TABLETOPTABLETOP Baseball Games APPENDIX This appendix provides background that is helpful to understanding the mate- rial in Chapter 1 of this book. 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, table- top 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 read- ers may be unfamiliar with and even highly skeptical of the statistical under- pinnings of one or more of these games. Nonetheless, we feel all of them are 385 386 APPENDIX interesting from a statistician’s point of view, so this appendix provides a more lengthy and detailed description of each. All-Star Baseball 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, a photograph of an All-Star Baseball disc (and a discussion of their col- lectibility) can be found at: www.beckett.com/vintage/news/index.asp?a=2636&s=27 In All-Star Baseball, the manager of each team is provided with a set of cir- cular 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 var- ious 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 Baseball APBA (American Professional Baseball Association) Baseball is the oldest table- top 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. TABLETOP BASEBALL GAMES 387 The batting ability is represented by a table on each card. Table A-1 is an exam- ple of an APBA 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 Table 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 Table 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 impor- tant 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 PLAYER NAME POSITIONS 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 TABLE A-1 Example of an APBA-Type Player Card 388 APPENDIX 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 Strat-O-Matic Baseball, designed by Hal Richman, was introduced in 1962. An interview with Richman can be read at: www.sportplanet.com/features/interviews/som/ Strat-O-Matic Baseball was the first tabletop baseball game to capture pitch- ing 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 PLAYER NAME POSITIONS 123 2–foulout 2–lineout 2–flyout 3–popout 3–walk 3–groundout 4–lineout 4–groundout 4–homerun 5–groundout 5–walk 5–homerun 6–groundout 6–strikeout 6–homerun 7–single 7–flyout 7–single 8–single 8–groundout 8–double 9–groundout 9–flyout 9–single 10–popout 10–groundout 10–single 11–popout 11–groundout 11–groundout 12–popout 12–flyout 12–triple TABLE A-2 Example of a Strat-O-Matic-Type Batter Card TABLETOP BASEBALL GAMES 389 Advanced and Super-Advanced versions that are built on the same operating principles, while providing even more detailed simulations of baseball. The sys- tem 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. Tables A-2 and A-3 are examples of a batter’s card and a pitcher’s 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.