The Tigers have gotten off to a dream start. They have a sparkling 11-2 record and lead the majors in run differential (runs scored minus runs allowed).
With such astounding success, it's natural to ask whether luck has helped the Tigers during the first two weeks of the season. While luck can affect a baseball team in many ways, let's focus on one called "cluster luck."
To understand cluster luck, consider two teams that both hit nine singles in a game. The first team clusters their hits in one inning, scoring seven runs. They get praised for their clutch hitting in scoring runs.
The second team hits one single in each inning of the game. They score zero runs, and the opposing pitcher gets credit for scattering hits in his shutout victory.
Despite the appearance of skill, my research shows that teams have very little control over the clustering of hits, both on offense and defense. The two examples above are extreme outliers, and hits tend to be evenly distributed over the innings.
What the ratio of runs to hits says about luck
To get a quick look at cluster luck, consider the ratio of hits to runs for a team. Joe Peta, who coined the term "cluster luck" in his book Trading Bases, noticed that teams score a run for about every two hits. Clearly, teams that hit for more power will score more runs per hit, but this 1:2 ratio serves as a benchmark when looking at a box score.
Despite their hot start, the Tigers have had bad cluster luck. To see this, consider Friday's game against the Chicago White Sox. They scored two runs on 10 hits. Yoenis Cespedes hit a home run in the fourth, and the Tigers scored the winning run in the ninth with two hits and a generous call on Nick Castellanos' slide into second base.
However, the remaining seven hits went to waste in creating runs. The Tigers had two hits in both the first and fifth innings, and added a lone hit in the third and seventh. They also added a single in the fourth after the home run by Cespedes.
You could bash the Tigers for their lack of clutch hitting. However, if they continue to rack up 10 hits per game, they're more likely to score five runs per game than two.
How to quantify cluster luck
In my research, I use run creation formulas to quantify cluster luck. These formulas take statistics such as singles, doubles, homers, etc. and estimate the number of runs a team should score.
In my tests of these run creation formulas, I found Dave Symth's Base Runs formula to be the most accurate. Over a 10-year period, it made a 1-percent error in predicting the number of runs a team scores over the season.
Cluster luck is the deviation of actual runs from the prediction of Smyth's formula. Most importantly, this quantity tends to be random. This means that a team's current deviation in runs has no ability to predict their future deviation in runs.
The Tigers have been cluster unlucky on both offense and defense this season. Based on their offensive statistics, the run creation formula prediction 72.7 runs while the Tigers have only scored 68 runs. They've also been unlucky on defense, as they have allowed more runs (35) than the run creation formula predicts (31.2). Only 4 teams have had worse cluster luck early this season (all statistics through Sunday's games).
Outlook for the remainder of the season
This cluster luck analysis does not suggest the Tigers will continue to win games at their current rate. They won't continue to hit .305 all season and score 5.7 runs per game.
However, the Tigers' early success has not been propelled by a freakish clustering of hits. They have actually been unlucky in this department. In the best case scenario, the Tigers start to get lucky in their sequencing of hits when the bats cool off.
How teams rank based on 'cluster luck'
(All statistics through Sunday's games.)
1. Arizona, 18.78. (6.27, 12.51).
2. Texas, 15.92. (8.33, 7.60).
3. Toronto, 13.22. (12.86, 0.36).
4. New York Mets, 12.00. (6.75, 5.25).
5. Atlanta, 7.25. (2.50, 4.75).
6. Pittsburgh, 6.93. (8.21, -1.29).
7. St. Louis, 6.46. (0.43, 6.04).
8. San Diego, 5.09. (0.12, 4.98).
9. Colorado, 3.49. (-2.58, 6.08).
10. Los Angeles Angels, 3.14. (2.72, 0.42).
11. Kansas City, 1.38. (1.60, -0.22).
12. New York Yankees, 1.33. (6.68, -5.35).
13. Oakland, 0.74. (2.39, -1.65).
14. Minnesota, 0.70. (2.13, -1.42).
15. Chicago Cubs, 0.17. (0.95, -0.77).
16. Boston, -0.28. (9.26, -9.53).
17. Philadelphia, -0.90. (-5.20, 4.30).
18. Cleveland, -1.36. (0.17, -1.53).
19. Chicago White Sox, -2.14. (-1.24, -0.90).
20. Cincinnati, -3.44. (-2.64, -0.81).
21. Miami, -3.75. (4.36, -8.10).
22. Baltimore, -6.25. (-0.50, -5.75).
23. Washington, -6.84. (2.08, -8.92).
24. Houston, -7.14. (-8.57, 1.44).
25. Milwaukee, -7.29. (-1.11, -6.17).
26. Detroit, -8.53. (-4.73, -3.80).
27. Seattle, -9.72. (-4.56, -5.17).
28. San Francisco, -11.98. (-12.87, 0.89).
29. Los Angeles Dodgers, -13.66. (-11.84, -1.82).
30. Tampa Bay, -15.86. (-2.70, -13.16).