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Home Game Design Game Design: Creating A System Formula – 101

Game Design: Creating A System Formula – 101

Published on 2013-08-22, by in Game Design.

In my last article “You are a Game Designer – So what do you do” I dropped a piece of information saying people should learn about the Fibonacci series, but I didn’t reveal it or why it mattered. The idea of course is that people who didn’t know it already would go look it up on their own, that is, if they were serious about game design.

So for those not familiar with it the series is basically:

0 1 1 2 3 5 8 13 21 and so on.

Or more importantly (to us) the next integer is the sum of the previous 2 integers.

But why is this important to game designers? Because it’s such a useful and simple way to create a progressive cost system.

Let’s Create A Design System Together

For example let’s say you wanted to make an RPG and what you really want is a cost curve so the player can’t buy his weapons too quickly. You could price each weapon individually, one a time, and finish your game sometime never. Or you could create a formula that prices each weapon for you. Fibonacci is great because it scales up very quickly, creating nice beautiful gaps between costs. So let’s not start with 1 1 2, because…well that’s silly and unnecessary. So let’s start with 50 and 100.

Sword A 50
Sword B 100
Sword C 150
Sword D 250
Sword E 400
Sword F 650
Sword G 1050
Sword H 1700
Sword I 2750
Sword J 4450
Sword K 7200
Sword L 11650
Sword M 18850
Sword N 30500
Sword O 49350
Sword P 79850

By the way this formula is really simple to setup in Excel =sum(C1+C2) then extend downwards will automatically populate C2+C3, C3+C4 and so on.

Notice how quickly the price begins to ramp up? This is really cool because were talking about 1 type of weapon, the sword. So we probably don’t want 2 swords to be of similar cost, we want them to have large power gaps and therefore we want large price gaps. What this doesn’t tell us at all is how quickly the player will buy them. For that we can create a new formula based on fighting monsters at his weapon level. So for example say the player Starts with no sword and kills 10 monsters before he can buy Sword A. Now he has Sword A and can kill Monster A for 10 gold a piece. This means we have a flat progression system. Everytime you kill 10 of a similiar level monster you should be able to afford the next sword, which leads to the next monster which leads to a new monster that rewards you with 0.10 cost of the next sword.

Whew a lot of words to explain something so lame and boring right? So let’s say we don’t want that flat progression, what we really want is for the player to grind a little more each time. So what happens if we try Fibonacci code *0.8, this means that as each reward value grows it also decreases by a substantial amount. Let’s see what that looks like shall we?

Monster Reward A Reward B
A 5 5
B 10 8
C 15 10
D 25 15
E 40 20
F 65 28
G 105 38
H 170 53
I 275 73
J 445 101
K 720 139
L 1165 192
M 1885 265
N 3050 365
O 4935 504

So what I’ve done now is shown you the flat progression on the left, so you compare it to the 20% degrade on the right. It makes a huge difference right? But now we need to compare it to sword costs to know what kind of effect it will have on our player grind.

Monster Reward A *10 Reward B *10 Difference  Grind Gap
A 5 50 5 50 0
B 10 100 8 80 -20 -2.5
C 15 150 10 104 -46 -4.42308
D 25 250 15 147.2 -102.8 -6.9837
E 40 400 20 200.96 -199.04 -9.90446
F 65 650 28 278.528 -371.472 -13.337
G 105 1050 38 383.5904 -666.41 -17.3729
H 170 1700 53 529.6947 -1170.31 -22.094
I 275 2750 73 730.6281 -2019.37 -27.6388
J 445 4450 101 1008.258 -3441.74 -34.1355
K 720 7200 139 1391.109 -5808.89 -41.7573
L 1165 11650 192 1919.494 -9730.51 -50.6931
M 1885 18850 265 2648.482 -16201.5 -61.1728
N 3050 30500 365 3654.381 -26845.6 -73.4615
O 4935 49350 504 5042.291 -44307.7 -87.8722

Ok so let me explain how I did this so it’s not too confusing for some of our readers. On the left we had our flat progression if you remember, so I took that and mulitplied it by 10 to get our weapon cost. In column 5 I did the same thing to our degraded reward system to see how much they would make after killing 10 monsters. Then I found the difference between those numbers to determine the monetary gap. We can see that the player is definitely falling behind monetarily each step and will have to grind more and more for each new level of sword. And finally in the last column I take the amount of money they make from killing monsters to determine how many more monsters they will need to kill at each step to earn the next weapon (in addition to the first 10).

So let’s zoom in on that.

Grind Gap

Here we can see at that level 1, no problem kill 10 monsters get a new sword. YAY! Feels pretty fast for the player, which is good they just started a game we don’t want them to get bored so let’s give them some quick rewards. Now how about level 2? Oh just 3 more monsters that’s not bad right? Then just +4 more, then +7, then +10.

Now let’s pause there for a moment; because I feel it’s important. Remember we started with 10 kills for Sword A. Then we added +3 (13), then +4 (17), then +7 (24). So by the 4th step we now have to kill 24 monsters to get our next sword this is the point where our beginning rate doubles (or another way to think about this is progression rate is 50% of our starting rate). The next step however adds +10 (37) so in a single level we again add 100% compared to our first step! WOW! This is a really really important thing to understand.

Let’s make sure every reader full grasps this curve that we created. In the beginning we leveled our sword up very quickly, just 10 kills. Then it took us 4 steps to double that progression rate. But then in the 5th step it doubles (the base not the current) instantly! This means that each step after this is going to add a huge amount of grind (compared to our first level).

So our progression curve still feels pretty good at this point, it should feel fine and will probably feel fine for a few more levels…. but it could get out of hand quickly. Let’s see what happens next

  • +13
  • +17
  • +22

This however is an important step, this last step now adds 200% more grind time, compared to our very 1st level. And then it gets steep as hell. Ok so clear up some assumptions that we didn’t discuss earlier. We didn’t talk about it but we assume: Monsters get harder at each new level, thus requiring the bigger swords to kill safely. We assumed that we were killing 1 monster per combat and that each combat took the same amount of time. (This is inherently assumed in our simplified progression rate because we just said “monsters” killed. What it could really mean is “units of monsters” if the game pits you against 3-4 weak monsters in 1 combat. If you don’t understand what I just explained in this () then just ignore it, it’s complicated stuff and not really necessary unless you are already a designer and thought I was doing something wrong.)

  • 28 (almost 300%)
  • 34
  • 42
  • 51

Now I haven’t even assigned a time value to any of this yet, but already I can tell just by looking at this formula that the player is going to have a very good early curve up until about level weapon 8. After that however getting weapons is going to be very time consuming.

So what do you do now? Well, you need to make some important design decisions. Is this the right time for a player level to plateau? If you built your game for players to explore most of the world, and get their abilities, and really enjoy the game at levels 7-12 this is probably a great curve. Because the player can reach levels 5+ relatively quickly and then the game will begin to slow down and by the time he reaches level 8 the progression really slows down giving him plenty of time to  enjoy the upper levels.


If however you want players to “power through” the first 20 levels; than either this curve is way too harsh or you will need to throw in lots of additional help. Such as quests that give big rewards, or lots of item drops.


You could use this curve for the first 8 levels. And then create a completely new curve.

And the reality is all of these solutions *can* work. You just have to decide what your goals are. How do you want the game to feel? How soon do you want to give players a sense of power over the world?  Where (in time and power level) do you want the player to really slow down? Where will players have the world really open up to them and let them explore.

Now remember, we did this with just a Sword cost.

(Which really could stand for EXP levels, or rifles or anything super useful to the player)

We didn’t even cover things like ranged weapons, axes, armor, boots, capes, helmets, potions and special items. So it’s completely broken right? Sorta….but not really.

Actually…I could see implementing this curve into a real RPG if: for the player to survive we would probably have to give lots of item drops and a low cost way of healing outside of combat. (Final Fantasy health potions anyone?).  We can also try to figure out what strategy the player will use to overcome this curve: What might happen is playersgrind longer at a given level to buy his armor and boots.

They might even skip weapon levels, instead of buying each one progressively they might save up money to buy 2 levels ahead, and then use that powerful sword in combat, if he has enough health to survive 1 combat he could use cheap healing outside of combat. In other words relying on that high level sword to get him through 1 combat and not worrying about keep up with armor until absolutely necessary. If we wanted to encourage this type of play we could set the monster damage levels at rates unlikely to kill a player in a single combat. Drop potions frequently and even give the player armor pieces as common rewards. Assuming he has free time out of combat to heal up to full without being attacked this would be a completely valid RPG style.


You could create these cost progressions using “suits” (Armor, gauntlet, belt, boots, helmet, weapon). Then assign % of that to each piece. For example:

Suits Total Cost Weapons Sword Cost Armor Armor Cost Helmet Helmet Cost
A 50 20% 10 25% 13 10% 5
B 100 20% 20 25% 25 10% 10
C 150 20% 30 25% 38 10% 15
D 250 20% 50 25% 63 10% 25
E 400 20% 80 25% 100 10% 40
F 650 20% 130 25% 163 10% 65
G 1050 20% 210 25% 263 10% 105
H 1700 20% 340 25% 425 10% 170
I 2750 20% 550 25% 688 10% 275
J 4450 20% 890 25% 1113 10% 445
K 7200 20% 1440 25% 1800 10% 720
L 11650 20% 2330 25% 2913 10% 1165
M 18850 20% 3770 25% 4713 10% 1885
N 30500 20% 6100 25% 7625 10% 3050
O 49350 20% 9870 25% 12338 10% 4935
P 79850 20% 15970 25% 19963 10% 7985

With this we have a general idea of how much the player is making and how much things should cost.

The most important thing is we didn’t have to spend hours making these prices individually.

We have at the very least a general guideline. And we once we have a guideline that works, that we understand, and that curves the way we want to (meaning the player progresses at a rate that we want them to, and slow down where we want them to). We can now add elements wherever we want. And feel free to Fudge the numbers, give the player a cool Fire Sword and increase the value 10%, or 5% or 500gp.

For the advanced designers out there:

  • What kind of curves and systems are the most addicting (drive long play sessions and retention)?
  • How could you drive retention at the cost of monetization?
  • How could you drive monetization at the cost of retention?
  • Which do you create first: The in game currency or the hard cash currency?


Bud Leiser

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