4.1 The flaw of averages
Life 2000 years ago in the Roman Empire was tough. The average life expectancy was between 20 and 33 – data is imprecise but the order of magnitude is what’s important here. What this fails to tell you, though, is that one of the biggest causes of death was infant mortality. 25% of children died before the age of one. If they did survive their first year, their average life expectancy was between 35 and 42 years. That’s already above average. 35-45% of children died before the age of five, but if they survived to that point they could expect to live to somewhere between 45 and 50 years old. If you made it to the age of 70 you would expect to live for another six to seven years. Now, consider you’re an ahead-of-your-time pension broker during the Roman Empire. If you sell your pension policies expecting the average lifespan of your customers to be 30 years, then when 50+ percent of your policy holders are still happily living at age 30 and expecting a few decades more worth of life, you’re going to run out of money fast to keep paying them.
Average numbers can hide many sins. An average of 200 downloads per piece of content could sound great until you realise that can be generated by four assets with 25 downloads and one with 900. People like averages when it allows them to tell a simple story in one number. They’re concise and, particularly when the number is good, memorable. But its always worth recognising that an average is not the same as a reality. If you see a marketing performance review that says each piece of content had an average of 200 downloads your likely takeaway is that each asset had 200 downloads. In reality, none may have achieved that figure. If the four worst performing assets had just over 10% of that, while the best performing one assets 450% of that then the lead was buried and the conclusions will be wrong.
Have you ever noticed how governments make open-ended commitments of $30 million here and £70 million there? They’re very good at sharing the number, less good at telling you when the number will be spent. In January 2021, the UK committed to spend at least £3bn on climate change solutions that protect and restore nature and biodiversity. I support and applaud this. But let’s dig a little digger before we break out the locally produced, low-carbon champagne. The commitment is over five years. That’s important as it takes the average annual commitment to £600 million per year, assuming the commitment is spread evenly, which there’s actually no reason to assume is the case. So it could be £200 million for the first year, then £700 million each year after that?
This next paragraph in the government’s press release is important: “The funding will be allocated from the UK’s existing commitment of £11.6bn for international climate finance”. What this means is that the money has actually already been committed to support climate initiatives, they just now recommitting it to a slightly different purpose. Governments are clever, and committing money you’ve already committed is a great way of showing action without having to actually act differently. A year after an announcement, who remembers the specifics or knows what has actually been spent? Say you did only spend £200 million of your £3 billion in the first year – could you commit to spend £3 billion again over five more years by adding another £200 million to the pot? That sounds like a bargain from a budget-balancing perspective as a great way of playing the ‘average’ game without actually spending the average. Eventually someone may find you out but when elections are every four to five years the goal may simply be to make it through to another election cycle without going broke in the process.
The takeaway here is not that averages are always wrong, but that they have their place. If you have some good performance and some bad performance and you don’t want to tell your boss, hide it in an average. ‘We averaged 200 downloads per asset’ sounds better than ‘four of our five assets were rubbish, but one worked really well.’ Ironically, that’s probably the insight that you should be sharing. ‘Let’s stop doing these things that don’t work and only do this thing that does.’ Averages should only be used to represent situations where it doesn’t matter what the maximum and minimum are. Don’t use average stress on a girder when working out if a bridge will collapse in the wind. Use maximum stress. If you want to work out how much water is flowing through a river, don’t look at maximum and minimum depth, use an average. Averages are great; people can just be bad at using them.