Can you tell if one board is balanced or not compared to the others?

Question

I've been playing 7 Wonders for a while now and I really enjoy it. I've played the standard game and with Leaders, Cities and Wonder Pack extensions.

I'm amazed that the wonders are pretty balanced. I mean, I do better or worse with one or the other, but that depends on my skill and luck on that game.
So I assume a lot of effort was put into balancing them somehow.

I've also seen a pack that contains a lot of other wonders, for example the fan pack "Lost Wonders". Some of the wonders in this one seam pretty overpowered to me, or others seam weak. I don't have facts to prove this, it's just my opinion which can be biased by my skill level and style of play.

Is there a way to compute (mathematically) the fairness of a wonder? Or should I trust the creator (which may not be the creator of the game)?

I mean is there a way to transform a wonder into a number (or approximate number) or something that can be comparable so it can be compared to the others?

Let me offer an example.
Let's take the standard wonder Halicarnassus side B.
At a first glance being able to look 3 times (once for each stage of wonder) in the discarded pile would look pretty fair to me.
But the author added 3 extra victory points on it (2 for stage 1 and 1 for stage 2).
3 points don't seem to be that much, but I'm thinking there is a reason they were added, to keep the fairness compared to the others because otherwise it would be under-powered.

I'm asking this because I would like to check the fairness of a (non standard) wonder before including it in the game.

[EDIT]

I'm not asking about sides being balanced. But about a way to compare 2 wonders based on a score or a range of scores based on a formula or algorithm, if any.

Answer 1

You probably could produce a mathematical formula taking into account the different factors that obtain you points based on your wonder. It would be long and arduous to figure out, especially considering all the different ways you can approach winning the game.

I think it's important to remember that a key component of Game Design is iteration. The designers will have played the game and redesigned it so many times during development that how the wonders originally looked is totally different to how they are now. Only through actual play can you truely determine how "balanced" a certain part of the game is. Sure you can use maths, but with so many different variables to take into account the level of work involved to get to some formula that calculates power compared to another wonder just doesn't seem worth it.

If you find some wonder out the fan pack is too overpowered, you can always erata it yourself to make it more balanced. I've done this with games before a lot. You create house "rules" or edits that help to improve the gameplay for everyone involved. It's like how in Monopoly you have free parking reward you. It's not an original mechanic, but something other people came up with as a catch up mechanic.