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"Normal" home runs are those that leave the park, that fielders don't have a chance of catching. As a result, they are not counted in the "balls in play" part of BABIP.
On the other hand, an "inside the park home run" is a hit that remained in the field, was presumably "fieldable," and just happened to go for four bases. Would it be excluded from the "balls in play" part of the BABIP calculation like the other kind of home run?
In the park Home Runs are not tracked separately from HR and would not be included in BABIP.
Neither Fangraphs, Baseball-Reference nor MLB have in-the-park-homers tracked and thus do not include it in their BABIP calculations.
As there are only a few each year, and the number is very small in relation to the total number of hits, at-bats and home runs, these are not really a factor in making BABIP unreliable.
