From: tedward@cs.cornell.edu (Edward [Ted] Fischer)
Subject: Luck report
Organization: Cornell Univ. CS Dept, Ithaca NY 14853
Date: Sat, 3 Oct 1992 04:21:52 GMT


Back at the end of July, I prepared the following analysis.  The
column headings are:
rs = runs scored in real life
RC = a simple runs created formula (TB * OBP).  Note that this is
     far from the most accurate formula, as it does not include
     the advancement factor for walks, and it does not include SB.
     Think of it as being an approximation of what the team was
     "supposed" to score.
ra = runs allowed in real life
wp = winning percentage in real life
PYTH = expected winning percentage, given the actual RS and RA
RCPY = expected winning percentage, given RC and RA.
OLUCK = (RS - RC)/10.  This is an approximation of how many wins
     a team has gained by producing more runs than you would expect.
PLUCK = Number of games difference between the PYTH and actual
     winning percentage.  This is an approximation of how efficiently
     the team has used its run differential to win games.
TLUCK = Games difference between RCPY and wp.  This is an approximate
     measure of total luck.

The numbers through the end of July:
Team  rs    RC    ra    wp    PYTH  RCPY  OLUCK PLUCK TLUCK
kc      378   383   398 0.439 0.474 0.481  -0.5  -3.5  -4.2
bal     464   481   400 0.551 0.574 0.591  -1.7  -2.3  -4.0
sea     419   435   520 0.390 0.394 0.411  -1.6  -0.4  -2.1
min     493   480   372 0.612 0.637 0.624   1.3  -2.5  -1.2
chw     407   399   402 0.485 0.506 0.496   0.8  -2.2  -1.1
cle     386   401   463 0.424 0.410 0.429  -1.5   1.4  -0.4
nyy     433   435   453 0.480 0.477 0.479  -0.2   0.2   0.0
det     474   462   492 0.470 0.481 0.468   1.2  -1.1   0.2
bos     349   351   375 0.469 0.464 0.466  -0.2   0.5   0.2
cal     368   350   412 0.439 0.444 0.420   1.8  -0.5   1.9
tor     458   457   403 0.592 0.564 0.563   0.1   2.8   2.9
mil     446   411   399 0.546 0.555 0.515   3.5  -0.9   3.2
oak     451   442   415 0.582 0.541 0.531   0.9   4.0   5.0
tex     456   452   478 0.525 0.476 0.472   0.4   4.8   5.3

Numbers through September:

Team  rs    RC    ra    wp    PYTH  RCPY  OLUCK PLUCK TLUCK
sea     653   697   776 0.385 0.415 0.446  -4.4  -4.7  -9.6
nyy     709   719   716 0.474 0.495 0.502  -1.0  -3.2  -4.3
kc      589   599   639 0.445 0.459 0.468  -1.0  -2.2  -3.5
det     773   741   767 0.471 0.504 0.483   3.2  -5.1  -1.8
bal     670   703   633 0.542 0.528 0.552  -3.3   2.1  -1.6
min     709   706   622 0.555 0.565 0.563   0.4  -1.6  -1.2
bos     575   580   644 0.449 0.444 0.448  -0.5   0.8   0.1
mil     715   656   572 0.571 0.610 0.568   5.9  -6.1   0.4
cle     648   668   716 0.471 0.450 0.465  -2.0   3.2   0.9
tex     657   681   727 0.474 0.450 0.467  -2.4   3.9   1.1
chw     710   674   656 0.542 0.539 0.514   3.6   0.4   4.4
tor     757   741   667 0.586 0.563 0.552   1.6   3.6   5.2
cal     553   521   644 0.439 0.424 0.395   3.2   2.2   6.8
oak     715   693   654 0.596 0.544 0.529   2.2   8.1  10.5

Analysis:
At the time of the first study, five teams were unlucky by a game or
more, and five teams were lucky by a game or more.  Since the first
study was done approximately 2/3 of the way through the season, if
these numbers showed any consistant pattern I would expect the second
numbers to be 1.5 times as large as the first, or in other words have
(TLUCK2 - TLUCK1) * 2 ~ LUCK1

Let's look at these 10 teams:

Team	Luck1	2*(Luck2-Luck1)
KC	-4.2	  1.4
BAL	-4.0	  3.6
SEA	-2.1	-15.0
MIN	-1.2	  0.0
CHW	-1.1	 11.0
...
CAL	 1.9	  9.8
TOR	 2.9	  4.6
MIL	 3.2	 -5.6
OAK	 5.0	 11.0
TEX	 5.3	 -8.4

Average luck for first group before the first study: -2.5
Average luck for second group before the first study: 3.7

Average luck for first group since the first study: 0.2
Average luck for second group since the first study: 2.3

Conclusions:
This is far from being an ideal study.  It is on a very small sample
set (only one season, one league) and I wasn't particularly careful
with the methodology used for the formulas.  Ideally, I would want to
split at the All-Star break, and use the half-season stats to compute
each study independently.  Instead, I do this subtract-and-normalize
stuff.

But the rough idea is clear: Luck is a fickle mistress.  If you aren't
hitting well enough to justify your run totals, you should expect a
decline in offense.  If you don't have a big enough run differential
to justify your winning percentage, you should expect to lose more
games down the road.

I would think that the Mariners would be greatly cheered.  Sure, they
sucked.  But they lost another 10 games this year on luck alone!  Look
for them to be greatly improved next year.  (Actually, I can think of
several reasons for the M's to be optimistic.  Randy Johnson, Kevin
Mitchell, and Brett Boone feature prominently among them.  Not to
mention that a couple of the young pitchers are looking pretty good.)

Oakland and Toronto are the two teams where this luck factor might
show something real.  Their bullpens are simply *not* in the habit of
giving up leads.  But the Angels?  I'd predict a slide, excet that I
think they will be fielding a better team next year.  I still predict,
however, less improvement in their record than in their stats.

Cheers,
-Valentine
-- 
Make outs, not walks!					tedward@cs.cornell.edu
Clemens four Cy Young!
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