How to succinctly and clearly connote the reverse of a statement

Solution 1:

[Setting aside all questions of the truth of the statment, or the authors original intent]

A cop is six times more likely to be shot by someone black than vice-versa.

Seems less ambiguous, vice-versa implying a transposition of roles.

I much prefer your precise elaboration of the meaning

Events in which a cop is shot by someone black are six times more frequent than events in which a someone black is shot by a cop.

In cases such as this I prefer clarity to concision. I would not seek to shorten your second clause.

Solution 2:

Setting aside any other biases of interpretation, in this case, the distinction is between the active and passive voice:

• A bird is eaten by a cat.

vs.

• A bird eats a cat.

The comparison is likelihood by a multiple of 6:

A bird is six times times more likely to be eaten by a cat than to eat a cat.

Passive is the opposite of active. Vice versa is less ambiguous than opposite. It is more succinct, but less precise, than expressing the actual point: sometimes birds eat cats, but usually they are eaten.