From: silber@m.cs.uiuc.edu (Ami A. Silberman)
Subject: Re: luck in baseball
Organization: University of Illinois, Dept. of Comp. Sci., Urbana, IL
Date: Wed, 29 Jul 1992 00:32:47 GMT

dkl@cs.arizona.edu (David K. Lowenthal) writes:

>I have a real problem with some comments made on this newsgroup about
>luck.  I have not read them all, but Ms. Nichols especially continually
>talks about how luck enters in to one run games, world series play, etc.

>Well, I do not believe in luck in baseball, because the game is based
>on skill.  I now explain a few scenarios mentioned often:
...
>My basic argument is that the good teams are the ones who don't allow
>luck to enter into the game.

You're wrong. I'm sure some of those who actually play the game on a high
level will join in with me, but there is a large random factor. First, lets
ignore gusts of wind, myopic umps etc. When a batter swings at a pitch, he
is physically incapable of hitting it exactly where he wants to. A good
pitcher might be able to hit a hanging curve (the nearest thing to a
T-ball in MLB) with the sweetspot of the bat say 50% of the time. The rest
of the time he will be a little off. He may hit a single, he may pop up,
foul one off etc. Now, a good hitter will be able to detect that this is
a hanging curveball, and will be able to swing the bat in such a way as
to maximize his chances of acheiving the desired result, but he will still
hit a homerun say 30% of the time and a basehit another 30% of the time.
This is on the best possible pitch. On a fast ball, the good hitter has
less of a chance of putting the sweetspot of the bat on ball, less still on
a knuckler, but a perhaps a greater chance of getting close to it. 
All this is predicated on the hitter knowing exactly what pitch the pitcher
will throw, he knows what to expect, and he still can't always get a hit.
Why? First, the motion of the ball is not always uniform. At some point
the hitter is committed to his swing based on the current trajectory of
the ball. If a micro-air current causes the ball to diverge in its
path just before the batter makes contact, the batter will not make good
contact. There is nothing the batter can do about this, it happens before
he can react and change his swing. It may even happen close enough to contact
that he can't even begin to react (especially if the ball is a knuckler).
Once again, we're assuming he knows what the pitch is going to be and where
it is being thrown. (For the pitcher, aside from outguessing the batter
one has the reverse problem, sometimes the ball will drift due to the
wind micro currents etc. In addition, no one, not even Clemens, can place
a ball perfectly.) We're ignoring curve balls, sliders, breaking balls.
The batter "knows" when he begins his swing where the ball should be,
but this knowledge is incomplete, the vaguaries of wind, scuffs on the balls
surface etc. give a volume (simlar to an electron cloud in quantum mechanics.)
The ball should be in that volume, and the likelihood of finding the center
of the ball at a given point is greatest in the center of the volume, but
it is not deterministic. 
	Now lets look at the swing itself. The human body is not capable
of infinite precision. The batter intends to swing the sweet spot of the
bat through the center of the balls "probability distribution" or "likely
trajectory" or whatever pseudo physics term you want to borrow. Let us
suppose that the ball is exactly there. The bat may not be. Even the best
atheletes in the world do not get absolutely reproducable effects out
of their muscles. The batter swings and a few more nerve cells than normal
fire, triggering a slightly early contraction of a muscle, and the sweet
spot of the bat arrives slightly to soon, the ball hits a half inch toward
the head and is pulled to left field. Or, the batter swings and his his
bat is a quarter inch too low due to sluggish response from his muscles because
his blood sugar is slightly low due to him eating a Milky Way bar instead of
the usual Snickers bar before the game because there were'nt any Snickers
bars in the clubhouse because... and the ball is a long fly out instead of
a homer. Combine the two effects, of the uncertainty as to the precise
trajectory of the ball and the precise trajectory of the bat, and you can
end up with a sharp ground out, towering pop fly or whatever. All this with
the pitcher obligingly throwing batting practice. (Note that you are trying
to hit an object about the size of a quarter (the center of the front of the
ball) going 90mph with an object about two inches long and one inch wide
that you are holding about two feet away from you and swinging at, what, 50mph?)
Now, it can also be that both the ball and the bat are low, or high, or 
otherwise off in the same direction, so the vagueries of fate cancel, but they
are more likely to be off in different directions, so that a failure ensures.
	Note that I haven't taken into account anything like dust in the
batters eyes, a passing cloud putting the ball in shadow as it is delivered etc.
Never mind any thought of deception on the pitchers part. I have described how,
even if you had the perfect human batting machine, there are, due to the
construction of the human body, the limitations of the human reflexes, and
the vagueries of the wind of the baseball itself, random factors.
Now, random factors proliferate. Still with the old batting practice pitcher
and the "perfect batter". Suppose that there is a 1/3 chance of his making
an out, a 1/3 chance of a base hit, and a 1/3 chance of a home run.
Suppose he hits a home run then. The presence or absence of men on base
ahead of him is partially dependent on chance. Did the perfect batter ahead
of him make an out, hit a base hit, a home run? I assume that by this point
I've made it clear that I, at least, consider that luck figures in even at
the lowest, most mechanical level.
	Real baseball has a lot more luck than this. In some sense, figuring
out what the opposing pitcher is going to pitch is luck. You can maximise your
chances of success of course, but luck is still involved. This is because of
game theory. (Game theory the branch of math, not anything directly due to
baseball.) Naive baseball theorists think that the pitcher says to himself
(or the catcher says) "this guy hits curve balls really well, so better pitch
him a fast ball, but then he'll be expecting a fast ball, so better pitch him
a curve, but..." But they don't. Although they function on hunches, on
progressions of pitches etc, the effect is to randomize the pitch selection
(a biased randomization, of course), including where in the plate the pitch
will be thrown (or rather, attempted to be thrown.) As a side note, even with
extreme practice, under ideal conditions, the human body is incapable of
producing a pitching so consistent as to always place the ball in the same
place. A delay in release of a fraction of a second, due to the varying
speeds of neural transmission, varying slickness of the ball and the hand
etc. will result in the ball being off target by a an inch or two. This is
for someone like Roger Clemens at the top of his game. No one can place balls
perfectly. Back to pitch selection. Lets play a game. You are the batter.
You can choose swings A, B, C, or D. I'm the pitcher, I can chose pitches
1, 2, 3, or 4. The effects of swings vs. pitches is given by the table 
below, with the number being the number of bases advanced.

	A	B	C	D

1	2	1	0	1

2	4	1	0	0

3	0	1	4	0

4	0	0	0	4

If my pitch selection was random, but you chose which swing, then clearly
A gives you more total bases, and B gives you a greater chance at a hit.
If your swing was random, then clearly pitch 4 is best, because there is
a 75% percent chance of an out. On the other hand, if I throw just pitch
4s, you'll swing only Ds and keep hitting homers. If you only swing As and
Bs, I'll keep throwing you pitch fours though. It turns out that in this type
of guessing game, the strategy that leads to the best return, assuming
a non-trivial strategy on the part of the opponent (i.e, not, swing at
what was best against the last pitch or whatever) is random. Not totatly
random, without working the math, I think that the best pitching strategy
for the table above is about 50% 4s, 30% 3s, and 20% others.  Baseball
is kind of like that. You have to keep the batter guessing. The batter
guesses based on what he knows about the pitcher, his preferences, best
pitches etc, and what he can hit best. It's much easier to be outguessed
if you think too much about it. Now, from the point of view of the batter,
the pitchers decision is somewhat random. The batter may say "Fred's best
pitch is his fastball, it has a lot of movement so it's hard to hit even
when you're expecting it. He likes to throw the curve ball when he's 
ahead in the count. I think he'll probably throw me the curveball, but
I'm better able to hit the fastball. I'll assume that what he throws is
a fastball, but if it begins to break before I swing I'll slow up and try
to fight it off, or take it if it looks like it'll be outside.
	Note that if a ball is close, it is essentially random whether it
will appear to the umpire as a ball or strike, and therefor it is random
whether the batter (who wants it to be a ball) will hold off for a called
strike or a ball.
	Heres some more food for thought. Human memory and senseory memory
is a strange thing. One reason why pitching up the progression (high, higher,
out of the strike zone) often works, or varying pitches or whatever is that
there is probably some residual data left in the system of the batter
from the last pitch. (Especially if the pitcher works fast.) His subconscious
expects a fast ball like he got last time. He may think to himself "he'll
throw a curve", but the body is preparing to react quicker. Its part of the
way we are made, we expect the world to be orderly and repetative. It makes
us function better that way. We couldn't drive if we had to analysis the
position of all the other cars everytime we looked around. Instead, we notice
them when they get closer or further, or we make a special effort to see the
cute blond in the Mustang. Baseball is like that.
	Now, don't get me wrong, a good baseball player both maximises the
likelyhood of a successful even by his actions, and trains his body and mind
to be more reliable and more under control. One of the reasons why Ted Williams
was such a successful hitter was that he forced pitchers to throw strikes, he
was very aware of the trajectory of the ball and would take a walk. He
wasn't afraid of the called strike with a 2-0 count. Sometimes his judgement
was wrong and it was a strike, sometimes the ump called it a strike when 
objectively it wasn't, sometimes the ball droped just that last inch in the
last six feet. When Williams swung, he knew the ball was in the strike zone,
he knew pretty much where it was going to be in the strike zone, what
its rotation was, pretty much. He probably knew as much as was possible
about what that ball was doing, probably more than the pitcher, who by this
time was getting ready to field his position. Williams maximised his chances
with a short compact swing (he did have an extended follow through, which
adds power, but the arc of his swing from the bat at rest to the bat
meeting the ball was as short as he could make it without sacrificing too
much power.) He didn't need an elaborate timing mechanism (which adds to
inaccuracy due to the momentum of the bat from being wiggled etc, but
increases accuracy due to forcing the batter to start his swing at about
the right time.) Williams delayed his decision on how he was swinging as
long as physics and human reaction time could allow. He totally maximised
his success at the plate. And yet, he only hit .400 He didn't even hit
.600 against lousy pitchers (OK, maybe the worst, but not .800). There is
no such thing as automatic success. Seeing the result of each at bat or
pitch as a success, failure, or draw is missing the point. The result of
any given at bat, or any small sample, is affected by "luck", it is random
to an extent. Where talent comes in is through using the ability.
Its equally random when a .250 hitter gets a hit as when a .350 hitter,
its just that in an equal number of at bats the .350 hitter will get a lot
more of them.
	I haven't touched on what many of the other denizeins here will
go into detail, of how the results of studies don't show a significant
non-luck component as to timing. (Shortly. We agree it isn't luck that
a given team has an OBA of .350 and a SLG of .410. Its due to the players
being good etc. By our mathematical models, a team with that OBA and SLG
should, purely through luck, score (to pull a number out of a hat) 750
runs. (We know it is through luck because we base our formula upon the
stats for the entire league for a number of years, this counts the lucky
teams and the unlucky.) If there was a large non-luck component to 
the timing of those hits and walks (i.e, if one team, the Strict Determinists,
also had an OBA of .350, but tended to work it so that they got them when
they needed them), then the run production would be higher than predicted
by a statistically significant amount. If there was a large non-luck
component to the timing of individual hits there would be persuasive
evidence that clutch hitting existed. (Clutch hitting, or at least 90%
of what passes for it, is a conflation of the fact that hitting is easier
with men on base, wishful thinking, personal reminiscences, and statsitical
inertia. Statistical inertia says that if I flipped a coin ten times and
it came up heads seven times, if I flip it another ten times its likely to,
after all twenty times, have been heads more than tails. Of course, to get
an even number of tails and heads, the second ten flips would have to have
included seven tails.)
	In summary, baseball is luck. Luck isn't total randomness. If I have
a team of coin flippers that use coins that turn up heads 60% of the time,
and you have a team using fair coins, I'll win about 56% of the time if
we each flip the coins 10 times. If we each flip them 1000 times, I'll win
almost all the time. Batting is like flipping the coins.
	Tennis, now there is a game with little luck. (I say this, not to
disparage tennis, but because it strikes me that upsets, in the sense of
the clearly inferior player winning, is fairly rair, and often attributable
to health, fatigue, unfamiliar surface etc. I think the real reason is
that luck is present in tennis as well, but the number of "swings" that matter
in tennis is much higher than in baseball, so everything other than
systemic effects tends to wash out."
-- 
ami silberman - janitor of lunacy
	silber@cs.uiuc.edu