# Scaling Enemy Difficulty per wave

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### » Tue Oct 15, 2013 8:04 pm

Is there a good formula for scaling enemies to make them more difficult per wave? Like enemies start out with 40 health, bullets do 10 damange each round add X to health, and each bullet upgrade add X to damage?   We're trying to figure out a good formula so we can make 50 + rounds of enemy wave in our game.
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### » Tue Oct 15, 2013 9:02 pm

Finetuning is reliant on playtesting. But I can give you some hints:
Depending on how long you want the TD to go, you need to use multi-order polynomials. 50+ rounds will need at least 3 I think, but 4 could be better. If you want it to go even longer, expand to 5.
So your basic formula could look like this:
HP(for wave x)= ax^4+bx^3+cx^2+dx+e

Now you need to calculate the gold that is available up to that level and you can calculate the difficulty:
difficulty = HP / (gold available until this point)

Make sure it gets harder with each wave, at first maybe a slight rise and later when you want the game to become really hard, you wanna have a bigger rise in difficulty per level.

This ofc means you need to balance out the gold income to your HP formula. And your towers need to be balanced around the money (or other ressources) they cost. Things you need to factor in when balancing towers are things like range (not linearly ofc), fire rate, damage, how much worth their special abilities are (like splash, slow, ...).

Hope that helps and happy playtesting.
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### » Tue Oct 15, 2013 10:28 pm

thanks! hmmm never worked with polynomials before, ill have to read into that. Are there any tutorials on how to use them?
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### » Wed Oct 16, 2013 7:38 am

"Game Economics" is a field all in itself and is part of the character of your game. Remember there is no right or wrong way, it is part of the game and if done well becomes the carrot that leads the player through the game. The economics, help them believe if they play just one more round they will be able to get that bigger gun.

You can do the health and gun strength linearly, add 20 to health each time, but increase number of enemies exponentially (using a polynomial as above). The choice is yours, provided it balances.

Ramp up difficulty to quickly and the player is overwhelmed. To slowly it becomes to easy. If they have to do some gold mining to get through the next level, it becomes a bit boring. To complicated and people will ignore parts of it.

A game with great graphics and sound, but bad economics is often still a bad game.

After the initial planning there is no substitute for play testing. Have fun.
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### » Wed Oct 16, 2013 10:57 am

@bscarl88:
Try to fit a polynomial manually to your need with difficulty in mind. A spreadsheet program like Excel is useful for that. Example: s000.tinyupload.com / ?file_id=08472573822564563391
More scientific approach: read into fitting polynomials (with Excel for example). Create a hp data point for some waves, then fit a polynomial to it.
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### » Wed Oct 16, 2013 11:42 pm

I guess a starting point would be to find out how many enemies will be in the game total, then decide how much XP to give the payer, and go from there. I'll do some reading into polynomials and stuff. Thanks guys!
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