Here's a published example of a problem I come across frequently:

A cop is six times more likely to be shot by someone black than the opposite.

Let us assume that the writer meant to say:

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.

Obviously a concise way of abbreviating the second clause would be desirable. But is there a way to do it that is not ambiguous?

The problem with the way the author did it originally is that the opposite could mean a number of things. E.g.,

  1. White (or non-black) is the opposite of black, so did he mean than by someone not black?
  2. Not getting shot is the opposite of getting shot, so did he mean than not being shot by someone black?

Granted those may seem like less likely interpretations, but they are not inconsistent with the original sentence.

My inclination is to replace the opposite with vice versa, but is that truly unambiguous in this example? I.e., is the original example so amended inconsistent with any interpretation other than the one desired? Or is there a better solution to concisely convey what I assumed was the intended fact?

For those who find the subject matter distracting please replace the original quote with ScotM's equivalent but less politically hot formulation:

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

Not that it's relevant to the question, but for reference here is the source and context of the original quote.

Homicide is the leading cause of death for young black men in the U.S., and around 90 percent of the perpetrators are also black. Yet for months we’ve had protesters nationwide pretending that our morgues are full of young black men because cops are shooting them. Around 98 percent of black shooting deaths do not involve police. In fact, a cop is six times more likely to be shot by someone black than the opposite. Race Relations and Law Enforcement — Jason L. Riley

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    I think it's a good question: assuming the meaning is as shown, how can we concisely express that meaning? The question remains interesting even if the meaning was intended to be something else.
    – djna
    Feb 20 '15 at 17:51
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    I'm not P.C., but I think you could have used a less inflammatory example sentence. The way this reads could be construed as trolling.
    – Robusto
    Feb 20 '15 at 17:52
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    I suppose it might work to say "...than vice versa" or "...than the other way round". It might. But I prefer the second sentence to the first or its concise modifications. Apart from the ambiguity, the first sentence seems to be trying to derive the probability of future events from the (alleged) frequency of past events, which might not always work. The second sentence does not seem to do that.
    – anemone
    Feb 20 '15 at 18:22
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    Come to think of it, the definition of succinct is brief and clear, so the original author was only brief.
    – ScotM
    Feb 20 '15 at 23:27
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    @FumbleFingers I agree with you here. One cannot ignore the fact that what is being offered is a meaningless statistic. To take an extreme case, suppose on an island there were ten 'cops' and a thousand 'blacks'. One night two cops and two blacks get shot. That means that one in five cops have been shot. But only one in 500 blacks have been shot. So a possible interpretation would be that a cop was 100 times more likely to be shot by a black than 'vice-versa'. So I strongly suspect the author is propagating a statistical sleight of hand.
    – WS2
    Feb 21 '15 at 0:11

[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.

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    I agree with this. What people consider to be 'opposite' might vary when discussing complex concepts. Up has a clear opposite, positive has a clear opposite; purple book bags on pirate ships in May don't have a clear opposite. Feb 20 '15 at 18:20
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    Clearly, @DaveMagner, the antonym would be: green bid dispensers off original divorces past nadir ;-)
    – ScotM
    Feb 20 '15 at 23:07
  • @ScotM You're right. I see that now. Feb 23 '15 at 15:57
  • Which proves the merit of your comment, @DaveMagner. Depending on which nuance of a word's meaning we focus on, the "opposite" varies greatly. The ambiguity multiplies with phrases, and explodes exponentially with complex sentences. Excellent example by the way; I really had to work at it :-)
    – ScotM
    Feb 23 '15 at 17:21

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.


  • 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.

  • Cute........ +1
    – anemone
    Feb 20 '15 at 19:17
  • Thank you for the more innocuous example, which I co-opted for my original question's addendum. However I don't understand the point you are making: how is "passive is the opposite of active" the "actual point?" You mean if the action is "to be shot by" then the opposite must be "to shoot," and that is the only or most logical interpretation of the original statement?
    – feetwet
    Feb 20 '15 at 21:25
  • That is a bit ambiguous, isn't it:-) Recognizing that passive is the opposite of active, you can make your point precisely.
    – ScotM
    Feb 20 '15 at 22:33
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    Remind me to stay away from that bird!
    – Hot Licks
    Feb 20 '15 at 22:42

Six times as many As are shot by Bs than the reverse.

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