Simplest model of replacing armor with hit points.  Hmmmm .....

Heavy weapons such as a greatsword would do 1d10 damage.  Average[d10] = 5.5

If a paladin without armor goes down in 2 hits, then the number of hit points they have should be 2*5.5 = 11.  If the paladin has plate armor, I suppose they can take 8 more hits.  So with the armor, they have an additional 8*5.5 = 44 hit points, giving a total number of hit points 55.

So with a 50% probability of hitting a plate armored paladin, it would take an attacker with a greatsword on average around 10/0.5 = 20 rounds (including misses) to eventually kill the paladin.  Other weapons with less average damage than d10, would take longer to kill the plate armored paladin.

For a physically fit commoner with only 11 hit points, it takes on average 4 rounds of a greatsword swinging at them to kill them (including misses) if there is a 50% probability of hitting them.

If a commoner has only 5 hit points, it will take on average 2 rounds of a greatsword swinging at them to kill them.

Quote from: Shazbot79;400635I get what you're saying...but there is a purpose for stat the bumps.

If you take 4E's level/2 progression and apply the same progression to monster stats, then stat bumps are what actually make your character better as they increase level.

In other words, at 1st level, Conan hits about 50% of the time...as he increases in level and gets a level/2 bonus, then he still hits 50% of the time.

However, if he gets regular stat bumps, then by the time he gets to 30th level, he is then hitting 70% of the time.

The problem that you cited with MAD classes could be mitigated if the stat bump is applied to all character stats.

OK. That's fairly valid. There's a certain 'feelgood' factor about having your 30th level demigod have awesome ability scores, if nothing else. There are actually lots of options for getting bonuses though the main difference between a +ability score method and another bonus source (like a feat, power, or implement) is that this boosts damage for powers as well, automatically. (Hmm...also note that the PCs are getting better from ability scores boosts only because the monsters can't add bonuses to defenses from their stats, which are probably bloating out much faster).

I have a couple of other ideas but I think I should schizm and have my own thread since they head off in other directions...

Quote from: Shazbot79;400610Ggroy's calculations are essentially showing that no matter what your characters level is, it always takes you about the same time to kill a monster, hence the term "always fighting orcs."

What about increasing the damage of Encounter powers?   Instead of doing 2D10+STR, have it D10 + 10 + STR?

Certainly monster HP should be halved.

Quote from: Shazbot79;400610Personally, I'm fine with PC's keeping pace with monsters in the damage race, as long as combat is simple, yet dynamic....and doesn't just feel like whittling a log.

Back in 4e playtests, there were monsters whose Encounter powers randomly recharged.  AKA, roll a D6 each round and on a 5+, the monster regains his power.   It added a cool random element to the battle and it meant that sometimes the monster got off a few nasty rounds, instead of just one.

I'd like to see more randomness in the damage.  

BTW, somewhere I saw a discussion about Critical Hits cutting your HP in half.  That was interesting.  No damage roll, just whap, half your current HP go away.

Quote from: Shazbot79;400631What if starting stats were determined by class instead of by point-buy or random rolls and race selection?

How about this:

1) Race gives a Baseline

2) Class adds +X to key Stats

3) Players get to add X points as they like.  Even if its just 3 point to spread as a customizer.

Quote from: Bloody Stupid Johnson;400632Conan already adds +1/2 his level to Strength checks, he doesn't need a higher Strength score as well.

How about if Classes add +1 per level for Key Stat checks?   Thus a Fighter (STR) would always outbonus a Paladin (CHA) in contests of Strength, even if they had the same score.

Quote from: Spinachcat;400670What about increasing the damage of Encounter powers?   Instead of doing 2D10+STR, have it D10 + 10 + STR?

Certainly monster HP should be halved.

I'd tentatively agree...

QuoteBack in 4e playtests, there were monsters whose Encounter powers randomly recharged.  AKA, roll a D6 each round and on a 5+, the monster regains his power.   It added a cool random element to the battle and it meant that sometimes the monster got off a few nasty rounds, instead of just one.

I'd like to see more randomness in the damage.  

BTW, somewhere I saw a discussion about Critical Hits cutting your HP in half.  That was interesting.  No damage roll, just whap, half your current HP go away.



How about this:

1) Race gives a Baseline

2) Class adds +X to key Stats

3) Players get to add X points as they like.  Even if its just 3 point to spread as a customizer.

That could work, though it makes race choices much more important...with the current importance rating of ability scores, each race becomes useful for one class, only.

QuoteHow about if Classes add +1 per level for Key Stat checks?   Thus a Fighter (STR) would always outbonus a Paladin (CHA) in contests of Strength, even if they had the same score.

+1 per level for some classes, a +1/2 for others is what Talislanta does for skill checks, and I think Castles and Crusades is similar (?). Under this system while they start out the same, eventually one character will more or less pass automatically rolls that another automatically fails.
Also, depends how skills fit into this, but C&C ended up with a problem where (say) Clerics are much better than Rogues at noticing things generally (and possibly finding traps?) since these are Wisdom-based skills.

Let's examine how the standard deviation (stdev) of N changes with level.

http://en.wikipedia.org/wiki/Standard_deviation

Recall from

http://www.therpgsite.com/showpost.php?p=400526&postcount=4

the average number of hits to kill a monster by a player character (of the same level) using an at-will power with weapon dice [W],

N = [ROLE*(level+1) + CON]/[level*(average[W])/10 + 7*(level-10)/20]

One of the egregious assumption made, was that the damage of at-will powers [W] increases each ten levels after level 10, in the pattern of:

level 21-30 --> 2[W]
level 31-40 --> 3[W]
level 41-50 --> 4[W]
level 51-60 --> 5[W]
etc ...

To get the standard deviation of N, there's the formula (from engineering or physics labs):

stdev[N] = |dN/d[W] | * stdev[W]

(with some abuse of notation).  The term in between the |  | absolute value brackets is the first derivative of N with respect to [W].

Doing this calculation and scaling the level to infinity, we get:

stdev[N] = (N^2) * (stdev[W])/(10*ROLE)


Recall that for individual dice like d4, d6, d8, d10, d12, etc ... the standard deviation is:

stdev[dN] = sqrt[(N^2 -1)/12]

where sqrt is the square root.

http://en.wikipedia.org/wiki/Uniform_distribution_%28discrete%29

For example,

stdev[d4] = 1.118
stdev[d6] = 1.708
stdev[d8] = 2.291
stdev[d10] = 2.872
stdev[d12] = 3.452


Recall from the linked post above, the scaled values for N as level is taken to infinity for a skirmisher monster (ROLE=8) being repeatedly attacked by a player character for various weapon hit dice [W].

http://www.therpgsite.com/showpost.php?p=400526&postcount=4

Calculating the standard deviations of N for different weapon dice [W], we get:

average[d12] = 6.5 --> N = 8 --> stdev[N] = 2.76
average[d10] = 5.5 --> N = 8.89 --> stdev[N] = 2.84
average[d8] = 4.5 --> N = 10 ---> stdev[N] = 2.86
average[d6] = 3.5 --> N = 11.43 --> stdev[N] = 2.79
average[d4] = 2.5 --> N = 13.33 --> stdev[N] = 2.48


Indeed even as the level scales to infinity, the standard deviation remains constant differing only by weapon damage dice.  This is "always fighting orcs" with even the variability in N not changing.  So for a player character hacking away with at-will powers using a greatsword (with weapon dice d10) at a skirmisher monster (of the same level as the player), the number of hits to kill the monster is between 6 to 12 hits for 68% of the time, or between 3 to 15 hits for 95% of the time.  (This is using the standard deviation in the bell curve approximation).  This remains the case even as the level scales to infinity.

http://en.wikipedia.org/wiki/Standard_deviation

"Always fighting orcs" indeed, even with the variability not changing much as the level goes to infinity.


EDIT:  This calculation is not entirely correct.  See next post.

Been thinking more about the standard deviation of N  ->  stdev[N].

It turns out the calculation of stdev[N] is slightly more complicated than I originally anticipated.

For weapon damage dice 2[W], it means that the number of weapon dice is doubled.  For example if the weapon dice [W] is a d6, then 2[W] means 2d6, 3[W] means 3d6, etc ...

The average of damage dice "level*[W]", turns out to be equal to level*average[W].

But the standard deviation of damage dice "level*[W]", turns out to be [sqrt(level)]*stdev[W].  ("sqrt" is the square root).  This can be found in any college statistics/probability textbook.

EDIT:  For example, (stdev[3d6])^2 = (stdev[d6])^2 + (stdev[d6])^2  + (stdev[d6])^2 which gives stdev[3d6] = sqrt(3) * stdev[d6].

Doing the calculation of the standard deviation of N, we get:

stdev[N] = N^2 *(stdev[W])/[ROLE*sqrt(level/10)]

when the level becomes larger and larger.

Hence the standard deviation of the average number of hits "N" to kill a monster by a player repeatedly using at-will powers against a monster (of equivalent level), scales as:

stdev[N] ~ 1/sqrt(level)


This means the standard deviation of N moderately gets smaller and smaller as the level gets bigger and bigger.  The number of hits to kill a monster (of the same level) deviates less and less from the average, as the level becomes bigger and bigger.

Basically while one is "always fighting orcs", the "orcs" are becoming more and more "predictable" as the level gets higher and higher.

Quote from: Spinachcat;400670Back in 4e playtests, there were monsters whose Encounter powers randomly recharged.  AKA, roll a D6 each round and on a 5+, the monster regains his power.   It added a cool random element to the battle and it meant that sometimes the monster got off a few nasty rounds, instead of just one.

Well, there are still plenty of monsters having special powers which recharge on d6 rolling a 5+. I guess your point was that the most powerful ones don't have that recharge mechanic but, if at all, a less randomized one (like "recharges when first bloodied").

What I like better than either of these is the 3.5 recharge mechanics that some dragons had with their breath weapon (iirc) - "recharges in 1d4 rounds". So instead of checking at the beginning of each round whether your dragon recharges, you as the DM know in advance when you'll be in a position to use it again - which means you can include this in planning in advance what your dragon is going to do. (I don't like the book keeping this involves though, esp. if you have to control 4+ monsters each with 1-3 such recharge powers.)

Quote from: Windjammer;400787What I like better than either of these is the 3.5 recharge mechanics that some dragons had with their breath weapon (iirc) - "recharges in 1d4 rounds". So instead of checking at the beginning of each round whether your dragon recharges, you as the DM know in advance when you'll be in a position to use it again - which means you can include this in planning in advance what your dragon is going to do. (I don't like the book keeping this involves though, esp. if you have to control 4+ monsters each with 1-3 such recharge powers.)

You could always fold that into prep time by rolling in advance.  Take 5d4, for instance, and you would have a maximum of 20 rounds planned out, on average 7 or 8 rounds.

Let's examine the scaling behavior of the encounter and daily powers, in the unrealistic scenario where they can be repeatedly spammed every round.  We will calculate the average number of rounds "R" to kill a monster by a player of the same level.

Recall from

http://www.therpgsite.com/showpost.php?p=400526&postcount=4

http://www.therpgsite.com/showpost.php?p=400552&postcount=11

a non-striker repeatedly using at-will powers against a monster of the same level, "R" approaches the limit

R = N/p -> N -> ROLE/{p*[(average[W])/10 + 7/20]}

as the level goes to infinity.

For different [W] weapons attacking this skirmisher monster (ROLE=8) with the player having a p=50% of hitting the monster, we have average number of rounds "R" as the level goes to infinity:

average[d12] = 6.5 --> N = 8, R = 16
average[d10] = 5.5 --> N = 8.89, R = 17.78
average[d8] = 4.5 --> N = 10, R = 20
average[d6] = 3.5 --> N = 11.43, R = 22.86
average[d4] = 2.5 --> N = 13.33, R = 26.66


For non-striker encounter powers, the average damage per hit scales approximately as (after level 10):

level*(average[W])/7 + 7*(level-10)/20.

So for non-striker encounter powers, the average damage per round scales approximately as (after level 10):

p*[level*(average[W])/7 + 7*(level-10)/20].

So as the level goes to infinity, "R" approaches:

R -> N/p = ROLE/{p*[(average[W])/7 + 7/20]}


For different [W] weapons attacking this skirmisher monster (ROLE=8) with the player having a p=50% of hitting the monster, we have average number of rounds "R" as the level goes to infinity:

average[d12] = 6.5 --> R = 12.51
average[d10] = 5.5 --> R = 14.01
average[d8] = 4.5 --> R = 16.12
average[d6] = 3.5 --> R = 18.82
average[d4] = 2.5 --> R = 22.63

On average, for a player hypothetically repeatedly spamming an encounter power against a skirmisher monster of the same level, the average number of rounds "R" to kill the monster is shorter by approximately 4 rounds (compared to at-will powers) as the level goes to infinity.  (For a 50% probability of hitting the monster, this would mean that it takes approximately 2 less hits to kill the skirmisher monster).

More generally, a hypothetical spammed encounter power takes approximately 15% to 20% less rounds to kill a monster (of the same level).

Let's do the same for daily powers, where the the daily powers have half-damage on a miss.

Recall for half-damage on a miss:

http://www.therpgsite.com/showpost.php?p=400569&postcount=13


For a daily powers, the average damage per hit scales approximately as (after level 10):

level*(average[W])/5 + 7*(level-10)/20.


For the easy case where the daily powers of non-strikers always miss, "R" approaches

R -> 2*ROLE/{p*[(average[W])/5 + 7/20]} = ROLE/{p*[(average[W])/10 + 7/40]}

as the level goes to infinity.

Comparing this to the expression "R" for at-wills, it means that daily powers always missing and producing half-damage, is slightly worse than generic daily powers.


For non-striker daily powers with half-damage on a miss and a probability p of a hitting a monster of the same level, the average damage per round scales approximately as (after level 10):

0.5(p+1)*[level*(average[W])/5 + 7*(level-10)/20]

So as the level goes to infinity, "R" approaches:

R ->  2*ROLE/{(p+1)*[(average[W])/5 + 7/20]}


For different [W] weapons attacking this skirmisher monster (ROLE=8) with the player having a p=50% of hitting the monster, we have average number of rounds "R" as the level goes to infinity:

average[d12] = 6.5 --> R = 6.46
average[d10] = 5.5 --> R = 7.36
average[d8] = 4.5 --> R = 8.53
average[d6] = 3.5 --> R = 10.16
average[d4] = 2.5 --> R = 12.55

On average, for a player hypothetically repeatedly spamming a daily power (with half-damage on a miss) against a skirmisher monster of the same level, the average number of rounds "R" to kill the monster is approximately shorter by a half compared to at-will powers, as the level goes to infinity.

This means a repeatedly "spammed" daily power (with half damage on a miss) attacking a skirmisher (of the same level), is on average damage-wise approximately equal to two at-wills in general.  If the daily power always misses and always produces half damage, it is damage-wise approximately equal to one at-will power.

More rigorous justification for the formula:

stdev[N] = |dN/d[W] | * stdev[W]


http://en.wikipedia.org/wiki/Delta_method

Let's examine the case for new encounter powers which produce half-damage on a miss.  (These are purportedly being introduced in 4E Essentials).  Let's assume the new encounter powers still follow the same damage of the Heinsoo 4E D&D encounter powers, but with the "half-damage on miss" tacked on.

For non-striker encounter powers with half-damage on a miss and a probability p of a hitting a monster of the same level, the average damage per round scales approximately as (after level 10):

0.5(p+1)*[level*(average[W])/7 + 7*(level-10)/20]

So as the level goes to infinity, "R" approaches:

R -> 2*ROLE/{(p+1)*[(average[W])/7 + 7/20]}


For different [W] weapons attacking a skirmisher monster (ROLE=8) with the player having a p=50% of hitting the monster, we have average number of rounds "R" as the level goes to infinity:

average[d12] = 6.5 --> R = 8.34
average[d10] = 5.5 --> R = 9.39
average[d8] = 4.5 --> R = 10.74
average[d6] = 3.5 --> R = 12.55
average[d4] = 2.5 --> R = 15.08

On average, for a player hypothetically repeatedly spamming a new encounter power (with half-damage on a miss) against a skirmisher monster of the same level, the average number of rounds "R" to kill the monster is approximately shorter by 45% compared to at-will powers, as the level goes to infinity.

Quote from: Shazbot79;400631What if starting stats were determined by class instead of by point-buy or random rolls and race selection?

How about adding Racial Minimums?
If you want to play a Dwarf, then its CON 10 and WIS 10 as a base.

Quote from: Windjammer;400787I don't like the book keeping this involves though, esp. if you have to control 4+ monsters each with 1-3 such recharge powers.

Recharge is cool, but less bookkeeping the better.   What if we just gave non-Minion monsters an Action Point?  And then let Action Points be used to recharge Encounter Powers?  

Elites would get 2 Action Points and Solos would get 3 (or 1 per player as I prefer).  Players and Monsters could choose to use APs as a reroll, a bonus action or just to recharge an Encounter power.

For completeness, there's at-will powers with half-damage on a miss.  (IIRC, there's a few monsters with such an at-will power from the 4E MM2 and/or MM3).

With half-damage on a miss, the at-will with half-damage on a miss reduces the number of rounds R to kill a monster by a factor = p/(1+p) in comparison to ordinary at-will powers.  (p is the probability of hitting a monster).

For different p:

p = 100% --> factor = 50%
p = 75% --> factor = 42.6%.
p = 50% --> factor = 33.3%
p = 25% --> factor = 20%

So with a probability 50% of hitting a monster, an at-will power with half-damage on a miss will reduce the number of rounds to kill the monster by 33.3%, in comparison to the same at-will power without the half-damage on a miss part.

Quote from: Spinachcat;400908How about adding Racial Minimums?
If you want to play a Dwarf, then its CON 10 and WIS 10 as a base.

I don't think racial minimums are a bad idea, in and of themselves, but it can limit player input.  I think the old standby was to boost scores to the minimum if they didn't already have that.  Again, not a bad option, depending on whether or not the unimplemented racial powers are introduced.

QuoteRecharge is cool, but less bookkeeping the better.   What if we just gave non-Minion monsters an Action Point?  And then let Action Points be used to recharge Encounter Powers?  

Elites would get 2 Action Points and Solos would get 3 (or 1 per player as I prefer).  Players and Monsters could choose to use APs as a reroll, a bonus action or just to recharge an Encounter power.

That would be somewhat less bookkeeping, but action points used that way would be about the same as Healing Word, where you can use it twice per encounter.  Probably the easier way is to just give monsters multiple use encounter powers like that.  For example, a dragon's breath weapon would be an Encounter power usable three times per encounter, with Bloodied Breath still available as a 'freebie' use of the power.  Recharge and immediate use is the same as a free use anyway.