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BASEBALL.INF
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1995-07-24
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BASEBALL.INF
August 1, 1995
JUST HOW DOES THIS THING WORK?
A few people have asked how SBS goes about simulating a game, so I
decided to write down a few notes for those interested.
HITTING vs PITCHING - the first step:
A hitter can do one of six things in SBS. He can:
1) Make an out.
2) Get a walk.
3) Get a single.
4) Get a double.
5) Get a triple.
6) Get a Home Run.
(He could also get on base on an error but that is really a subset of
making an out as far as the stats are concerned). SBS calculates from
the hitter's record the probability of each occurrence. Then the
pitcher's record is considered which modifies the probabilities. This
will be demonstrated by working through an example. Consider the batter
named Joe Hitter:
AB Hits 2B 3B HR BB K AVG
Joe Hitter 482 147 20 4 12 41 71 .305
Compute PA (Plate Appearances) = AB + BB = 523
(ignore sacrifice hits and Hit-By-Pitched-Balls which would make PA a
little larger)
Compute HBB (probability of Walk) = BB / PA = .078
Compute H1 (probability of single) = (Hits - (2B + 3B + HR)) / PA = .212
Compute H2 (probability of double) = 2B / PA = .038
Compute H3 (probability of triple) = 3B / PA = .007
Compute H4 (probability of HR) = HR / PA = .023
-------
.358
What's left is the probability of making an out (or possibly getting on
on an error): 1.000 - .358 = .642
We have determined Joe's probabilities as a whole against all the
pitchers he faced that particular season. But now we have to calculate
probabilities given a particular pitcher. Consider a player named Jack
Pitcher:
IP Hits HR BB K
Jack Pitcher 200 210 15 50 80
If a pitcher threw 200 innings we know he got approximately 600 batters
out. The ones he did not get out got hits or walks or reached on errors.
Compute BF (batters faced) = (IP x 3) + Hits + BB
Sometimes a pitcher gets a few extra outs such as double plays and
runners getting thrown out on the bases. On the other hand sometimes he
faces extra hitters because his defense makes errors. These two factors
just about cancel each other out so we can leave the BF equation alone
for purposes of explanation.
We now need to compute the probabilities for the pitcher for the same
events that we calculated for the batter.
Compute BF (batters faced) = (IP x 3) + Hits + BB = 860
Compute PBB (probability of Walk) = BB / BF = .0581
Compute P1 (probability of single) = Hits x .717 / BF = .1751
Compute P2 (probability of double) = Hits x .174 / BF = .0425
Compute P3 (probability of triple) = Hits x .024 / BF = .0059
Compute P4 (probability of HR) = HR / BF = .0174
The statistics do not usually tell us how many singles, doubles and
triples a pitcher allowed. Usually just the totals hits and home runs
are given. However, we can use the multipliers .717, .174 and .024 to
estimate singles, doubles and triples from the total number of hits.
[If all "HR's allowed" are zero in the .DAT file, SBS uses a "league
average" for P4 found from data in the .CFG file. This essentially
removes any influence a pitcher has over this statistic, however].
Comparing the percentages we obtained from the hitter with the pitcher
we have come up with the following:
Event Hitter Pitcher
------ ------ -------
walk 7.72% 5.81%
single 20.90% 17.51%
double 3.77% 4.25%
triple 0.75% 0.59%
home run 2.26% 1.74%
out 64.60% 70.10%
At first glance it might seem that all we need to do now is average the
hitters and pitchers events like this:
single = (20.9% + 17.51%) / 2 = 19.21%
etc. for the rest of the events
This method is unacceptable, however, because it penalizes the outstanding
players and rewards the poor players. That is, it tends to lump everyone
together too much. In our example above we have a good hitter, (.305 vs
the league) against a quite average pitcher. Certainly we could not
expect his single% to DROP to 19.21% from 20.90%! After all if this is
an average pitcher we would expect our batter to do at least as well
against him as he did against the rest of the league!
The solution is to use "league averages" for the events and to compare
our pitcher's performance against the league averages. For example, we
can pick up a baseball statistics magazine containing the statistics
from the preceding year, and calculate the total "batter's faced" for
all the pitchers for the entire season. We can also total the number of
walks, hits, and home runs -- and estimate using our multipliers above
-- the total number of singles, doubles, and triples. Then we can
calculate our "league averages".
For example, we find that for an entire season there was 17,500 innings
pitched, 16,500 hits, 1450 Home Runs, 6,300 walks. Calculate League
Averages:
League Avg. BF = 17,500 x 3 + 16,500 + 6,300 = 75,300
" " " " LABB = 6,300 / 75,300 = .0837
" " " " LA1 = .717 x 16,500 / 75,300 = .1571
" " " " LA2 = .174 x 16,500 / 75,300 = .0381
" " " " LA3 = .024 x 16,500 / 75,300 = .0053
" " " " LA4 = 1,450 / 75,300 = .0193
Finally we can combine our hitter percentages with our pitcher
percentages to get meaningful probabilities:
Combined percentages:
walk% = HBB * (PBB / LABB) = .0536
single% = H1 * (P1 / LA1) = .2329
double% = H2 * (P2 / LA2) = .0421
triple% = H3 * (P3 / LA3) = .0083
home run% = H4 * (P4 / LA4) = .0204
Note that if the pitcher's percentages are nearly equal to the League
Averages, the second factor becomes essentially 1 and the hitter
performs as expected. But if the pitcher's percentages are substantially
better (lower) than the League Averages, the second factor will be less
than 1 and the hitter will suffer. The reverse is true if the pitcher's
percentages are worse (larger) than the League Averages.
RIGHTYS VS LEFTYS - the second step:
The example above is the basis of how a given hitter is expected to
perform against a given pitcher. But we also can fine-tune our model to
correct for the baseball maxim that right-handed batters do better
against left-handed pitchers and vice-versa. [A batter facing a
like-handed pitcher suffers somewhat]. This is, of course, a very
individual thing -- not affecting some players while severely affecting
others. SBS does not know which players are exceptional in this area --
the data files do not show a breakdown versus right or left handed
opponents. But we can make some broad assumptions which are useful in
large simulations.
Approximately two-thirds of all innings pitched are by right-handers.
Because a typical batter will see so much more right-handed pitching
than left-handed pitching, his average vs. left-handed pitching will
show a greater fluctuation.
Consider the following typical scenario for a RIGHT-handed hitter:
AB Hits Avg.
_________________
Total | 600 180 .300
|
vs. Right-Handed Pitching | 400 116 .290
|
vs. Left-Handed Pitching | 200 64 .320
Notice that his boost vs left-handed pitching (20 points) is twice that
of his penalty vs. right-handed pitching (10 points). This is because he
sees approximately twice as much right-handed pitching over the course
of a season.
For the typical LEFT-handed hitter:
AB Hits Avg.
_________________
Total | 600 180 .300
|
vs. Right-Ha