Suppose a particular firm’s revenue rose from $1 million to $7 million from one year to the next. How would you describe that increase? If you wanted to show off, you could say the revenue septupled. A less pretentious description would be that the new revenue is 7 times as high as previously. Alternatively, you might say it is 6 times higher (since 1+6=7). What you absolutely should not say is that the revenue is 7 times higher (since 1+7=8≠7). Unfortunately, this seems to be the formulation that people use most frequently.
I’ve never quite been able to figure out why. Are most people just completely mathematically illiterate? That might well be the case, but mysteriously people tend to do this correctly for smaller increases. If in our example the firm’s revenue had grown to $1.2 million, most everyone would correctly say that it was 20% larger than before, not 120% larger. Probably the explanation is just that most people are very unreflective about language and hardly every pause to think about whether what they’re saying actually makes sense and when talking about small increases, whether or not to add one is a lot more obvious.
But it gets even worse when people talk about decreases. If the revenues of our hypothetical firm fell from $1 million to $250,000, many people would say that the revenue became four times smaller. What this would mean logically is that the revenue would now be -$3 million, which obviously makes no sense. Again, people handle small changes just fine. If revenue fell to $800,000, most would correctly identify this as a 20 per cent decrease and no one would even think of calling the new figure 125% smaller.
If people could just get this small thing right, there would be one less reason for me to be annoyed at the world. It’s really not that complicated.