swings |
36 |
Batter Swings |
|
17 |
Out |
27 |
Batter Swings |
37 |
Batter Swings |
|
18 |
Batter Swings |
28 |
Out |
38 |
Batter Swings |
|
19 |
Batter Swings |
29 |
Batter Swings |
39 |
Batter Swings |
Figure A-4. Example of a Sports Illustrated type pitcher chart
When the fifth result, “Batter Swings”, occurs, the batter rolls the dice and looks up the play result on one of two charts. One chart is used when facing right-handed pitchers, and the other is used against left-handed pitchers. Figure A-5 provides an example of a batting chart for a Hall of Fame caliber hitter. In general, dice rolls in the 20s and 30s are twice and three times as likely respectively as dice rolls in the 10s.
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Batter Chart |
|||||
|
10 |
Double |
20 |
Home Run |
30 |
Flyout |
|
11 |
Single |
21 |
Single |
31 |
Flyout |
|
12 |
Triple |
22 |
Single |
32 |
Single |
|
13 |
Strikeout |
23 |
Strikeout |
33 |
Flyout |
|
14 |
Double Play |
24 |
Home Run |
34 |
Flyout |
|
15 |
Double |
25 |
Single |
35 |
Flyout |
|
16 |
Double |
26 |
Groundout |
36 |
Groundout |
|
17 |
Error |
27 |
Groundout |
37 |
Double Play |
|
18 |
Strikeout |
28 |
Strikeout |
38 |
Double Play |
|
19 |
Double |
29 |
Strikeout |
39 |
Strikeout |
Figure A-5. Example of a Sports Illustrated type batting chart
The evolution of tabletop baseball board games is almost as fascinating as the history of baseball itself. Readers who would like more detail on this subject can find a brief history of these games in Diamonds in the Rough, by Joel Zoss and John Bowman (Macmillan 1989). A book dedicated entirely to this subject is Baseball Games : Home Versions of the National Pastime, 1860s-1960s by Mark Cooper and Douglas Congdon-Martin (Schiffer Publishing,1995).