Charles on… anything that comes along

If you saw a race report and it said that X ran 100% faster than Y, would that instantly say to you that X ran the race in (say) 5 seconds, and that Y took 10 seconds?

How about if something about building B said it was 200% taller than building A? Would you instantly realise that building B is three times higher than A?

I don’t think so. Percentages are an odd beast: a piece of precision mathematics that get routinely misused. Often, people use them because they think that they sound scientific, and precise, but the reality - as with the buildings and running example - is that using percentages (if you use them properly) can downplay the impact of the raw numbers.

Things get even more confusing when you get figures like “A did 250% more business than last year”. What on earth does that mean? It should mean that A this year did 3.5 times more than last year. But often it doesn’t - people see “2.5x greater” and stick that into a percentage.

My own thoughts on percentages: if they not less than 100 (or precisely equal to it), then leave them alone and quote the actual factor of improvement.

Things get worse of course when you want to talk about decrement. If you had 100 and now you’ve got 1, how much have things got worse? 99%, you murmur, and you’re right. That’s OK when you’re talking about the price of a share. But if you’re talking about people, it works better just to say “Last year it had 1,000 employees; this year it has 10.” It’s stark. It’s accurate. And it says it so much better than the glib “Staff were reduced by 99% in the fiscal year.”

What am I saying? That using percentages greater than 100 leads - sometimes intentionally, sometimes accidentally - to obfuscation. It’s not clear to the reader.

And to return to the example from the top, what would you understand by “a 20% faster bootup time”? It means that rather than waiting (say) 10 seconds, you wait 8 seconds. (Of course if you wanted to run it to expand the number, you’d say that the bootup time used to be 25% slower. Wow, that sounds huge!) It’s still better to give the reader the numbers, I think. 10 seconds, 8 seconds. OK, quicker. The question becomes then, what do you do with those two seconds?

Of course, it might be 100 seconds vs 80 seconds. Even so, you know that the extra 20 seconds “gained” are going to be spent emptying spam from your mail folder..

These posts might be related (the database thinks..):
• The 9 rules of journalism.. just marvellous (13 June 2007; score: 41.95%)
• More statistical syllogisms (21 August 2004; score: 35.46%)
• The curse of Radiohead strikes X-Factor again (8 October 2007; score: 29.11%)