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Local and global maxima

This is a math-y topic but I promise it’s important, and I promise it’s not over your head. Explained correctly, the concept of local and global maxima will convince even the most timid of stakeholders to test big changes and tolerate poorly performing variations.

Local and global wha?

Local and global maxima are two theoretical ideas about where your conversion rate might be, and where you want it to be. Like this:

Graph of 2-d space with local and global maxima

The little hump is a local maximum - it’s higher than all the points around it. The BIG hump is the global maximum - higher than all other points.

If you imagine that every possible version of your site (or page, CTA, etc.) falls somewhere on this 2D graph, with higher conversion rates falling at higher points on the graph, your task is clear - find the version at the global maximum.

Why does it matter?

Things get scary when you imagine that your current site might be somewhere on that cute little local maximum hill.

If this is the case, you can climb up the hill by testing small, iterative improvements. But these improvements will never lead you down the hill, through the valley, and over to the global maximum mountain.

Oh no, what should I do then?

Test big changes! Maybe not every test, but as often as possible. Run variations that are as different from each other as you can. If your variations are all over the map, your chances of landing somewhere on the global maximum mountain are much greater.

It’s not all hi-fives and bonus checks, though. If your variations are all over the map, some will fall in the valleys. Or splash into the ocean and sink:

Annotated 2-d graph of local and global maxima

Steel yourself for the harrowing experience of watching these variations fail. Remind yourself (and your team) that these low-performing variations are evidence that you’re testing big enough changes to find huge improvements.

Be strong! Happy optimizing.

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© 2022 Brian David Hall