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Thinking More About Luck

I am not claiming that the following incorporates all the avenues that luck could be influencing team offenses. Please note that all totals do not include yesterday's games.

A natural extension to the posts about the regressed wOBAs for Mariner players is to ask how the team's total of 23.3 runs compares to the rest of the league. That is easily doable for me, but it got me thinking because simply regressing a team's wOBA does not tell a majority of the story. Importantly, there is also the large degree luck in actually scoring runs. You might recognize this sector of luck from the standard intro into why we evaluate teams with BaseRuns. 

I feel that aspect is important to consider in conjunction with the regressed wOBA because I see the two pieces as independent of each other. A team might be unlucky in having many of its line drives caught but might also be lucky in getting hits with runners in scoring position. Regressed wOBA isn't going to measure the latter and BaseRuns isn't going to measure the former. Hence, the below attempt at combining the two. 

You already know how I come up with the difference in runs due to regressed wOBAs. For the other part, I could have just used BaseRuns subtracted from actual runs scored, but I wanted to keep things grounded on wOBA so instead of BaseRuns, I used expected runs scored calculated from the team's wOBA.

Let me explain the table below. The column titled 'wOBAr' is what you are used to from before - how many runs you would add (or subtract) to the team by regressing the wOBAs of the individual players. The column titled 'BsR' is on the same scale and is the number of runs you would add (or subtract) to the team by substituting in your run scoring estimator (e.g. BaseRuns, wOBA) in place of actual runs scored. The 'Luck' column is the addition of those two numbers. The final column is the projected runs scored for the team if you adjusted their actual runs scored by the 'Luck' and extended it over 162 games.

So far the Chicago White Sox turn out to be the most unlucky offense; regressing the team wOBAs (like I did here) would give them an additional 37.6 runs. However, they have scored 8.8 more runs than one would expect given their actual team wOBA so those 8.8 runs are subtracted away from the 37.6 they get back from wOBA regression to leave them with a total unlucky deposit of 28.8 runs. They have actually scored 152 runs in 37 games. Upping that to 180.8 (152 + 28.8), gives them a projected RS of 792 for the season.

Team wOBAr BsR Luck RS*
NYA 6.0 1.1 7.1 964
BOS 15.6 11.2 26.8 955
MIL -2.9 19.7 16.8 933
PHI -0.3 -6.1 -6.4 900
MIN -1.1 20.3 19.2 884
CHN 2.2 19.5 21.7 830
LAN 0.4 -3.9 -3.5 821
DET -4.0 19.1 15.1 815
CHA 37.6 -8.8 28.8 792
COL 1.5 2.5 4.0 789
SLN 13.3 10.4 23.7 788
ATL 6.6 5.0 11.6 778
TOR 5.0 -14.4 -9.4 776
WAS -0.3 12.4 12.1 740
CIN -3.2 -7.7 -10.9 734
KCA 2.2 15.2 17.4 733
ARI -17.5 -5.8 -23.3 730
FLO 8.9 -14.2 -5.3 730
TEX 9.3 -18.0 -8.7 720
ANA 20.3 -9.7 10.6 707
CLE 1.1 16.9 18.0 707
NYN 7.9 -9.7 -1.8 699
SFN -1.9 1.8 -0.1 696
TBA -7.0 -31.5 -38.5 693
OAK 6.8 -5.2 1.6 650
SDN 8.0 -12.5 -4.5 633
SEA 23.3 -0.3 23.0 631
BAL 4.4 14.2 18.6 630
PIT 9.0 0.5 9.5 607
HOU 24.7 -21.5 3.2 491


























The columns are sortable by the way. Just click on the column headers.

You'll notice some intuitive results here. Jeff has mentioned that the Rays' lineup has not actually been that potent in 2010. And we all remember how much talk there was about their hitting with runners in scoring positing during the series they swept us. Accordingly, they have been exceedingly lucky in plating runs and have actually been a rather mediocre offensive team. 

Houston is wow so very very bad.