Maybe a dumb question but... in the age of Steam, what does the publisher do these days? Advance funding? What do those numbers look like?

Most of the marketing will come from the publisher. It's easy for a game not to be noticed, and to crater thanks to no audience. The publisher runs the early and mid ad campaigns.

Depends on the deal. Promotion and fronting of cash are the big ones (usually). They can usually also offer various development services (testing, translation, porting, getting special deals with platform holders). They can also act as a stakeholder for quality, advising on certain things that should be improved (as an editor would in book publishing).

Really depends on the deal, but porting, marketing, localization and cash advances are common ones (Porting for the switch for example is known to be a big one, even for experienced solo/indie devs)

You're right, but unfortunately you forgot that:

1 - Before Steam take it's cut there are taxes and refunds, 15-20% depend on geography of sales.

2 - Publisher need to recouperate spendings agreed in contract, but yeah then it's likely between 40 and 60%.

For 1., I had the taxes afterwards and since every factor is just multiplied, it doesn’t matter for the end result. And do refunds count into the final sales number?

For 2., I linked the page where you can find the document where the publisher claims to take 50%, if I didn’t miss something while skimming it.

Unfortunately when selling games on Steam you pay taxes twice. First of all Steam pay VAT all around the world. It's not included in their 30% cut. And then you pay corporate tax from your net profit after Steam or publisher sent royalties your way.

Refunds on Steam can happen after a while so it's important to keep them in mind. If you sold 100 copies of your game 5-10% will be refunded.

> I linked the page where you can find the document where the publisher claims to take 50%.

I havent worked with Raw Fury and wouldn't be able to talk about it then anyway, but:

1 - If a publisher funded your game they will recuperate expenses by taking 70-100% of net profit. After that it can be 50%

2 - Some publishers also include localization, QA, LQA and even marketing budget into recoup amount.

Who is the publisher? Isn’t it steam or the author itself?

If you look on the Steam page it's Raw Fury.

Steam is just the storefront. A game publisher's role varies a lot - sometimes they're just financing the project, usually they handle stuff like PR and marketing, and sometimes they help quite a bit more with the development of the game (sounds like the case in this case based on his other answers) as in programming/art/sfx/whatever else.