Osmosis in Graphs: Validator Parity

There is definitely a non-normal spread of voting power among validators. That's not necessarily a bad thing. This is not a critique of anyone's staking selection or of any validators in general!

Currently, there's no incentive to stake with a smaller validator aside from your own desire to decentralize voting power and support individual validators' efforts. Larger validators have pre-established reputations and are trusted for that reason.

Validator power

I was inspired by a lot of the recent Prop 120 discussions, a recent post by u/Gohodoshii, plus the spreadsheet u/JohnnyWyles maintains.

To assist in these discussions, I decided to bring out the relevant stats and graphs to demonstrate the lack of symmetry in voting power. In statistics, a lot of things are compared to the Normal Distribution (a.k.a. the bell curve). There are two metrics that indicate how far off a set of numbers — in this case the voting power of validators — is from the Normal Distribution.

Skew

The first of these metrics is skew. Skew tells us how symmetrical a set of numbers is. The more skewed the numbers, the higher or lower the skew, depending on which way it's skewed. Typically, any skew greater than 1 or less than −1 is considered “highly skewed” (though some people permit skews up to ±3, we don't need to sweat that too much here). Here is the skew of the Osmosis validator set:

Note that for the most part, we sit around 4. That's highly skewed. This indicates that the mean (average) voting power for a validator is much higher than the median. You can see that here:

What's the difference between the mean and median? Think of the mean as a completely even split of the votes/staked OSMO. If we gave all the validators the same number of OSMO from the currently staked amount, they'd all have ~682k OSMO staked to them. But the median tells us that half the validators actually have less than ~184k OSMO, roughly a quarter of that mean.

That large difference is demonstrated by our skew!

Kurtosis

While skew looks at the middle of our set of numbers — the median and mean — kurtosis looks at the extremes, also known as the tails. In a bell curve, 99% of data points occur within 3 standard deviations of the median/mean. The normal distribution has a kurtosis of 3, so anything higher than that indicates we have more voting power in the edges of our dataset (i.e. very small or very large validators) than a bell curve would. With that said, let's take a look at Osmosis today:

In statistics, we sometimes refer to those edge numbers as the tails of a distribution — and in this case, we'd call these some pretty fat tails. There's definitely been a thinning out of the edges over time though, so perhaps that will continue to be the case as we go through 2022.