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.  

IGDA Game Design SIG at GDC2014

If you're at GDC2014 today, please join us for the IGDA Game Design SIG Roundtable in the North Hall, Room 114, fom 2:30 - 3:30 PM.  Anyone with a GDC pass can participate in the Roundtable.  The IGDA sessions are open to people with just Expo passes.

Join students, professionals, academics, and other interested people in discussing the craft of game design and how the IGDA Game Design SIG can move forward in the future.

Game Design: Creating a System Formula (Part I)

In Part I of this article, game designer Bud Leiser explains how to use the Fibonacci series in system design.

In my last article, You are a Game Designer, 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 Game 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. Every time you kill 10 of a similar 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

[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. 

March 2014: System Design

March 2014's topic is System Design.

How does a game designer create systems?  What are the nuts and bolts of balancing such a system?

Ian Schreiber alluded to the challenges of creating balanced systems in his articles on Pacing and Bud Leiser mentioned in his article, You Are A Game Designer, that the "mysterious" job of game design may include wrangling with Excel spreadsheets.  For would-be designers, system design may be one of those big mysteries. 

I welcome articles on the topic.  As always, submission guidelines along with submission procedure can be found on the right hand side of the blog.  Topic suggestions and articles are appreciated! 

Some questions:

• What is good (or bad) system design?
• How can formal theories guide system design?

Feel free to add more questions in the comments.