Does your brain hurt trying to work out the permutations for the ATP Finals?

Roger Federer beat Dominic Thiem on Tuesday to keep alive his hopes of making it through to the semi-finals at the 02 Arena in London.

But whether or not he will qualify is horribly complicated.

You can’t say he is through if he beats Kevin Anderson in his final group match on Thursday, because there are several different scenarios that can happen.

Thiem faces Kei Nishikori in the other Group Lleyton Hewitt match on Thursday and either of those could progress.

Federer could win in straight sets and still not make it through. He could lose in straight sets and qualify. So how does that work?

Before we look at that, here’s how people reacted on social media after the ATP tweeted this graphic:

‘My brain hurts’

Some of you just replied with emojis of confused faces.

But many of you responded with funny gifs including this one from Abel Morton.

And this one from Roger Buchana.

Though most of you just said what we were all thinking…

Optimist: I have a headache!

Marcou: I’m lost!

Adeyanju Michael: This is Maths 🙁

Aditya Jain: Don’t understand anything.

N Kessler: My brain hurts.

So, is there an easy way to understand it?

In short, no.

Here’s our attempt at a ‘simple‘ breakdown of how the top two are decided in each of the two four-player groups:

• Greatest number of wins
• If two players are tied: Head-to-head results
• If three players are tied: 1) Highest percentage of sets won; 2) Highest percentage of games won; 3) Players’ ATP Rankings coming into the tournament

So with that in mind, Federer will go through if any of these situations happen:

1. He wins in two sets and Thiem beats Kei Nishikori in two.
2. He wins in two sets and Thiem wins in three.
3. He wins in two sets and Nishikori beats Thiem in two sets. Highest % of games won will then be the decider.
4. He wins in two sets and Nishikori wins in three.
5. He wins in three sets and Thiem wins in two.
6. He wins in three sets and Thiem wins in three.

This is how the group currently stands:

If you’re still not sure what’s going on, the best thing to do is to follow our guide on the group standings, results and fixtures and just trust us when we say Federer is through or not.