Playing the percentages

There are some nuggets of knowledge that you come across that make you want to throw your arms to the heavens and ask "Why didn't somebody tell me that years ago?" Meanwhile, there are other facts that seem, at first glance, nonsensical but, upon further examination, come to sound actually quite reasonable. Sadly, really good examples in each case are as rare as hen's teeth but it's been my very good fortune this week to have been blessed with a fine instance of both. I thought I'd share the joy of them here and apologise profusely if you were already aware of either.

First, something I wish I'd known for the last fifty years of my life rather than the last five days. It's this: all mathematical percentages are reversible. For example, 20% of 10 gives the same answer as 10% of 20 (2 in both cases) and 90% of 80 is the same as 80% of 90 (72 in both cases).

You can have hours of endless fun concocting ever-more weird examples of this phenomenon on a calculator. Is 17.5% of 86.2 the same as 86.2% of 17.5? Well, yes, by golly it is! (15.085). It's also possible you have a social life but, come on, that's just outstanding isn't it? It's clearly the first thing that should be taught in all schools everywhere- 'Put those crayons away, children, and take a look at this beauty...'

All of which brings us to Roger Federer who, during a commencement speech he gave in 2024, offered a couple of fascinating statistics concerning his career. For example, over a twenty year period during which he earned twenty Grand Slam titles, he won just under 80% of his matches.

This might seem like a low figure but, taking into account the greater number of losses he will have incurred as a callow youth and then, later, as an aging champion, it sounds about right. But here's the extraordinary fact: the percentage of individual points he won during those two decades. Go on, have a guess before I tell you. I was miles out. Ready? ...Sure? ...OK, here goes...54%.

That's right, Roger Federer came out on top in only just over half of all of those grunting rallies and precision serves. One of the greatest tennis players in history ground out his many victories dealing in the smallest of margins. This means that, tomorrow, I'll wake up determined to get the details right, to gain the little victories wherever I can. It might not make me a world champion but It should mean I get the floor tiles I'm working on grouted a bit more quickly.

That's the funny thing - 54% of a hundred is exactly the same as 100% of 54.

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