Hi, This is a piece of Procedural Rhetoric; I am implicitly favoring a point of view, which I will make explicit at the end. To begin, let me present the most often stated "diminishing returns", an outwardly visible surface description of a procedure that I wish to improve upon: Diminishing Returns in video games are often modelled with little planning. There is some underlying sense that continued gains in a particular value should somehow be of less merit. This is a strong motive, and the truth of it is reflected throughout the witnessed world. However, in complex systems the desire for diminishing returns becomes a recurring theme. Variables that have this ethos built in are combined, and the result is compounded, often with undesirable results. Those undesirable results could be described as an Emergent Bug. Consider a game with weapons that have a chance of a critical hit for extra damage. The player's ability to increase critical hit % is doled out with great reserve. But so is the amount of extra damage. And the chance to hit. The result of multiplying these factors together is that player effort in this area of the game becomes inconsequential. The whole model of increasing each factor becomes wasted programming, to be ignored by the gamer. To examine where things went wrong, let's look more closely at some natural phenomena that exhibit this pattern of Diminishing Returns:

Pour a tablespoon of water onto the table, and the liquid forms a circle. Add another tablespoon of water, and the circle grows. But add a third tablespoon of water, and we begin to see the circle is not growing by as much as it did before. The diameter is growing more slowly than the area.

Whisper to someone inches away. Talk to someone several feet away. Shout to someone across the noisy street: As the distance grows, the amount of energy needed is much more than it was before.

Pay to flip a coin to win a pot on heads. You can forego the winnings, and pay again to flip again, with an added incentive of double the pot.

In each case, what is happening is that we are adding a dimension to the problem. An x becomes an x^2. The view of "Diminishing Returns" is looking at the x^2 element, and saying that x grows as the square root. Therefore, a good solution to avoiding this type of Emergent Bug is to keep track of the dimensions used in the problem space. Instead of simulating diminishing returns, consider that there is an extra dimension to be expressed. For instance, in the weapons modification example above, the extra dimensions were toHit, extraDamage, and criticalHitChance. They did not need individual artificially induced diminishing returns, because together they express their extra dimensionality. So, to make explicit the point of view, the desire for Diminishing Returns can be profitably construed as the anthopomorphic meme "This variable wants company."

Another example problem and it's solution, using the above metaphor:

A game has monster treasure drops, and some of them are magic. The player can improve the chances of getting magic drops by wearing 'lucky' items. But there's a desire for luck to provide diminishing returns. Therefore 'luck' wants company.

EDIT:
Luck becomes a generic category, with two desirable sub-legs. The player can buy units of the generic Luck category, but must choose the split between the legs. Perhaps one leg is MonsterDrops and the other is EncounterFrequency.

[Edited by - AngleWyrm on May 4, 2008 12:35:49 AM]

Quote:Original post by AngleWyrm
Therefore, a good solution to avoiding this type of Emergent Bug is to keep track of the dimensions used in the problem space. Instead of simulating diminishing returns, consider that there is an extra dimension to be expressed. For instance, in the weapons modification example above, the extra dimensions were toHit, extraDamage, and criticalHitChance. They did not need individual artificially induced diminishing returns, because together they express their extra dimensionality.

So, to make explicit the point of view, the desire for Diminishing Returns can be profitably construed as the anthopomorphic meme "This variable wants company."

Interesting point. This is where statistics - and good testing - should come into play.

Personally I don't think the returns have to be modelled according to a simple function, it could be more complex, such has having quick initial learning, some stagnation and an over-the-average point for example.
I agree this requires alot of context information. Balancing games isn't easy.
I game mod I've recently found is really well balanced - so much I admit I haven't yet understood how to win. According to the author, extensive playtesting and multiple iterations were absolutely necessary to tune it.

Quote:Original post by Kylotan
Adding dimensions doesn't break multiplication. ...
the diameter grows directly proportionally to the area...

Quote:Original post by thre3dee
I've tested the 1/R, 1/R² and 1/Sqrt(R) relationships. Its probably dependant on the type of gameplay and development speed you are looking for in your game but this shows the amount of effort required in gaining 100% return.

Nice graphical study; a consequence of using dimensionality -- of multiplying variables together -- is that the curve will be a parabola on it's side. If we did three dimensions, as in a cube, the growth of a side with respect to the cube's volume would be the cube root of x:



Another way to put it is: Any time two or more variables are multiplied together, there is automatically a natural diminishing returns for the individual variables with respect to the multiplied total.

[Edited by - AngleWyrm on May 1, 2008 8:42:13 AM]

Quote:Original post by Kylotan

Quote:Original post by AngleWyrm
Another way to put it is: Any time two or more variables are multiplied together, there is automatically a natural diminishing returns for the individual variables with respect to the multiplied total.

...There's no problem here that is inherent to the numbers or in multiplying them together, but in how you choose to use them to dictate gameplay.

Give an example of multiplying variables together, and I will show the diminishing returns that is inherent to those numbers.

For instance A tech tree with Research Costs. As players accumulate planets, their ability to manufacture Research Points grows. So high tech items ought to cost a lot more than low tech items...but by how much? This is a Diminishing Returns problem.

[Edited by - AngleWyrm on May 1, 2008 3:43:39 PM]