You're right, I hadn't noticed it in the 3e description. Now my 7 foot tall full plate wearing Dex 11 Cleric can hide!!
But seriously, I still think -1 for every 10 feet is a bit harsh. Spotting someone at least a charge distance away becomes pretty hard, considering that you can only hide with half cover or better, and with 3/4ths vovre or bettre you're getting circumstance benefits as well.
frank, a 1st level fast hero (16 dex) will have the following hide modifier:
Hide (1/2) = +7
Hide (3/4) = +5+7=+12
Hide (9/10) = +10+7=+17
Dan, a 1st level Dedicated (16 wis) will have the following spot modifier:
Spot =+7
What follows is a very long analysis of the math and statistics involved in the opposed check rolls. If math isn't your shtick, you might consider not reading this
The mechanism of opposed checks is quite interesting. An opposed check basically follows the following rule:
d20_A+CM_A>=d20_B+CM_B
were d20_X is the roll fo character X, while CM_X is character X's relevant check modifier. The check modifier's are fixed values, so we are interested in finding the probability for when character A beats character B. In this case, characeter A is the agressor, and in case of a tie he will win the opposed check (this is what I use in my games).
Using probability ditributions we have that a d20 has a discrete uniform distribution from (1,20). But we need the distribution of the random variable OCD (opposed check difference) defined as:
OCD=d20_A - d20_B
A little work with probabilities (that I'm not going to show here
) shows that OCD has a triangular distribution that varies from -19 up to +19, with a peak at 0.
This means that the probabilities of OCD turning up as 0 are 5%, while the probabilities of rolling +19 or -19 are 0.25% (that's 1/400). This means that the probabilty density function for OCD is:
p(OCD) = 5 - 0.25*abs(OCD) (values in %)
abs(OCD) is the absolute value of OCD
But we're not interested in finding the probability distribution function, but instead we want the cumulative distribution function. Luckily, we can find one from the other
The probability of OCD < XX can be found simply as:
P(OCD<= N)=sum(p(k))
k=-19 ... N
It's easier to find these values if we divide into two zones, N>0 and N<=0.
P(OCD<= N)=.125*(20+N)(21+N) -19<=N<=0
P(OCD<= N)=100-.125*(20-N)(19-N) 0<=N<=+19
Now that we´ve obtained the above, we can return to our example:
Our two character's are Frank the fast (F) and Dan the Dedictaed (D). Assuming half cover (+5 to F) we have that D (the agressor) spots F when
d20_D + 7 >= d20_F + 12
d20_D-D20_F >= +5
which basically means that rolling 5 higher than (F) will guarentee (D) will spot him:
if we define d20_D-d20_F as OCD, we can find trhe probability of D rolling +5 or highre than F is:
P(OCD>=+5) = 100-P(OCD<=+4)
= 100-P(OCD<= CM_F- CM_D- 1)
This translates to the following for Frank and Dan:
For 1/2 cover Dan will spot frank 52,5 % of the time. For 3/4 cover Dan will spot Frank 30% of the time. Pretty good. For 9/10s cover, Dan will only spot frank 13.75% of the time.
If we use the ruling that every 10' means a -1 penalty to spot, the above percentages represent Dan's chance to spot when within 10'. I would give him a circumstance bonus at this distance cause he could probably smell Frank.
At 30' we have the following chances to spot
1/2 = 38.25%
3/4 ths = 19.5 %
9/10ths Cov= 7 %
I believe this is pretty low, considering 30' put's you pretty close to your rival. This means Point blank shot, plus actions invloving a move and an attack action.
At 60' it becomes
1/2 = 26.25%
3/4 Cover = 11.25 %
9/10 Cover = 2.5 %
The above example is using two characetrs who have dedicated the sam effort into their particular skills. Let's analyze what happens when dan tries to spot Ted, the tough hero who uses a concealable vest (-3) but is not particularly nimble (Dex 11). This means his modifiers become +2 (1/2 C) and +7 (9/10 C);
At 5'
1/2 Cover = 88.75%
3/4 Cover = 73.75 %
9/10 Cover = 52.5 %
At 30'
1/2 Cover = 80.5 %
3/4 Cover = 61.75 %
9/10 Cover = 38.25 %
At 60'
1/2 Cover = 70 %
3/4 Cover = 47.5 %
9/10 Cover = 26.25 %
Now all of this is with good lighting. Now I understand adding a distance modifier, but maybe it should be every 20' or even every 30'.
I wanted to present this analysis in order to clearly illustrate those differences. If you find any holes in my math please tell me, although it probably means just a small shift in the probablities. By the way, the chance to win an opposed check when your modifier is the same as your rival's (assuming a tie favors you) is 52.5%.
Now that we have some numbers I believe we can begin to discuss wether -1/10' or something larger is more appropriate. I think we should determine an appropriate chance to spot a hidden individual at 100 ft for a given level of cover. Once that's determined we can decide on the correect distance modifier.
Well that's all. I hope I didn't bore anybody with this, but it probably will help decide appropriate circumstance modifiers for any other opposed check rolls.
