Why Your Rating Swings More Than You Think

In February 2022, I hit a new peak blitz rating of 2474. I had been grinding online blitz hard for several years, gradually improving from the 2100s, and finally I was ready to sniff the rare air of 2500. But just a little later, I had fallen out of the 2400s. No big deal; I'd be back soon. Except, I continued falling, all the way through the 2300s, and then more. At the end of a one-month, 253-point downswing, I was only a couple of losses away from being in the 2100s again.

I recall, embarrassingly, considering getting bloodwork or a brain MRI to check if something was wrong with me. 2200 and 2500 are substantially different strengths. How had I become such a worse player in just a month?

It was because both ratings were, in a sense, wrong. My true strength throughout that month had always been around 2350. If you play lots of games, your rating will fluctuate. 125 points, in either direction. This happens to be about the exact threshold of "this is pretty unusual, but it'll happen every few thousand games." To understand that, we should discuss math.

The Drunkard's Walk

Your rating progression over many games is an example of a Markov chain, a math term for a series of random events that only depend on where you are now, not whatever happened before.

A famous simple example is called "the drunkard's walk." Below we have a stick figure standing outside his house (he lives at address 0 of a number line). He takes a series of steps, each one chosen at random. With probability 50%, he takes a step to the left; otherwise he takes a step to the right. After 1,000 steps, he gets tired and goes to sleep. How far away from home will he be when he wakes up?

Naturally, most of the time he will end up close to where he started. But on around 10% of nights, he ends up more than 50 steps away from home. Approximately 1% of the time, he ends up more than 100 steps away.

This example is simple enough to calculate with pure math, but the rating system is a little more complex than a coin flip. For that, it helps to use the Monte Carlo method.

The Monte Carlo Method

A good technical way to understand how random things work is similar to how I gained my intuition for rating changes—just roll the dice a lot and see what happens. I wrote a simple simulation that assumes my true strength is 2350, and that I play a series of 10,000 games, as I did over three years starting in January 2021. I assumed I play an equally-rated player each game, and I modeled draws with a fixed percentage drawn from my own games. I ran 10,000 trials of these 10,000 games. My actual results were extremely close to the ones from the simulation. Both my 2474 and 2221 ratings were approximately a 1 in 1,000-game fluke.

If It's All Random, Who Cares?

So far, I have argued that if you play a lot of games, your rating will swing around wildly, and that there is actually nothing you can do about this, and that even if your rating goes up or down 100 points, that might just be total dumb luck.

How do we make sense of anything, then?

We can take a wider view. The first graph below is my actual five-year blitz rating chart. It is so noisy you can barely make sense of it, although it does illustrate how incredibly common a 100-point rating swing is.

The next graph smooths out that mess by graphing my average rating over the previous 1,000 games. Now we see something nice. Across this 5-year period, despite the seismographic noise of rating swings, I was gradually getting better at blitz! My 1,000-game average climbed from 2187 to just shy of 2400 during this period.

Relax A Little

It took me years and thousands of games, but experience and a little math eventually helped me relax about my rating. 

These days, now mostly on my anonymous titled account, I still play a lot of blitz. Losing a lot of games in a row can still be upsetting (I think it should be; I take chess seriously), but I no longer consider dropping 200 points a potential medical emergency.

I've found it freeing to accept a kind of paradox—that my rating at one particular moment in time has limited meaning, even though ratings in general, especially over many games, still mean a lot. With a little change in attitude, I've found I have more energy for actual chess stuff, and that my blitz habit has become more fun and less stressful.

So, the next time you suddenly drop 100 or even 250 rating points, remember that there is a lot more randomness governing chess results than you might think. We are all bouncing around on waves of variance out there. Take a deep breath and enjoy the ride.