## Billy Butler's Home Runs

More than once this year I have heard references to Billy Butler hitting home runs in "bunches". This tested my patience, but now that the season is over I thought I might look at the data and see if this assertion bears out. The following graph shows how Billy's home runs were distributed based on number of games between each homerun (y-axis is count of the times each gap defined by number of games appeared).

This chart seems to back up the bunching of home runs. As we would expect the average gap between home runs was 5.46, he hit 29 in 161 games played which would lead to a HR rate of once every 5.55 games. If the homeruns were normally distributed the expected histogram would have higher frequencies around the average of between 5 and 6, but we see a lot of 1, 2, 3, and 4 game gaps along with some very large gaps in the right-hand tail. This is a fairly small sample, so I did this again for 2011 with the following results.

He hit fewer home runs in 2011, so the average gap was higher, but the chart looks somewhat similar, and combining the two only serves to highlight it.

Over the last two season a Billy Butler homer will be followed by another homerun in the next four games almost 61% of the time. Otherwise a drought of 9 or more games shows up a little over 30% of the time. The composite average gap for the two years is 6.5 games between home runs, so a normal distribution would expect the preponderance of observations in the five to eight games between home runs area, and we see the exact opposite. Maybe Billy really is a streaky home run hitter. Once again there is a pretty small sample here though. My next step will be to look at all the batters who hit 30 or more home runs in 2012 and see if they all tend toward this, or if Billy might just be coming into his power and can be expected to be more consistent like the other sluggers in the future.

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