This is the first of a four-part series. Please bring to my attention any typo's or something that just doesn't make sense......scanners are not 100 percent. I appreciate all the kind words for posting these articles. I know that true APBA Baseball fans will benefit from the wealth of information here. Reward yourself and get the updated, 1995 edition of this four-part article from the APBA Journal - see Redskin's home page for the address to order. APBA Primer Reading The Cards --- Part 1, The Basics by Stephen Hall reproduced with permission The APBA Journal, April 1991 Before the introduction of the APBA Baseball Computer game, everyone who experienced baseball APBA style did so by way of the player cards which APBA produces to recreate the playing abilities of the 676 selected players for a given season. If a player had just had a good season an experienced APBA manager would say that that player was going to get a good card. Any judgment concerning a player's day-to-day worth in a lineup depends on the manager's ability to analyze his card within the context of the game system. Learning to read the card is not a skill that can be acquired overnight. To the untutored eye, a player card is a mass of red and black numbers with no apparent organization. Even after learning the procedure of... 1) rolling the red and white dice, then reading the result as a two digit number (e.g. a red 3 and white 5 is a 35); 2) locating that result as the black number on the player card; 3) reading the corresponding red number beside it; 4) consulting the proper on-base chart for the play result... the same number often varies from one on-base situation to another ... it is still initially difficult to determine just how any given player will perform on a game-to-game basis. Now that more and more team managers are becoming acquainted with APBA Baseball exclusively via the computer game, the APBA Journal has received several requests for a discussion of the basic structural mathematics behind the APBA game. Articles which talk about a player's 1-5-6 power or another's seven red 14's are understandably meaningless statements to these fans. Additionally, the ability to understand a sophisticated discussion of APBA is useful for the computer gamer, playing and seeking competitive advantages in a draft league, because the computer game is a direct derivative of the Master Game table version with each player on the diskette assigned numeric data which precisely recreates the numbers on the printed card. For those gamers, and for the relative novices who are dice rollers, playing the Basic and Master Game versions of APBA Baseball, this is how one experienced APBA manager looks at a player card. The Playing Card The lower two-thirds of every APBA baseball card consists of three columns of twelve black and red numbers. For each black number (called the dice result) there is a corresponding red number entry (called the play result). The black numbers represent the 36 different possibilities when rolling two dice of different colors and reading them in the above stated two digit manner. According to the law of probability, each of the 36 different dice results should come up 1/36 of the time or .02777. This means, in theory, (but not quite in actuality ...more on that at another time) the 36 results can be said to represent 36 plate appearances by the batter. Since each of the 36 results don't come up equally within each 36 dice roll sequence, the unpredictability of randomly generated play results is captured in APBA. This also means that the sample size must be very large to determine the game's accuracy about 50,000 times at bat. Single Column Card In the early days of APBA, from its inception in 1951 through the 1956 card set, all players in the set had Single-Column cards. These cards have only one red number play result next to each black number dice roll. During these early years when ever an individual batter’s real-life stats had a result that occurred less than 1 out of 36 plate appearances ...say he had hit a homerun every 75 plate appearances. . . he didn't have the potential to get that result 100% of the game during a game. For example, that batter couldn't homer with the Bases Empty, creating an inherently unrealistic situation. However, in 1957 APBA developed the first Double-Column card, Still, the single-column card remains, now almost exclusively reserved for those batters whose homerun to plate appearance ratio is at least 1 to 36 and whose doubles and triples can be mathematically well expressed within this configuration. Double Column Card Double-Column cards are those batters' cards with two columns of red play result numbers following the dice result black number. These cards are the same as Single-column cards except they will have a O or O's in the first column. The play result from a double column card will be based on the red number in the first column unless the dice results corresponding red number is 0. When that happens, the dice are re-rolled to find a value in the second column of red numbers. By having double columns, the APBA card was able to expand the card's ratio parameters from 1 out of 36 times to 1 out of 1296 times, more than enough to account for any single result occurring within each players entire season. In this first look at the cards, we will concentrate on the single column card, saving the analysis of the double column card for the next installment. The Red Numbered Play Result The red numbered play results on a single column card range from 1 to 42 and are customized to produce each player's offensive statistics for that year. These numbers are the possible play outcomes available in baseball and are grouped into a series of ranges. The numbers 1 through 6 normally produce extra base hits. Numbers in the 7 to 11 range produce singles. The number 13 is always a strikeout and the number 14 is a walk (or a ball against pitchers with superior control). Play results 12 and 15 through 41 can be referred to as the fielding play results since they interact with the fielding ratings of the defense to produce the entire gamut of baseball play results. Within this large group, play result 12 often produces an out ...sometimes a double play out . . . but it can also produce a single, a strikeout or a walk. Play results 15 through 23 generate the brunt of the errors but they will also produce hits and hit batters while results 24 through 29 produce infield ground balls that will lead to outs or, with runners on base, groundouts with either runner advancements or fielder's choices, or grounding into double plays depending on the fielding level of the defense. Occasionally, with a runner on third, a drawn in infield will cause one of these results to be a base hit. Play results 30-32 produce outfield fly results ...sometimes sac flies with a runner on third, depending on the depth of the fly and the arm strength of the outfielder against the speed of the runner and 33-34 are infield pop outs with a potential for a strikeout against certain pitchers. Result 35 is generally a pop out but may under certain conditions yield a walk or a single. Numbers from 36-41 create the possibility for wild pitches, passed balls, balks, and the great array of rare plays. Rounding out the results is the 42 which is always a Hit By Pitch unless the pitcher in the game did not hit a batter in real-life during the season. The Basic Math of the APBA Card The basic mathematics of producing an individual player's batting average from his card is easy to understand. Say a-batter has 10 hit numbers and 3 walk numbers (14’s). Subtracting the 3 walk numbers from 36 leaves 33 play results. Dividing 10 by 33, gives an answer of .303, the figure a player should hit in the simulation over the course of the season if all 10 hit numbers went for a hit all the time. However, if the batter only has 2 walk numbers, you'd divide 10 by 34, giving an answer of .294, what he should hit over the replay. Using one more example . . . if a batter has 9 hit numbers and three walks, you'd divide 9 by 33 to get .273 the figure he should hit. That's the basic method APBA uses to customize each batter’s card to reproduce his batting average. However, because the APBA system factors in the effect of pitching, fielding, and the batter's handicap against same-side pitching in altering most hit and out results, each result can rarely be expressed as occurring 100% of the time. The genius of the system is its interweaving of pitching, defense and offense within a deceptively simple framework that makes the game such an appealing simulation. Offensive Value of a Card The offensive value of a batter’s card results from the assignment of the hit numbers (1-11). Generally speaking, the more of these hit numbers on a card, the greater the likelihood of that batter getting a hit during a plate appearance; and the more extra-base hit numbers (1-6) on the card, the higher the power average. The combination of hit numbers, walks and HBP (42's) create the player’s on-base average. A player with a total of 14 on base numbers (hit results+walk results+HBP results) has a good card. If he has 15, he has a very good card. Any combination totaling over 15 means he has an excellent card. The effect of adding on-base results to a batter’s card has a reciprocal effect on the number of out results. Since the context of the card is always 36 play results, the addition of, for example, another 14 (walk or ball) means one less out result as well. This means that two players with the same collection of hit numbers can have strikingly different averages, based on the distribution of other out and non-out results. For example, Jack Clark and Jim Presley may both have nine hit numbers on their cards, but since Clark has eight red 14's to Presley’s two, both his batting average and on-base average will be much higher than Presley’s. There is a definite pattern to the assignment of numbers on a card. The best result the card has to offer is found next to the black 66. That's why APBA fans live for boxcars. Most single-column cards will have a red 1—most of the time a homerun—next to dice roll 66, meaning that they hit a homer at least once out of every 36 plate appearances that season. All double-column cards will have a 0 on 66. The next best play result for that batter will be assigned to dice roll 11. The third best is at 33, the fourth, at 22, the fifth, at 44, and the sixth, at 55. Looking at Kevin Mitchell's card from 1989 (see graphic ...the black- numbers are in bold face), the red numbers in order of value ...1-1-5-5-6-8 appear on dice rolls 66-11-33-22-44-55. Additional hit numbers if warranted appear at other dice results. The hierarchical assignment of these non-double dice results are ... 15-25-51 31-35-42-64. That provides us with 13 dice rolls for hit numbers and it's rare that any batter needs more these days to have his card reproduce his average. Looking further at Mitchell's card we can locate the red results 8-8-9-9 at the dice roll numbers 15 25-51-31, for a total of 10 hit numbers. Since five of these ten are extra base hit numbers we would expect Kevin to hit at least at many extra base hits as singles, which is what he actually did (71 singles and 87 EBH's in 1989). With five numbers (1-1-5-5-6) that produce extra base-hits, Mitchell is said to have a “five-power number card”. This would be a great card even if he walked about as often as Oscar Azocar. Added to the hits, how ever, are Kevin's walks. There are five 14's sprinkled about Mitchell's '89 card, giving him a potential walk or hit on 15 of the 36 card results. Clearly, this is a very good card which, with the remarkable productivity of five power numbers, makes Mitchell MVP material (which he was) using it in APBA. We would expect Kevin Mitchell to have a good card but how does one quickly size up a more ordinary card? Take the '89 card for Lance Parrish. His hit numbers listed in order of importance are 1-7-7-8-8-8-9-9. Lance also has three red 14's. We see at a glance only nine hit numbers, just two of which are for extra bases. That, combined with three 14's ...average, reflects a very modest card for a power hitter. To shorten the process, the two key play results for a quick study of a card, are those at dice rolls 31 and 51. If their are 8's at 31 and 51, the player will have 12 hit numbers on his card. If there is a 9 at 31 and an 8 at 51, hell have 11 hit numbers; a 9 at each and he has 10 hit numbers; a 9 at 51 and a 14 on 31, 9 hit numbers; and if both 31 and 15 show a red 14, then the card has eight or fewer hit numbers. Another quick key is the value at 35. If his card has a hit number (usually 8 or 9) on 35 then there are eleven or more hits on the card (the twelfth, if warranted, would appear at 42 while the 13th would appear at 64. When I glance at a card for the first time, my eyes go first to the 31 and 51 results. If they're both 9's this is an average hitter. If one or both are non hits, then this is a low-average hitter. If one or both are hit numbers other than 9's, this is either an above average hitter or some kind of base stealer. Then l look at 42 and 64. If either of these are hits, this is a high average hitter. Next I look at power numbers ... how many and which ones? If there are four, I begin to salivate for this is a great powerhitter. If there are five, this batter is some kind of wonderful. Then the last thing I look for are the number of 14's. Some hit numbers can become outs, but 14's can never be outs. Either the batter walks or gets another chance to hit. The more 14's, the better I like the batter. Jack Clark routinely gets seven or eight 14’s every year and will therefore, not make many outs. Check out Lonnie Smith’s ‘89 card...four power numbers, eleven hits in all, five 14’s and a bonus 42 (HBP). In all, 17 potentially good results out of 36. A very powerful card! If you are looking for the walk numbers, the red 14's, you can spot them quickly at dice rolls 45 and 13 and the higher hit number spots like 35, 42, and 64. A guy like Smith will have 14's at odd locations because so much of his card had to be used for his hit numbers. A low average hitter will have his 14's appear at 31 and 51 in place of the hit numbers than a batter with more hits will have. After getting the count of the hits and EBH numbers, it is worth considering the value of each. Extra Base Hit Values Not all EBH numbers are created equal. The almighty 1 is impossible to argue with; it’s a homerun unless it's reduced to a double by the pitcher's homerun allowance letter (a G or H) in a particular on-base situation. One might naturally assume that the next best result is a 2 and then a 3 and so on. Not so! The hit numbers do not always equate to the same result in each on-base situation. If that were the case, there would be a need for only three EBH numbers, one each for the homerun, the triple, and the double. Instead, the play results from 2 through 6 are asked to perform multiple duty ... sometimes producing doubles, sometimes triples, and sometimes, homeruns. The how and when of all this is linked to the on-base situation. With the bases empty, the 2 and 3 result in triples while the 4, 5, and 6 yield doubles; but put a runner on first and this pattern is changed. Now the 2 and 4 are triples, the 3 and 6 are doubles while the 5 becomes a homerun. In fact, play result 5 is a homerun whenever there is a runner on first, on second or first and third. We know from accepted percentages of on-base frequency that play result 5 is worth a homerun about 1/3 of the time. The 2 is nearly always a triple and for that reason is rarely given since few batters hit a triple .0277 of the time during a season ...one with 600 plate appearances would need 16 triples to qualify for a first column 2. The 3 and 4 yield homeruns with less frequency than the 5 and they also appear much more rarely on single column cards than the 1, 5 and 6 since they have a relatively high triple value. The lowly 6 is nearly always a double. Only with single column batters with a runner on third or when the pitcher has a negative homerun rating (L or M) applying in that on-base situation (Open the window, Aunt Minnie!) will it be a homerun. Most of the time it results in a double. The reason APBA changes the power numbers play results from one on-base situation to another is to provide fractional values for these hits .… made necessary due to the 36 possible play results on the single column card. The normal values for the power numbers are as follows .… If you are exclusively an APBA Computer Baseball player, get a copy of Innovator or the Journal utility DSPLCARD so you can see what each player's card looks like. Next month, we will take the art of card reading further to examine the double column card, the value of the various base hit numbers and the influence that pitching and fielding have on batter outcomes in APBA Baseball.