Nobody knows what an 850% increase is, so please stop saying it

If a company is worth $1,000,000 at the start of the year, and $1,200,000 at the end of the year, its value has gone up by $200,000. We might say that its value is 1.2 times greater, or that it has increased by 20%.

In this case, saying that the amount is 1.2 times greater, and saying that it is 20% bigger, both mean the same and convey the same information - both in the literal mathematical sense, and in terms of how people understand them. People will quickly grasp the size of the increase.

But suppose instead of going from 1 million dollars to 1.2 million dollars, the company had gone from 1 million dollars to 4.5 million dollars. Now you could say that its valuation has increased 4.5 times, or that it has... increased by 350%.

Except now these two ways of expressing the growth are not equally useful. They are both still literally correct in the mathematical sense. But saying that something has grown by 350% does not convey the same information in terms of how most people will understand it - even if they eventually reach the right conclusion.

You might see '350%' and think something like oh wow 350x bigger - no wait it's a percentage so you divide by a hundred, it must be 3.5x - oh no wait it's off by one isn't it? So is it 2.5x or 4.5x, I can never remember. Well 2x is a 100% increase, so 3x is 200%, so this must be 4.5x, right?

And you'll generally get to the right answer. But why did the person telling you make you waste all that mental effort? Because best case scenario they are a poor communicator of ideas, or worse case scenario they are actively trying to make an increase seem bigger than it is.

If you ask a hundred people what a 350% increase on a million is, how many would correctly tell you the answer is 4.5 million? How many would say 3.5 million? How many would say 2.5 million? How many would say 350 million? If you ask them what a 4.5x increase on a million is, probably almost all of them will give you the correct answer immediately.

When people see percentage increases greater than 100, they have to stop and do a manual calculation. They are wasting mental resources and missing whatever comes next - and you as the person who was supposed to communicate the increase have made them do it for some reason. If your main aim is to quickly and efficiently communicate the magnitude of an increase and if that increase is more than double, it is almost always better to express it as a relative increase (2.5x bigger) than as a percentage (150% increase).

Probably the worst attitude to have is smugly remarking that it's not your job to educate people about how mathematics works, and they they should know this stuff, and that it's not your fault if they're mathematically illiterate.

First of all, this is why nobody told you about the Christmas party until after it had happened and why your friends 'forget' to reply to your messages more and more these days. Secondly, it is your job to communicate effectively even to people who don't know as much as you, always. And thirdly (and most importantly) even people who do know how percentages work will still have a minor mental stumble at being made to do these needless mental gymnastics.

When you are trying to communicate something to a listener/reader, your job is not to show off how clever you are for knowing how to use big percentages, or to trick them into thinking an increase is bigger/smaller than it really is, or to give them a mental workout.

It's to communicate efficiently.