Is a 14 better than a 9 — Finding Out the Monte Carlo Way (Part 3)

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 part two, I went over the error and rare play numbers and found out that everything was pretty much the same. Now we can move on to the parts of the card that won’t help you, the outs.

As I explained in the In the introduction, the APBA card in a “pure” state would consist of a 12, a 31, a 35, the position-determined error and rare play numbers, and a mélange of 26s through 30s and 32s and 34s.  A player’s hits, walks and hit by pitches will slowly remove the mélange.  However, there are other batter actions that will not remove numbers, but at least change them from one out to another:

  • Strikeouts are the most obvious, basically 1 per 36 PA minus 1.1.  So if someone had 5.6 K per 36 PA, that would go down to 4.5, which would round back up to 5.  The subtraction is to account for strikeouts obtained through pitcher subratings and hits into outs.
  • 24s come into play for generally every .0125 GDP per 36 PA, or .0035 GDP per PA.
  • Players with a good hit-and-run reputation receive a second 31.  Players with an excellent reputation receive 3 31’s (only 5 in 2012).
  • 33s and 34s used to be based on a straight batting average formula, .250 and above meant you got one or the other, under .250 you got both.  That no longer seems to be the case as there are some (but not many) players on both sides of the line.  It does not seem to be a function of outs needed or something to do with bat control, as Juan Pierre has the intriguing combo of 3 31’s but both a 33 and a 34, the latter two are DPs on a hit and run.  Nor does it seem to tie to bunting.
  • The good bunt numbers (26, 28, 30 and 32) are given more to good bunters while the bad bunt numbers (27 and 29) are given to the poorer bunters.
  • Extra numbers can also be pull related, with righties tending to get extra 27s, 28s and 30s and lefties 26s, 29s and 32s.

This phase of the project proved to be a little more difficult to implement.  Unlike adding hits, which was merely replacing one out result with the desired hit, adding an out would involve recalculating the card.  I really didn’t want to do that.  So what I did instead was removing 1-11, 14, 22 and 42 proportionally off everyone’s card so that there would be about 7% less of each over the course of the set, replaced by the out number being tested.

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Is a 14 better than a 9 — Finding Out the Monte Carlo Way (Part 2)

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.

Is a 14 better than a 9 — Finding Out the Monte Carlo Way (Part 1)

In the introduction, I explained a set of tests I did to find out the true value of an APBA baseball card.  This section will deal with the valuation of those numbers that the hitter controls to some extent: hits, walks and hit by pitch.  The error and rare play numbers will be in a future post.

Before we get started, let’s establish what the Major Leagues did on a divided by 36 plate appearances for the 2012 season:

Test R/36PA 1B/36PA 2B/36PA 3B/36PA HR/36PA BB/36PA SO/36PA HP/36PA GDP/36PA
2012 MLB 4.11 5.46 1.61 .18 .96 2.88 7.12 .29 .71

I played 5 seasons with the 5.75 computer game using Buck Jr. as the manager. The numbers were fairly close:

Test R/36PA 1B/36PA 2B/36PA 3B/36PA HR/36PA BB/36PA SO/36PA HP/36PA GDP/36PA
Baseline 4.04 5.40 1.53 .18 .94 2.80 7.84 .23 .59
Difference -.07 -.06 -.08 +.00 -.02 -.08 +.72 -.06 -.12

Runs are down a little bit, mostly due to a combination of my over-zealousness of making sure I didn’t have to manually fiddle with lineups by giving some scrubs more playing time, and the micromanager using the better pitchers a little more often than he should.  For comparison purposes, these are fine numbers and can be used as a baseline when I start adding numbers to the cards and running the simulations.

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Is a 14 better than a 9 — Finding Out the Monte Carlo Way (Intro)

My APBA playing involves a solo league I put together 16 years ago.  The premise is I make either 6, 8, 10 or 12 teams out of that major league season and play a 30 game schedule using the Master Game and the approximately one million innovations I’ve added through the years.  So far I’ve played 35 seasons with every season since 1996, most of the 60s, and some scattered years from the past.  One of the things I have to do is come up with the base lineup(s) for each team.  In the modern area, it usually involves two lineups because of the more pronounced platoon splits.

One decision I had to come up with this year for a team is the rightfield position that came down between Jay Bruce and Torii Hunter.  Normally I would look at a formula that is essentially modified OPS (with an addition/subtraction for SB/CS) and make sure the platoon situation wasn’t terribly weird in one way or another.  My formula had a very close call between the two, showing that classic tough call on do you go complete player over raw power.

St-E29 Sp-10 Ar-37
Jay Allen
BRUCE
Outfielder (3)
11- 5 31- 9 51- 14
12- 25 32- 26 52- 27
13- 14 33- 5 53- 15
14- 30 34- 31 54- 32
15- 10 35- 40 55- 8
16- 28 36- 33 56- 13
21- 32 41- 26 61- 29
22- 6 42- 13 62- 13
23- 12 43- 29 63- 32
24- 13 44- 8 64- 13
25- 9 45- 14 65- 25
26- 13 46- 13 66- 1
J-1 PR-6/+1
St-F-34 Sp-13 Ar-35
Torii Kedar, Sr. “Spiderman”
HUNTER
Outfielder (3)
11- 0 -1 31- 8 -1 51- 9 -1
12- 25 -7 32- 26 -7 52- 27 -7
13- 22 -6 33- 0 -1 53- 19 -6
14- 30 -6 34- 31 -6 54- 32 -6
15- 10 -1 35- 9 -1 55- 8 -1
16- 13 -6 36- 14 -6 56- 13 -6
21- 40 -6 41- 24 -8 61- 24 -3
22- 7 -1 42- 9 -6 62- 13 -6
23- 12 -6 43- 29 -7 63- 31 -6
24- 13 -6 44- 7 -1 64- 22 -5
25- 8 -1 45- 14 -6 65- 35 -8
26- 13 -6 46- 13 -6 66- 0 -1
J-2 SA +2/-2

So I began to wonder: what is the true value of an 9, or a 14, or a penalty for a 24, in the context of runs?

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Introduction

I’ve been playing APBA since I was 10.  Over the years, I’ve noticed things that sometimes fall in the space of “do I ignore it and keep it real” or “do I take advantage of it and have it be a little odd.”  Setting up your outfield based on the other team’s error numbers, playing high shot forwards during penalty kills, etc.  Since I don’t want to clutter my regular blog with this, I’ve set up this one to be the place for my brain droppings when it comes to APBA.