I'm sure you're all waiting for more uses of statistics in baseball-related activities, so here we go:

In head-to-head fantasy baseball leagues, each team competes against another team in different statistical categories. If a team wins 8 categories, loses 3 categories, and ties the opponent in 1 category, then that team's record for the week is 8-3-1, for a .708 winning percentage.

Since the results of head-to-head fantasy baseball leagues are affected by the quality of one's opponents, I want to determine how lucky each team in my league has been through week one.

What I need to do first is determine the expected winning percentage each team would have based on how they did in each of 12 categories.

For example, my team had 2 saves in week 1. To calculate my expected winning percentage for that category, I need to know how many other teams had fewer saves, more saves, and the same number of saves.

In this case, 6 teams had fewer saves, 4 teams had more saves, and 1 team had the same number of saves. And so I would’ve beat 6 teams, lost to 4 teams, and tied 1 team in this category. Having an expected record of 6-4-1 in the saves category gives me an expected winning percentage of .591 for this category.

Here are the expected winning percentages of each team for each hitting category:

Player	R	HR	RBI	SB	OBP	SLG
Mejeld Lee (c/o '03)	0.773	0.273	0.636	0.727	0.909	0.182
Dan Kim ('02)	0.545	0.818	0.273	0.818	0.182	0.318
James Kang ('06)	0.455	0.545	0.545	0.364	0.636	0.455
James Song ('03)	0.318	0.364	0.455	0.636	0.364	0.318
Crew Andy ('02)	0.773	0.545	0.091	1.000	0.545	0.636
Jaepil Kim ('02)	0.182	0.545	0.727	0.364	0.000	0.091
Daniel Hahn ('06)	0.636	0.818	0.818	0.045	0.455	0.909
Tommy Lee ('03)	0.091	0.091	0.000	0.364	0.091	0.000
Gee-Won Kim ('03)	0.000	0.818	0.364	0.364	0.818	1.000
Jomo Lee ('02)	1.000	0.091	1.000	0.364	1.000	0.818
Jiehoon Lee ('02)	0.318	0.091	0.182	0.909	0.727	0.545
Stephen Lee ('02)	0.909	1.000	0.909	0.045	0.273	0.727

Here are the expected winning percentages of each team for each pitching category:

Player	IP	W	SV	K	ERA	WHIP
Mejeld Lee (c/o '03)	0.727	0.773	0.773	0.364	0.273	0.091
Dan Kim ('02)	0.318	0.500	0.136	0.864	1.000	0.727
James Kang ('06)	1.000	0.909	0.136	1.000	0.727	1.000
James Song ('03)	0.182	0.045	0.773	0.091	0.000	0.000
Crew Andy ('02)	0.000	0.045	1.000	0.000	0.636	0.818
Jaepil Kim ('02)	0.909	0.500	0.909	0.864	0.545	0.636
Daniel Hahn ('06)	0.636	0.773	0.136	0.545	0.455	0.318
Tommy Lee ('03)	0.455	0.227	0.591	0.636	0.091	0.182
Gee-Won Kim ('03)	0.091	0.500	0.591	0.455	0.909	0.909
Jomo Lee ('02)	0.318	0.500	0.409	0.273	0.818	0.455
Jiehoon Lee ('02)	0.545	0.227	0.136	0.182	0.364	0.545
Stephen Lee ('02)	0.818	1.000	0.409	0.727	0.182	0.318

A player's overall expected winning percentage is the mean of the 12 expected winning percentages by category.

Comparing the overall expected winning percentages with each team's actual winning percentage gives us a chart that includes the following:

Luck: W% - E(W%)
Actual winning percentage: W%
Overall expected winning percentage: E(W%)

Player	W% - E(W%)	W%	E(W%)
Mejeld Lee (c/o '03)	0.291	0.833	0.542
Dan Kim ('02)	0.166	0.708	0.542
James Kang ('06)	0.060	0.708	0.648
James Song ('03)	-0.003	0.292	0.295
Crew Andy ('02)	-0.008	0.500	0.508
Jaepil Kim ('02)	-0.023	0.500	0.523
Daniel Hahn ('06)	-0.045	0.500	0.545
Tommy Lee ('03)	-0.068	0.167	0.235
Gee-Won Kim ('03)	-0.068	0.500	0.568
Jomo Lee ('02)	-0.087	0.500	0.587
Jiehoon Lee ('02)	-0.106	0.292	0.398
Stephen Lee ('02)	-0.110	0.500	0.610

Positive luck totals indicate lucky teams.

Looking at the luck column, we see that Mejeld and Dan The Man were helped out significantly by playing teams who had bad weeks. Meanwhile, Jiehoon and Stephen had the unluckiest teams.