Hi,
I've been working on a web-page that shows some rather amazing findings
about how 'Diminishing Returns' works/fails within the game programming
context.

http://home.comcast.net/~anglewyrm/diminishing_returns.htm

What do you think?

AngleWyrm wrote:
http://home.comcast.net/~anglewyrm/diminishing_returns.htm

We have no idea what you're talking about, and neither do you.
Nice graphics, though. Try peddling that in some management forum.

"John Nagle" <na... at (no spam) animats.com> wrote in message

news:484ccf75$0$17153$742ec2ed at (no spam) news.sonic.net...

AngleWyrm wrote:
http://home.comcast.net/~anglewyrm/diminishing_returns.htm

    We have no idea what you're talking about, and neither do you.
Nice graphics, though.  Try peddling that in some management forum.

The greatest discoveries of mankind are not heralded by "Eurika, I've found
it!", but are instead heralded by "Hmm...That's odd."

Well you've certainly got the odd part down. Unfortunately,
99.9999% of the "Hmm...That's odd." herald little more than
muddy thinking.

Oh, I agree whole-heartedly!
Black holes for instance: If we were just to compress the mass of a planet
into the space of a pinhead, then...
Or gravity wells for instance: If the entire mass of a planet were to
suddenly vanish from the universe, or be suddenly altered in direction,
then...

AngleWyrm wrote:

The greatest discoveries of mankind are not heralded by "Eurika, I've
found
it!", but are instead heralded by "Hmm...That's odd."

In article <CYqdnbyEZ8ypPc3VnZ2dnUVZ_j6dnZ2d at (no spam) comcast.com>,

Here's the problem: you seem to think you've made some profound
insight. The rest of us are saying "if you get in the same timezone as
a point, make it." To me, your posts need a lot more thought before
they'll have any useful content.

"Nathan Mates" <nathan at (no spam) visi.com> wrote in message
news:fsSdnTAJaMKcNc3VnZ2dnUVZ_vSdnZ2d at (no spam) posted.visi...
In article <CYqdnbyEZ8ypPc3VnZ2dnUVZ_j6dnZ2d at (no spam) comcast.com>,

Here's the problem: you seem to think you've made some profound
insight. The rest of us are saying "if you get in the same timezone as
a point, make it." To me, your posts need a lot more thought before
they'll have any useful content.

This study shows the effect of using more stats. We can see how quickly the
product drops away from max, as the number of stats increases. If the stat
average takes even a tiny step to the left, the product plummets.
Also, as the number of stats increases, the product hangs around the bottom
until the very end. The situation devolves into a set of boolean
maxed/not-maxed prerequisites, making the individual stat ranges rather
pointless.

So if many variables are desired, then it's probably best to just model them
as a set of boolean prerequisites. This eliminates the false sense of a
range of values, for both the designer and the player.

I would describe the previous paragraph as containing both a point, and
useful content, the two metrics you proposed. However, since you didn't pick
up on it the first time through, I must ask you: (1) Why not? and (2)
Anything you can think of that would have gotten you to see it better the
first time?

Your "study" makes the assumption that the product of all stats is somehow
meaningful in terms of game balance, and that all stats are equally
important, and that maxing everything is the only valid "best". That's one
amazingly huge set of assumptions.

Support that claim, and it -may- be worth paying attention to...until that
is done, it's just random noise.

"Russ Whiteman" <russ... at (no spam) swbell.net> wrote in message

news:5Kp4k.3058$cW3.841 at (no spam) nlpi064.nbdc.sbc.com...

Your "study" makes the assumption that the product of all stats is somehow
meaningful in terms of game balance, and that all stats are equally
important, and that maxing everything is the only valid "best". That's one
amazingly huge set of assumptions.
Support that claim, and it -may- be worth paying attention to...until that
is done, it's just random noise.

1). "The product of all stats"
This is somewhat of an exageration. All products of stats is more to the
point. As in any time multiplication is used. And products are quite often
meaningful.

2). "That all stats are equally important"
This is the primary reason for using a range that goes from 0 to 1. It can
be easily scaled to any desired range, and may be scaled differently for
each variable. The result is still the same: All that has happened is that
the box is stretched/squished along one or more dimensions. The shape and
proportions remain intact, relative to the newly distorted box. I should
probably illustrate this point, because it's not obvious.

3)."That maxing everything out is the only 'best'"
Unfortunately, maxing everything out is often over-used. For instance, tech
trees are almost universally a 'bigger is better' affair. IMO that isn't
necessarily true, and it would be great to have some better models.
Character skill trees are another example where the 'bigger is better'
philosophy is again out of it's element. It forces a character down a path
without the possibility of 'forgetting' a skill, in order to re-use the
skill point elsewhere. So I agree that maxing everything out is not the best
solution to even some common situations.

On Jun 14, 5:03 am, "AngleWyrm" <anglew... at (no spam) yahoo.com> wrote:
"Geoffrey Summerhayes" <sumr... at (no spam) gmail.com> wrote in message
news:0dd22911-c0fa-4762-a012-bf1f85d5941f at (no spam) z72g2000hsb.googlegroups.com...
Ok, here's an example of a damage model that uses a lot of stats
average damage=
(max 0,
((max((minimum chance to hit),
min((maximum chance to hit),
(base % to hit for class and level)+
(agility bonus)+
(equipment hit bonus))))*
((average weapon damage)+
(strength bonus)+
(equipment damage bonus)+
((critical %)*
(average critical damage)))*
(100% -
(shield block %)+
(enemy agility bonus)+
(enemy equipment block bonus)))-
((enemy armour absorption)+
(enemy constitution bonus)))

The problem is that the full range is obfiscated. It is no longer clear
what
the maximum 'average damage' is, even though of course there is one.

If you want obfuscated, look at look at quantum physics, this is basic
high school algebra, it doesn't even require Newton's method to find
the minimum and maximum. And the curve is no where near the
"scary" seven stats line you posit.

"Geoffrey Summerhayes" <sumrnot at (no spam) gmail.com> wrote in message
news:16b1f2f7-5b28-452d-8175-a7fbb5d46e4d at (no spam) r66g2000hsg.googlegroups.com...
On Jun 14, 5:03 am, "AngleWyrm" <anglew... at (no spam) yahoo.com> wrote:
"Geoffrey Summerhayes" <sumr... at (no spam) gmail.com> wrote in message
news:0dd22911-c0fa-4762-a012-bf1f85d5941f at (no spam) z72g2000hsb.googlegroups.com...
Ok, here's an example of a damage model that uses a lot of stats
average damage=
(max 0,
((max((minimum chance to hit),
min((maximum chance to hit),
(base % to hit for class and level)+
(agility bonus)+
(equipment hit bonus))))*
((average weapon damage)+
(strength bonus)+
(equipment damage bonus)+
((critical %)*
(average critical damage)))*
(100% -
(shield block %)+
(enemy agility bonus)+
(enemy equipment block bonus)))-
((enemy armour absorption)+
(enemy constitution bonus)))

The problem is that the full range is obfiscated. It is no longer clear
what
the maximum 'average damage' is, even though of course there is one.

If you want obfuscated, look at look at quantum physics, this is basic
high school algebra, it doesn't even require Newton's method to find
the minimum and maximum. And the curve is no where near the
"scary" seven stats line you posit.

Really? Ok, what's the maximum value of the above "average damage"?

(max 0,
((max((minimum chance to hit),
min((maximum chance to hit),
(base % to hit for class and level)+
(agility bonus)+
(equipment hit bonus))))*
((average weapon damage)+
(strength bonus)+
(equipment damage bonus)+
((critical %)*
(average critical damage)))*
(100% -
(shield block %)+
(enemy agility bonus)+
(enemy equipment block bonus)))-
((enemy armour absorption)+
(enemy constitution bonus)))

((max((minimum chance to hit),
min((maximum chance to hit)*
((average weapon damage)+
(strength bonus)+
(equipment damage bonus)+
((critical %)*
(average critical damage)))*
(100%

(maximum chance to hit)*

((average weapon damage)+
(strength bonus)+
(equipment damage bonus)+

((critical %)*
(average critical damage)))

"Geoffrey Summerhayes" <sumrnot at (no spam) gmail.com> wrote in message
news:0dd22911-c0fa-4762-a012-bf1f85d5941f at (no spam) z72g2000hsb.googlegroups.com...
Ok, here's an example of a damage model that uses a lot of stats
average damage=
(max 0,
((max((minimum chance to hit),
min((maximum chance to hit),
(base % to hit for class and level)+
(agility bonus)+
(equipment hit bonus))))*
((average weapon damage)+
(strength bonus)+
(equipment damage bonus)+
((critical %)*
(average critical damage)))*
(100% -
(shield block %)+
(enemy agility bonus)+
(enemy equipment block bonus)))-
((enemy armour absorption)+
(enemy constitution bonus)))

This example displays a firm grasp of what these values are generally used
for. I just want to make it clear that I'm not implying anything less. But
the general use pattern -- not the designer -- has a problem.

The problem is that the full range is obfiscated. It is no longer clear what
the maximum 'average damage' is, even though of course there is one.

Isn't that a little bit like the real world?

A lovely demonstration, which should be sufficient proof that:
[...]
is the same thing as
This * That * Another * YetAnother

In article <862dnVC3MJN6BcjVnZ2dnUVZ_oLinZ2d at (no spam) comcast.com>,
AngleWyrm <anglewyrm_nospamthanks at (no spam) yahoo.com> wrote:

is the same thing as
This * That * Another * YetAnother

Once again, you seem to be convinced that you're making a
point. Yet, I fail to share your enthusiasm that you've communicated
anything.