Game Design: Creating a System Formula (Part II)

In Part I, game designer Bud Leiser explains how to use the Fibonacci series in system design. In Part II, he shows the grind gap and how the amount of grind can quickly accelerate when using the Fibonacci series.

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
0
-3
-4
-7
-10
-13
-17
-22
-28
-34
-42
-51
-61
-73
-88

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.

[This article originally appeared on Bud Leiser's personal blog.]  

Bud Leiser beat Nintendo’s original Zelda when he was just 3 years old. Then went on to win money and prizes playing: D&D Miniatures, Dreamblade, Magic the Gathering and The Spoils. He’s just returned from Vietnam where he helped manage Wulven Studios as their Lead Game Designer. He was responsible for creating internal projects, game design documents and communicating with clients to help them succeed in the post-freemium app market.