I got a lot of this from a old APBA Journal article "Summary Of Card-Makers' Theories, Investigations" by Aaron W. Shomo (I don't know the issue -if anyone does, please let me know!), supplemented by my own reseach into cards from the 1988-92 era, and some much more recent studies.
Caveat: I may be wrong about some or most of this. If so, I'd welcome comments and corrections!
I use the following stats:
AB, H, 2B, 3B, HR, BB, SO, SB, CS
HP (hit by pitch), GDP (grounded into DP), SH (sacrifice bunts),
SF (sacrifice flies), IBB (intentional walks), and the player's position.
I'd use the player's normal batting order position if I could get it. (This determines the error number result on "53".)
The basic stuff:
1. compute the player's plate appearances:
FudgeBB = BB - (2/3)*IBB
PA = AB + HP + SF + SH + FudgeBB
(Note the fudge factor on IBB. I'm completely unsure of this, but it makes pre-1992 data fit well.)
2. figure the number of 14s:
n14s = round(36*FudgeBB/PA)
3. Figure the Hit by Pitch numbers:
nHPs = (36*HP)/PA
n42s = (nHPs/0.9)
residHPs = nHPs - int(n42s)*0.9
Now, if residHPs is:
>0.6, give another 42
<0.60 and >0.45, give a 19 and a 22 if 1Bman, 3Bman or catcher
give a 15 and a 22 if an outfielder or DH,
give 2 22s otherwise
<0.45 and >0.30, give a 22
<0.30 and >0.13, give a 19 if 1Bman, 3Bman or catcher
give a 15 if an outfielder or DH
4. Figure the power numbers:
n2B = (36*2B)/PA
n3B = (36*3B)/PA
nHR = (36*HR)/PA
nXBH = n2B + n3B + nHR
You must decide if you can do a 1 column card.
If nHR is >0 and <0.9, or if the fractional part of nXBH is between 0.4 and 0.67, you must do a 2 column card.
If 1 column is still a possibility, try to fit round(nXBH) power numbers to match your n2B, n3B and nHR numbers using the following values for result numbers 1 through 6:
# nHR n3B n2B
1 1.0 0.0 0.0
2 0.044 0.956 0.0
3 0.088 0.603 0.309
4 0.071 0.356 0.573
5 0.356 0.071 0.573
6 0.027 0.027 0.946
If you like the best fit you get, then use it.
Else, use 2 columns. Assign n1 = int(nHR) 1's, then n0 = nXBH-n1 rounded up to the next integer. Assign n0 zeros, and figure the second column, assigning 36*(nHRs-n1)/n0 1's, 36*n3Bs/n0 2's, 36*n2Bs/n0 6's, and the rest 7s.
5. Figure the hit numbers:
nHits = (36-n14s-n42s)*H/AB (Note: AB *not* PA)
nSingles = nHits minus the number of 0s through 6s you assigned in step 4.
if nSingles is:
<1.25, give an 8 and a 9
>1.25 and <2.00, give a 7, an 8 and a 9
>2.00 and <3.00, give a 7, an 8 and 2 9s
>3.00 and <3.75, give a 7, 2 8s and 1 9
>3.75 and <4.25, give a 7, 2 8s and 2 9s
if nSingles>=4.25, n8s = 3 and n9s = 2, and n7s = the integer part of nSingles-4.
then if the fractional part of nSingles is >0.70, add a 7.
the fractional part of nSingles is >0.25, add an 8.
*** I think APBA has changed this fractional part bit over the years ***
6. figure speed numbers (10, 11, and 14*):
The only way I can describe this is by an algorithm that will read like code:
nSBs = 36*SB/PA
If nSBs < n7s (from step 5),
n11s = int(nSBs)
n7s = n7s - n11s
nSBs = nSBs - n11s
if (nSBs > 0.9) and (n7s>0)
n11s = n11s + 1
n7s = n7s - 1
and we're done
By this point, we've given all the first column 11s we can. If by now nSBs<0.25, we're done.
Now assign 10s:
Try for second column 11s:
n2SBs = 36*nSBs/n0s
if n2SBs <= nSecondColumn7s (from step 4)
change n2SBs second column 7s to 11s
and we're done
if instead, n2SBs > nSecondColumn7s
change nSecondColumn7s to 11s
nSB = nSBs - nSecondColumn7s*n0s/36
Now, if nSBs < 0.25, we're done.
if nSBs > 0.25 and <0.65, change an 8 to a 10 and we're done
if nSBs > 0.65, change 2 8s to 10s and reduce nSBs by 0.8
If nSB<0.25, we're done.
Otherwise, assign 14*s:
change int((nSB+0.15)/0.40) 14s to 14*s, assuming there are enough 14s.
Finally, we're done.
7. figure 13s:
nKs = (36*SO)/PA, and use this table:
nK < n13s:
1.17 0
1.90, 1 13's
3.62, 2 13's
4.66, 3 13's
5.70, 4 13's
6.74, 5 13's
8.02, 6 13's
9.26, 7 13's
10.49, 8 13's
11.32, 9 13's
12.66, 10 13's
14.0, 11 13's
15.5, 12 13's
more?
8. figure 24s:
nDPs = 36*GDP/PA, and use this table:
nDPs < n24s
0.54 0
0.82, 1 24's
1.10, 2 24's
1.35, 3 24's
1.60, 4 24's
1.91, 5 24's
2.19, 6 24's
2.40, 7 24's
2.75, 8 24's
3.10, 9 24's
more?
9. assign rare play numbers:
Position: Rare Play Numbers:
P 23, 36
C 36, 38
1B 37, 41
2B 36
3B 39
SS 23, 39
OF 40
10. compute number of 31s:
This is a complete guess. It even works sometimes.
nSO = 36*SO/PA
nHITS = number of 0s through 11s
if nSO > 6, give 1 31
if nHITS < 8, give 1 31
if nSO <= 6 and >2.5, give 2 31s
if nHITS >= 8 and < 10, give 2 31s
otherwise, give 3 31s
11. steal rating :
if attempts = 0, steal rating = "N0"
steal letter:
nSA = (SB+CS)/PA
nSA > 0.140 = "A"
nSA > 0.100 = "B"
nSA > 0.070 = "C"
nSA > 0.045 = "D"
nSA > 0.026 = "E"
nSA > 0.019 = "F"
nSA > 0.007 = "G"
otherwise = "R"
steal number:
if (SB = 0) number = 0
if (CS = 0) number = 36
otherwise
number = the lesser of int(36*(SB/(SB+CS)) + 2.5) and 36