Thinking about it, if the clock runs backwards at the same rate, so -1 hour per hour, the rate of randomly being right is 2x the stand-still rate. This is also a linear function, at -1 its 4x per day, -0.5 is 3/d, 0 is 2, 0.5 is 1. When it runs true it is however very different, as it is either always exactly right (no offset) or never (with offset).
I think that’s why this sort of phrase never made much sense to me, because in the same sense that the broken clock is right, a working clock with an offset (technically all of them) is almost never right (as you mention). Maybe it extends the metaphor, though, because while the working clock is never completely accurate, it’s much more useful by being closer to the truth the vast majority of the time.
Thinking about it, if the clock runs backwards at the same rate, so -1 hour per hour, the rate of randomly being right is 2x the stand-still rate. This is also a linear function, at -1 its 4x per day, -0.5 is 3/d, 0 is 2, 0.5 is 1. When it runs true it is however very different, as it is either always exactly right (no offset) or never (with offset).
I think that’s why this sort of phrase never made much sense to me, because in the same sense that the broken clock is right, a working clock with an offset (technically all of them) is almost never right (as you mention). Maybe it extends the metaphor, though, because while the working clock is never completely accurate, it’s much more useful by being closer to the truth the vast majority of the time.