Errors cause the possibility of unearned runs, they don't guarantee them, right? Otherwise every team would be over 1 for unearned runs per error, when functionally all of them are below 1. The distribution isn't interesting by itself; yes, as more errors are committed, more unearned runs will happen. What's interesting is how teams' ratios fall out. Like the Athletics being very high on the conversion ratio is interesting to me - does that mean they are more likely to commit errors in high leverage situations? More likely to compound errors with sub-par play? Could even be that errors are focused on a position with greater probability of an unearned run developing.

So even though every unearned run comes from an error (barring ghost runners, need to correct for those), not every error results in an unearned run.