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Solo Shots Overblown

The Mariners continue to tread water with agonizing victories and a few frustrating losses thrown in for good measure. It is not quite a frustrating team to watch, but not a satisfying one either. They need to improve to make the playoffs, and it seems reasonable to expect them to improve on their own.

Their have been some claims that the Mariners are victims of hard luck. One stat that has popped up in the past week are the high volume of solo home runs the Mariners have cracked. So far, statistically, they are one of the more powerful teams in baseball this year, but don't have an above average offense overall. The solo home runs have been pointed to as a possible culprit.

I decided to dig a little further. To date, the Mariners have hit 54 home runs as a team. 41 of them are solo blasts. That feels like a high number, but how high is it in reality? The platonic world of mathematics can tell us.

In essence, this question boils down to the odds that a batter has reached base before a Mariner hits a home run. The Mariners, as a team, sport a measly .298 on-base percentage so far this season. So, one quick way to get a feel for how many solo home runs the Mariners should have hit is to assume every home run hit included exactly one batter that came up before the dinger, and that batter has a .298 on-base percentage. This sets up a case where binomial distributions are helpful. Given 54 trials (representing 54 home runs), with a .298 success rate (runner reaching base), how many times will a runner be on when a home run is hit? I built a binomial distribution simulator for my Hall of Fame posts this year, and the math works the same way in this case, so I fired it up again. After 100,000 simulations, here were the results. I present them to you as cumulative subtracted probabilities so that the odds represent the chance of at least that many solo home runs:

0-28: 100%
29: 99%
30: 98%
31: 97%
32: 94%
33: 90%
34: 84%
35: 76%
36: 67%
37: 55%
38: 44%
39: 33%
40: 22%
41: 14%
42: 8%
43: 4%
44: 2%
45: 1%
46-54: 0%

This is an oversimplification, but starts to give a feel for the M's luck so far this season. Yes, they have had bad luck, but not historically bad luck. Moreover, the 50% mark (which represents the average value and thus the predicted value) is right around 37.5, which is only 3.5 home runs away from the M's actual total. Therefore, the tough luck has cost the Mariners roughly 3.5 runs. To put that in perspective, Fangraphs defensive data suggests that Nelson Cruz's defense in right field has cost the Mariners 7.6 runs so far this year.

The main reason the Mariners have so many solo home runs is the same reason every baseball team piles up solo home runs. It's hard to get on base, especially the last few years as pitching has slowly sunk the game down towards lower offensive outputs not seen in decades. The Mariners are particularly bad at getting on base so it should come as no surprise that they hit more than their fair share of solo home runs. In fact, their high slugging, low on-base approach to hitting make them a good bet to lead the league in solo home runs.

The lack of baserunners for M's home runs is a little bit of bad luck, but driven much more by the design of their offense. It is hard to hit home runs with runners aboard when there are no runners aboard. Very hard, actually. Literally impossible.

If the Mariners want to hit more runners on base, the fix is to get more runners on base. The luck will even out a little bit as the season unfolds, but regression to the mean will be imperceptible. Solo home runs should be expected from this offense, and they should come in bunches just like they have.