“Percent of profit” is meaningless

Today’s news:

A new estimate shows Apple took 103.6 percent of the profits from all smartphone sales in the third quarter of 2016.

“Huh,” I said. “That doesn’t make a lot of sense. How can you take more than 100% of profit?” The answer is that the math is correct, but the result is meaningless.

Here’s why. Say there are only two handset makers, Company A and Company S. In the first quarter, they both make a profit. Company A nets $9 billion and Company S makes $1 billion. In this situation, it makes sense to report “percent of profit”. The total profit is $10 billion; Company A made 90% of profit and Company S made 10%. (I would present this as tables, but Medium doesn’t support tables. Sorry!)

In the second quarter, sales dip. Company A’s profit drops to $5 billion. But Company S does even worse: it loses $1 billion—also known as a profit of minus $1 billion. In this quarter, the total profit is $4 billion, and Company A made 125% of profit. (Company S made -25% of profit, whatever that means.)

Time marches on, and in the third quarter, Company A makes another $5 billion. It’s good to be the king. Things have gotten ugly over at Company S. Something about phones bursting into flames. Company S loses $4.9 billion. The total profit is now $100 million, and Company A made 5000% of profit. Are you seeing yet why this is stupid?

In the fourth quarter, Company A makes $5 billion again. Company S loses $5 billion. The total industry profit is zero. Company A’s percent of profit is NaN/undefined/divide by zero error/core dump.

Reporters need to stop reporting this “percent of profit” number. It’s silly and it doesn’t tell you anything useful.

What would be a useful way of looking at the industry? Well, you could say “only Company A and Company C were profitable this quarter.” You could provide some historical context like year-over-year profits. You could look at the market cap of one company as a proportion of the industry, because market cap is always a positive number, so you can divide it by the total without ending up in numerical purgatory.

The reason people report numbers like “104 percent of profit” is because it only sounds a little bit crazy. But it’s no less misguided than reporting 5000% or a billion percent any other obviously ludicrous number. Can we cut this out now, please?