A discussion on how Passive Defenses are calculated and a suggestion for a houserule to use 3 times Ability and 2 times relevant Specialty instead. Any comments much appreciated.
I've looked around and haven't been able to find any discussion concerning the way Passive Defenses are calculated. Looking on the statistics of it, abilities seem heavily favored over specialties in the 4/1 scheme, in a way I actually find a little counter-intuitive. The abilities are pretty broad, and some of the applications of Passive Defenses are pretty specific.
For a more mechanical reasoning the example for the opposed test comes to mind. It pits a sneaker (Stealth) trying to circumvent a guard (Awareness, lets say he has 3). Unaware of the intruder the guard utilizes his passive Awareness (12) to set the difficulty for the sneaker, but if the alarm bell rings and the guard snaps to attention it actually, on average, becomes easier for the sneaky git (Average Awareness roll 10,5).
If we consider a bit of specialized training (Specialty Notice 1B) the guard's passive awareness increase to 13, and the average to 12.24. 2B equals a passive defense 14, and an average roll of 13.43. 3B equals a passive Defense of 15, and an average roll of 14.27. So in every scenario passive outperforms active, leading to a scenario where it could be considered always beneficial for a player to rely on not rolling. That is ofcourse unless the player gets really excited about rolling dice and don't care about statistics. This seems a bit boring to me on a game related level, and breaks immersion somewhat looking at the above stealth versus awareness example.
Considering specialties a Fastmath approach on this forum seems to be adding 1 per bonus die, which lines up with the benefit gained on Passive Defenses, but the actual math is a bit higher. The average value of each bonus die diminishes the more you get, but it never goes below 1 on average, if it is compared to any raw Ability above 1. The average value of the first specialty die goes from 0.97 for an Ability of 1, over 1.46 for an Ability of 2 and steadily climbs from there, reaching 2.06 with an Ability of 5. So concerning passive defenses bonus dice seems undervalued in the rules as written.
In the 4/1 scheme for passive defenses the low value of specialties are more than made up by the fact that Abilities are over valued at 4 instead of the real average value of 3.5 per die. But as stated above I find these high base defenses problematic. Now I want to avoid going into a long discussion of the meaning and impact of Abilities versus Specialties right now, so instead I'll look at the rules for jousting as a narrative example. Lets compare Heath the good shepherd and Pret the hedge knight. Relevant for this comparison is Heath's high affinity for animals (Animal Handling 5, Passive Defense 20, roll average 17.5) and Pret's mediocre, but focused, skills as a rider (Animal Handling 3 Ride 2B, Passive Defense 14, roll average 13.4). Lets set their fighting at 3 and 5 respectively, neither having the Spear specialty.
Heath has a 16.2% chance of of getting a 1 degree success, which has a 10.5% chance of letting Pret taste dirt. Pret can actually achieve up to 3 degrees but with increasingly low chances. 1 degree 30.5%, 0.7% for Heath to taste dirt. 2 degrees 3.2%, 5.9% for Heath = Dirt. 3 Degrees 0.01%, 22.15% for a Heath dirtburger. Might be me, but these numbers seem really low. Without some quick luck jousting looks like it can take quite a while, if the opponents have the AR to absorb a single degree. (A no armor scenario results in meatburgers on top of horses, not anymore throwing).
Now what i propose is changing the formula for passive defenses to 3 times ability + 2 per relevant specialty die. With this Heath has a passive defense of 15 and Pret a passive defense of 13. Heath now has almost 26% of getting a hit and a small (0.46%) chance of getting 2 degrees with 22.5% chance of throwing Pret. Pret on the other hand sees the bigger difference. He now has a 77.85% chance of getting a hit, but more importantly 30.5% and 3.2% for 2 or 3 degrees. Now because their stats are somewhat mirrored, the average result is probably still the same, Heath will end up groggy in the saddle and forfeit, but because of Pret's increased chance of getting 2 degrees, they'll get there significantly faster.
Most discussions involving specialty dice I've seen concerns themselves with their contribution to averages, but this doesn't address their other impact, namely the ability to weed out poor results. If we look at a similar xp cost of 4D+3B and 5D and compare three values, 90% chance of reaching, average and chance for average + 1 degree, we get:
4D+3B = bit less 15 - 18.4 - 6.4% for 23
5D = slightly more than 13 - 17.5 - 9.8% for 23
This, I think, lends itself as to why specialty dice should be overrated, instead of ability dice, when calculating passive defenses. Acquiring specialty dice suggest a higher base-line performance.
Now concerning how passive defenses stack up against average active (e.g. opposed) rolls, you can still get ahead of the curve, but instead of being the baseline you now need to get the maximum possible amount of bonus dice for abilities from 2 to 5, or max or one below for higher. These levels of investment are generally discouraged because such a high amount of bonus dice lack an impact on average and maximum achievable result.
A side effect of changing it to three times ability is that, for tertiary opposition at least, the passive defenses line up with the difficulty increments and that passive defenses becomes more similar to Combat Defense and Intrigue Defense.
Current uses of Passive Defenses and ideas and thoughts regarding implementing a 3/2 scheme:
Awareness - has a variety of related applications for it's Passive Defense value, The added cost of raising both empathy and notice to get a similar level of passive radar as under the current rules seems preferable. Biggest offender as to how it sometimes isn't advantageous to roll or be active.
Animal Handling/Jousting - With the double test of first using passive as defense followed by a rolled test to stay in the saddle, a generally lower passive seems preferable to resolve jousts faster.
Animal Handling/Other - Most uses refer to rolling against the animal's passive Will, not sure I see a problem in these tests being easier. For the story sake you could invent a stubborn specialty for a specific animal.
Cunning/Logic - mentions a use against Passive Warfare of the enemy commander to find flaw in planning. Apply Strategy or Tactics depending on situation.
Fighting - The advanced reach rules use Passive Fighting to determine result of Free Attacks. Lowering the high passive Fighting, or shifting the focus to Specialty dice at least, lessen the chance of black holes of death coming from people with high damage/high fighting compared to normal Combat Defenses.
Persuasion/minor tasks - Versus Will. Might be considered too easy even under the current rules. Maybe apply Courage or Dedication depending on situation and the DR from disposition as a modifier.
Intrigue Maneuvers -
Fast Talk - Maybe apply Decipher or Logic or accept lower resistance.
Manipulate - Silly strong as I read it, equates to mind control. Probably require at least 2 or 3 degrees or maybe change the effect from choose to opponent must use different,
Read Target - Apply Bluff or Act as relevant.
Shield of Reputation - Make the Test opposed.
Combat and Weapon Maneuvers -
Disarm - Apply relevant weapon specialty.
Distract - Could use the awareness specialties as warranted.
Grab - Use oppposed test instead.
Knockdown - Use opposed Athletics (Strength) or Agility (Dodge) instead of passive when aware, otherwise Passive Athletics (Strength).
Knockout - Add Resilience as applicable, possibly AR rating with helmet.