Percentages can be tricky

Talking in percentages can be challenging at times.

If your success rate increases from 25% to 30%, what is the increase? Is it 5% (30 minus 25) or is it 20% (100 x 5/25). If you're proud of it, you'd probably choose the latter, proud of the large increase you've achieved. However if we were measuring failure rate, you might instead adopt the lower value so as to make things appear as good as possible.

This is why percentage points were invented. This allows us to be more specific about whether we are talking about the raw percentage or else a new percentage.

Now, if we are talking about our success rate, we should either say that we increased it by 5 percentage points, or by 20%. The two possibilities are now distinguished and there is no ambiguity.

But percentages can still be a challenge.

If we speed something up and make it twice as fast, how would we describe the percentage decrease in time taken?

For example, a web page might load in 100 seconds. If we double the speed, it would instead load in 50 seconds. So the time taken has decreased by 50%.

But it's easy to get confused.

Two times faster?

In this landing page for a web site, they advertise that their "2x Faster" package will reduce your load time by "up to 100%".

Now, ignoring for the moment the lack of any meaningful statement in "up to 100%" (I think that's one for another post), I think what they actually mean is that the site's load time will be reduced by up to 50%. If they could get the load time to decrease by 100% that would actually be equivalent to an infinite speedup.

But the confusion continues!

Four times faster?

Now we're getting crazy! The "4x Faster" package can "only" make your site up to "200% faster". That's somewhat misleading somewhere - I would expect a four-fold increase in speed to lead to a 400% faster site, or at least an increase in speed of 300% - but certainly not 200%. In terms of loading time however, I would expect the loading time to decrease by up to 75%.

I think this is simply a confusion of marketing materials - the 2x Faster has become 4x Faster, so the 100% from the first screenshot "surely must become" a 200%. Except that it's talking about different things, and so it makes no sense. Oh, and the fact the first claim is mistaken doesn't help.

SpeedupSpeed IncreaseTime Decrease
1x0%0%
2x100%50%
4x300%75%
10x900%90%

This table should help somewhat. If we have a 2x speedup, we increase the speed of the page by 100% (it's gone from X to 2X). We also decrease the time taken by a factor of 2 - i.e., from 100% to 50%.

Similarly, if we have a 4x speedup, we increase the speed of the page by 300% (it's gone from X to 4X). We also decrease the time taken by a factor of 4 - i.e., from 100% to 25% which is a 75% reduction.

Talking in percentages can definitely be a challenge. But it's not incomprehensible and you just need to be clear about what you are talking about in any given statement.

[Image credit: Leo Reynolds]