There were no matches yesterday or today so I wanted to take this moment to start a new mini-series: **VBelo Explained**.

I haven't properly compiled an explainer on VBelo since the very early days.1 Since there are plenty of new readers and the model has changed a little bit over the years, it feels like a good time to explain how the model works. The hope is to have about 4 parts to this mini-series.2 If everything works out right (and I make time to write), the series will culminate in the release of the latest VBelo rankings.

So let's get to it!

## What even is Elo?

The core of the VBelo model is the Elo rating system. The initial idea, from Hungarian-American physics professor Arpad Elo, was to find the skill level of chess players. If you have an idea of how good a player is at chess, you can better test your skills and know when you are getting better or worse.

Chess was a fantastic starting place for this system. For starters, the outcomes are clear: win, lose, draw. You don’t have to worry about margin of victory. Since most chess is single-player, it is easy to track the results of each individual.

At its very simplest, when a player wins, their Elo rating goes up. When they lose, it goes down.

The amount it goes up or down depends on the opponent. If a player beats someone with a higher Elo rating (i.e. a good opponent), their score goes up more than if they beat someone below their Elo rating.

#### An Example

This is very abstract, so let's put it in volleyball terms. Here are the final conference standings of the MIVA in 1990.

If Ohio State (2-4) beats Ball State (5-1), they would get rewarded for beating a strong team. If Ohio State beats Graceland (0-6), they would be rewarded less.

The reverse is also true. If Ohio State loses to Ball State, that is more of an expected outcome, so they don't lose a lot of points. Additionally, if Ohio State beats Graceland, they don't receive a lot of points because you would expect them to win.

Good teams tend to win, which reinforces the fact that they are good teams.

## What about the math part?

Don't worry. I won't go too deep here. *If you don’t want any math, just skip to the next section.*

If you want a more in-depth explainer, the internet is full of them. There are two main math parts to elo: projecting the outcome and updating ratings after matches.

The fun part about Elo ratings is that they help give projections for future matches. The farther two Elo ratings are away from each other, the greater the likelihood that the favorite will win. If we look purely at the conference records above, you might expect Ball State and IPFW to have similar Elo ratings and thus the match might be close.

You take these ratings and plug them into this formula, and you get projected outcomes. This is what the daily projections are based on in every VBelo newsletter.

The secretly powerful coefficient hidden in the math is called K. The K-factor determines how much each outcome could potentially change ratings. The K is kind of like the money being bet in poker. The higher the K, the more points wagered with each match. After each match, both team’s ratings are adjusted according to the actual outcome, the expected outcome, and the K value.

Getting this number dialed down is pretty important. This year (2024), I adjusted the K value fairly significantly due to a reader's suggestion.3 In chess, where Elo is still used, the K value changes depending on the Elo rating of the teams. This might be a future enhancement to the model, but right now everyone has the same K-factor.

## What’s Next?

This is interesting, but volleyball isn't chess. Sure, there are wins and losses. Thankfully, there are no draws! But not all wins are the same. You also have sets and points and countless other factors that go into a match.

In the next part of this series, I will look at what modifications VBelo makes specifically for volleyball.

Where I thought GitHub was the best place to explain this.

We will see where we end up, but I will update all of the posts in the series to have the links to every part.

Thanks, Eric! If anyone has great suggestions, please let me know.

Interesting! I'm diving deeper in hopes of understanding more...

Thanks for the explanation of the terms. I'm sure this will be an annual event