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# Just how lucky have the Mariners been?

A deeper look at quantifying luck on the ball field.

The Mariners enter the month of May with their best record since 2003. They’re coming off a ten-game road trip where they won two series against the soft underbelly of the American League and then laid waste to the Cleveland baseball club, one of the best teams in the majors. They also suffered five blowout losses during the month pushing their overall run differential down below zero. There’s no question the Mariners have had some good luck on their side to post such a good record in April. But how lucky have they really been?

If we base measuring their overperformance simply on their run differential, the Mariners come out looking incredibly lucky. A -2 run differential translates to a .493 win percentage using the Pythagorean formula to estimate a true talent level. That means the Mariners have won almost three games more than we’d expect based on how many runs they’ve scored and allowed. But relying only on run differential is a simplistic way of discerning true talent. It’s useful for broadly describing team performance, but those blowout wins and losses have a way of skewing the data a bit.

If we want to take our luck analysis a bit further we can turn to a concept known as Cluster Luck. Conceived by Joe Peta and further developed by Ed Feng, Cluster Luck attempts to provide some additional context for a team’s performance that a simple run differential may miss. A team that hits nine singles in a one game could have vastly different outcomes depending on when those singles occurred. Nine in one inning could result in a number of runs scored but one per inning would likely result in a shutout.

I’ve discussed the BaseRuns formula before, when talking about the preseason projection systems. In brief, the BaseRuns formula attempts to estimate run scoring based on the number of baserunners, how many of those baserunners advanced, and the number of outs created. With that estimate for expected runs scored and allowed, we can compare actual results to come up with a tangible measure of how lucky a team has been.

On his site, Ed Feng uses a more basic version of the BaseRuns formula to calculate his results. With full box scores available, I’ve gone through every game the Mariners have played to add a little more complexity to the BaseRuns formula, including events like stolen bases, double plays, and hit batters. Below is a line graph and table showing the Mariners actual run differential, expected run differential, and Cluster Luck through April.

### Mariners Cluster Luck

Run Differential Expected Run Differential Cluster Luck Offensive Luck Pitching Luck
Run Differential Expected Run Differential Cluster Luck Offensive Luck Pitching Luck
-2 -8.5 6.5 -5.1 11.6

As you can see, the Mariners accumulated around six runs of good luck in April. But it gets even more interesting once you break Cluster Luck into its two component parts, offensive luck (expected runs scored vs. actual runs scored) and pitching luck (expected runs allowed vs. actual runs allowed).

The Mariners pitching staff was pretty lucky in April. They allowed 130 runs to score but BaseRuns thought they should have given up around 142 runs. The dominant performance of Edwin Díaz and the rest of the bullpen helped the Mariners outperform their expectations. The underperformance of the offense in April could be encouraging as well. BaseRuns thinks they should have scored five additional runs during the month. And now that the entire lineup is fully healthy, we had a brief glimpse of what they’re capable of in Cleveland.

Here are just a few more tidbits from the data:

• The Mariners luckiest win in April was probably their 9-7 victory over the Rangers on April 21. The pitching staff should have given up two more runs than they did and the offense was lucky to score that ninth run. In that game, Díaz walked three batters and gave up a single in the ninth inning but escaped with just one run allowed.
• The very next day, the Mariners suffered their unluckiest loss in April. Martin Pérez allowed only two runs on seven hits and a walk and Keone Kela allowed two hits in the ninth without allowing a run. BaseRuns thought the Mariners should have scored three additional runs and given up one fewer run in that game.