[MUD-Dev] [DGN] The psychology of random numbers

[Travis Casey]

On Monday 05 January 2004 19:42, Ted L. Chen wrote:

> It's been a while since my last post, and it has taken some time
> to catch up on the interesting reading.

Finally getting around to responding to this...

> The old thread about hiding numbers from players has got me
> thinking about the probability-based formulas that rely on said
> numbers.  This musing has generated an interesting dilema:

> How does one convey, to the player, the fact that the output is
> probalistic when most numeric measures appear determinant?

> To illustrate, take your standard RPG combat roll

There ain't no such thing.  The closest thing there is to a
"standard RPG" is D&D and its derivatives... but even there, there
are multiple kinds of combat (ranged vs. melee, for example).

> and answer the following two cases:

>   A) Bubba is fighting Buffy.  He has a STR of 255, she a STR of
>   240.  Who will win?

Well, first off, you're violating my expectations of "standard RPG"
-- D&D and derivatives generally don't have strength scores that
high.

I'd have a lot of questions.  How are they fighting?  Unarmed?  With
swords?  A gunfight at high noon?  How skilled are they at fighting?
What's their agility/dexterity/whatever you want to call it?  What
armor are they wearing?  Etc., etc.

Assuming that say, it's with hand weapons and "all else being
equal", I'd expect Bubba to have a very slight advantage... after
all, his strength is less than 10% higher than Buffy's.

>   B) Bubba is fighting Buffy.  He is very strong.  She is also
>   very strong.  Who will win?

> My supposition is that most people are inclined to say that Bubba
> will win in A (strong expectation), while they remain unsure as to
> the winner in B (weak expectation).  While both win-distributions
> are almost even, the weaker expectation matches reality more
> closely.

> Why the fuss?  When Bubba plays and sees his stats greater than
> Buffy, his expectations of winning are skewed by the concrete
> measuring yardstick.  When he loses to Buffy, his world view is
> shattered and the game becomes bugged, Buffy is cheating, or he
> somehow has nerfed equipment.

> Working on the loose assumption that displaying some sort of
> measure is inevitable, is there some way we can better manage
> player expectations?

>   NB: The discretized vagueness of case B is one obvious way.  I'm
>   just looking for other possibilities here.

You can have vagueness with numbers -- give a range instead of a
single value.  If, for example, you're working with a D&D3-style
system, you might list Bubba's strength as 17-55, and Buffy's as
14-52.  (Giving Bubba a base strength of 15 and Buffy a 12, then
adding the 1d20, x2 since your actual strength *bonus* only goes up
every other point of strength).  This should convey to players that
there's a large amount of overlap in what can be expected from Bubba
and Buffy.

  (And, yes, I know that many players are going to scream bloody
  murder at seeing ranges like that.  There's also many who will
  scream at seeing things like "very strong".)

You might also wish to remind players that multiple factors play a
role.  One way to do this would be to give a "combat factor" which
is calculated from multiple things -- potentially even including
what armor and weapons a character is carrying.  Or you could break
it into "attack factor" and "defense factor".  And, of course, you
could also break it down for different types of combat -- e.g., with
a "ranged attack factor".

Alternatively, you could give actual calculated game statistics.
E.g., in a D&D-esque system, the range of armor classes that a
character can hit, the character's armor class, the character's hit
points, and the character's damage roll.  Going back to my example
above, with all else being equal, this would show players that all
Bubba's 3 extra points of Strength give him over Buffy is a +1 to
hit and a +1 to damage.  You could also combine this with giving
ranges as above.

Scaling things differently may also help.  In the example you gave,
cutting the scale by a factor of 10 gives Bubba a 26 and Buffy a 24.
Will people expect Bubba to have as much of an advantage as they did
with the 255 and 240?

For very high scores, a logarithmic scale can be a help as well.
With a logarithmic scale, the difference in scores depends on the
proportional values... so, for example, if the scale is x2 -> +5, if
A is twice as strong as B, A's strength will be 5 points higher than
B's... no matter what the actual scores are.

To give an example; let's say that A has a strength of 10.  B is
twice as strong as A, C is four times as strong as B, and D is twice
as strong as C.  In a linear scale, their scores would be:

  A:  10
  B:  20
  C:  80
  D: 160

Many people will expect that D will beat C in a direct contest of
strength (say, arm-wrestling) much more easily than B will beat A --
after all, D is 80 points stronger than C, while B is only 10 points
stronger than A.  But when you get down to it, twice as strong is
twice as strong, so D's chance of beating C at arm-wrestling should
be the same as B's chance of beating A (all else being equal).

In contrast, with the x2 -> +5 logarithmic scale, their scores would
be:

  A:  10
  B:  15
  C:  25
  D:  30

That may make it easier for some people to see that D's advantage
over C isn't greater than B's over A.

(And, of course, if you combine this with giving a range, it becomes
much more apparent.  Let's say the game's standard roll is 1d10 +
attribute -- then we have:

  A:  11-20
  B:  16-25
  C:  26-35
  D:  31-40

... which instantly gets across that A and B can never beat C or D
without something to help them, but that A/B and C/D both have
overlapping ranges, so either could beat the other!)

--
       |\      _,,,---,,_     Travis S. Casey  <efindel at earthlink.net>
 ZZzz  /,`.-'`'    -.  ;-;;,_   No one agrees with me.  Not even me.
      |,4-  ) )-,_..;\ (  `'-'
     '---''(_/--'  `-'\_)
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