In the introduction, I went over what the heck this project is all about.  In part one, I broke down all of the possibilities of the batter-influenced hit numbers.  In this part, I examine the error and rare play numbers.

When I was a wee lad, I was playing a game that involved the 1981 Cincinnati Reds.  Johnny Bench was playing first and he made four errors.  I just remember that was unusual but what I didn’t realize at the time that also happened when the same batter was up.  Only later did I realize the simultaneous cleverness and frustration with APBA.  In order to distribute errors without re-rolls, the error numbers have to be split in the offensive lineup.  And what better way to do that than to base it on offensive position.

They are generally distributed based on two factors, the position of the player and the hit by pitches needed:

• Pitcher: gets a 21 and a 23
• Infielder: Pretty much distributed league wide so that the 18, 19 and 20s are distributed evenly.  Older sets will likely see more 18s and 20s and less 19s.  The players who need more HBP will get the 19s, the ones who need little HBP will get 20s.  Usually one utility infielder per team gets a 21 instead of 18-20, especially in the American League.
• Outfielder: 15 for the high HBP folks, 17 for the low HBP folks.

In the basic game, the rare play numbers were mainly used to handle non-at bat situations, such as wild pitches, caught stealing and pickoffs.  In the Master Game, they serve a dual purpose.  The first purpose being wild pitches, balks and pickoffs.  The second purpose is to have actual rare plays: multiple-base errors, ejections, rain outs (grr), injuries and the like.  Those numbers are also mostly distributed by position:

• Pitcher and Second Base: gets a 36
• Catcher: gets a 36 and a 38
• First Base: gets a 37 and 2/3rds also get a 41
• Third Base and Shortstop: 39
• Outfielder: 40

There are some variances to have the numbers properly distributed by team.  For example Michael Cuddyer for 2012 Colorado is treated as a first baseman.

Some of the more sophisticated mail leagues created what were called error and/or rare play redistribution charts.  If you rolled a 15-23 or a 36-41, you rerolled this chart to get the actual number.  I bring this whole history lesson up because it is pretty obvious once that the computer game at least uses an error redistribution.  First, he are the error numbers from MLB and my baseline replay, per 36 PA:

Test	P	C	1B	2B	3B	SS	LF	CF	RF
2012 MLB	.08	.05	.06	.07	.12	.11	.05	.03	.03
Baseline	.06	.11	.06	.08	.10	.15	.05	.03	.04

First thing you see between real-life and APBA is that catchers make way too many errors and pitchers not enough, mostly because with more HBP than ever before more 22s are issued.  The number of errors by 3B has also recently gone up and although APBA has done some changes to catch up (hence the extra 19 and less 18 and 20), it still isn’t enough.  For my leagues, which I use the master game, I actually have era specific error randomizers.

When you look at the results of the various tests, all of the errors go up proportionally, the only variant being HBP.  Here’s the data, ranked from high HBP to low HBP:

Test	P	C	1B	2B	3B	SS	LF	CF	RF	HBP
Baseline	.06	.11	.06	.08	.10	.15	.05	.03	.04	.23
15 (HBP runner on 1st)	.09	.15	.09	.12	.14	.22	.07	.04	.06	.42
22 (HBP runner on 1st)	.09	.15	.08	.13	.14	.22	.07	.03	.06	.42
19 (HBP runner on 2nd)	.09	.15	.09	.14	.16	.24	.06	.03	.06	.30
17 (HBP runners on 1st and 2nd)	.09	.15	.09	.14	.15	.23	.07	.04	.06	.30
18 (HBP runners on 1st and 3rd)	.09	.15	.09	.14	.16	.25	.07	.04	.06	.26
16 (HBP runner on 3rd)	.10	.15	.09	.14	.16	.24	.07	.04	.06	.25
20 (HBP Bases full)	.10	.15	.09	.15	.15	.24	.07	.04	.06	.25
21 (HBP runners on 2nd and 3rd)	.10	.15	.09	.14	.16	.25	.07	.04	.06	.25
23 (No HBP)	.10	.15	.09	.14	.16	.25	.07	.04	.06	.23

Not surprising at all once you realize that error randomization is going on. Since the error numbers are not always errors, there’s hits or outs in there too, let’s rank them by their runs over baseline potential:

Test	R/ 36PA	1B/ 36PA	2B/ 36PA	3B/ 36PA	HR/ 36PA	BB/ 36PA	SO/ 36PA	HBP/ 36PA	GDP/ 36PA
Baseline	4.04	5.40	1.53	.18	.94	2.80	7.84	.23	.59
22 (HBP runner on 1st)	4.36	5.50	1.53	.18	.94	2.81	7.85	.42	.59
15 (HBP runner on 1st)	4.35	5.49	1.54	.19	.94	2.80	7.85	.42	.61
17 (HBP runner on 1st and 2nd)	4.34	5.50	1.52	.18	.95	2.81	7.77	.30	.58
20 (HBP bases full)	4.34	5.54	1.53	.18	.94	2.80	7.77	.25	.60
19 (HBP runner on 2nd)	4.32	5.54	1.52	.18	.93	2.80	7.76	.30	.58
18 (HBP runners on 1st and 3rd)	4.31	5.50	1.52	.18	.94	2.82	7.78	.26	.59
23 (no HBP)	4.31	5.50	1.52	.18	.94	2.81	7.75	.23	.58
16 (HBP runner on 3rd)	4.30	5.52	1.53	.18	.94	2.81	7.75	.25	.58
21 (HBP runners on 2nd and 3rd)	4.29	5.51	1.52	.18	.93	2.81	7.80	.25	.60

Weird that the 19 as that jump in singles, especially with 19 having more than the average amount of singles on an non-randomized board. Maybe it’s “sort of” randomized? Poring through assembly code was not in scope for this project, so we’ll move on to the comparison:

• Jay Bruce has a 15. Adding .31 (the expected runs for a 15 minus the baseline) to his previous 7.69 now gives him an 8.00
• Torii Hunter has a 19 and two 22s. Adding .28 for the 19 and .64 (.32 * 2) for the two 22s to his previous 7.51 now gives him an 8.43

Moving on to rare plays, there seems to be somewhat the same randomization as the error plays.  On the boards, the 36 and 40 are the wild pitch possibility, 38 the passed ball possibility, 37 and 39 have possible pickoffs, and 41 is just wacky.  Also, any non-baserunner event could lead to the rare play boards, which can mean more errors.  So let’s pull the baseline in from above, and this time add wild pitches, passed balls, pickoffs and balks to the mix.

Let’s check the new stats, looking at the MLB baseline, APBA baseline and the results from the six play results:

Test	WP	BK	PK	PB
MLB	.30	.03	.07	.07
Baseline	.12	.01	.05	.08
36	.23	.02	.09	.14
37	.23	.02	.09	.13
38	.23	.02	.09	.13
39	.23	.02	.09	.13
40	.23	.02	.09	.13
41	.22	.02	.09	.14

Glaring obvious even from the baseline is the lack of wild pitches and balks.  Even adding an extra chance per card doesn’t produce enough.  As a consequence, the rare plays get called a bit too much, and could inflate the error numbers a bit.  You get about 10% too many errors in a non-adjusted replays, errors that could be taken away with wild pitches and balks.  Anyway, here is the breakdown for the different numbers when it comes to errors, and it’s not much different by number, furthering the randomization theory:

Test	P	C	1B	2B	3B	SS	LF	CF	RF
Baseline	.06	.11	.06	.08	.10	.15	.05	.03	.04
36	.07	.13	.07	.09	.12	.16	.07	.04	.06
37	.07	.13	.07	.09	.12	.15	.07	.04	.06
38	.07	.13	.07	.09	.12	.15	.07	.04	.06
39	.07	.13	.07	.09	.11	.16	.07	.04	.06
40	.07	.13	.07	.09	.11	.16	.07	.04	.06
41	.07	.13	.07	.09	.11	.16	.07	.04	.06

Not quite to the level of adding to the errors that a error number does, but there is a noticeable increase.  But the important question is, of course, how does this translate to runs:

Test	R/ 36PA	1B/ 36PA	2B/ 36PA	3B/ 36PA	HR/ 36PA	BB/ 36PA	SO/ 36PA	HBP/ 36PA	GDP/ 36PA
Baseline	4.04	5.40	1.53	.18	.94	2.80	7.84	.23	.59
36	4.32	5.62	1.56	.18	.96	2.84	7.90	.23	.58
37	4.32	5.66	1.58	.19	.95	2.83	7.84	.23	.59
38	4.31	5.62	1.56	.19	.96	2.85	7.89	.23	.59
39	4.31	5.65	1.56	.18	.96	2.83	7.88	.23	.59
40	4.29	5.61	1.56	.19	.96	2.85	7.90	.23	.59
41	4.29	5.61	1.56	.19	.96	2.85	7.90	.23	.59

A little surprising that despite little variation between the various non-hit elements, the hit elements are a bit different, and therefore the runs by number are slightly different.  Nevertheless, the number does produce some runs over average, and those players who get two of them have a bit more value than those who get one.

Back to our comparison of Jay Bruce and Torii Hunter, there isn’t a difference here, since being outfielders they each have a 40.  Add .25 to each of their scores (4.29 – 4.04), giving Bruce 8.40 and Hunter 8.68.

We move on to our next installment, the plays that will be knocking Bruce’s and Hunter’s scores down, the out numbers.  You will soon learn that not all out numbers are created equal.

NOTE: Edited on 7/22/2013 to reflect Torii Hunter’s 2 22s and the use of scaling from Part 1.