I think it's worth adding in variables for your Attack Bonus and the Defense to hit. If you have an attack bonus of +10 and you want to hit Defense of 16, that means only 30% of your rolls would be subject to either the static or dynamic bonus and the dynamic bonus runs a higher chance of wasted bonus since a roll of 5 would "waste" 5% or more to-hit chance.
I think the forumla is more complex than you've created, but I'm not enough of an expert to apply all of the numbers needed to make it more accurate.
That's included.
Insightful Riposte has a .15 chance of changing a hit, and will give you (approximatly) .8 more hit's per encounter. +1 is a .05 chance of changing it, and will give you (approximatly) .5 more hit's per encounter.
F-111 Interdictor Long (200+ squares) distance ally teleporter. With some warlord stuff. Broken in a plot way, not a power way. Thought Switch Higher level build that grants upto 14 attacks on turn 1. If your allies play along, it's broken. Elven Critters Crit op with crit generation. 5 of these will end anything. Broken. King Fisher Does an excellent job at keeping an enemy disabled in a few ways. Strong. Boominator Fun catch-22 booming blade build with either strong or completely broken damage depending on your reading. Very Distracting Warlock Lot's of dazing and major penalties to hit. Overpowered. Pocket Protector Pixie Stealth Knight. Maximizing the defender's aura by being in an ally's/enemy's square. Yakuza NinjIntimiAdin: Perma-stealth Striker that offers a little protection for ally's, and can intimidate bloodied enemies. Very Strong. Chargeburgler with cheese Ranged attacks at the end of a charge along with perma-stealth. Solid, could be overpowered if tweaked. Void Defender Defends giving a penalty to hit anyone but him, then removing himself from play. Can get somewhat broken in epic. Scry and Die Attacking from around corners, while staying hidden. Moderate to broken, depending on the situation. Skimisher Fly in, attack, and fly away. Also prevents enemies from coming close. Moderate to Broken depending on the enemy, but shouldn't make the game un-fun, as the rest of your team is at risk, and you have enough weaknesses. Indestructible Simply won't die, even if you sleep though combat. Sir Robin (Bravely Charge Away) He automatically slows and pushes an enemy (5 squares), while charging away. Hard to rate it's power level, since it's terrain dependent. Death's Gatekeeper A fun twist on a healic, making your party "unkillable". Overpowered to Broken, but shouldn't actually make the game un-fun, just TPK proof. Death's Gatekeeper mk2, (Stealth Edition) Make your party "unkillable", and you hidden, while doing solid damage. Stronger then the above, but also easier for a DM to shut down. Broken, until your DM get's enough of it. Domination and Death Dominate everything then kill them quickly. Only works @ 30, but is broken multiple ways. Battlemind Mc Prone-Daze Protecting your allies by keeping enemies away. Quite powerful. The Retaliator Getting hit deals more damage to the enemy then you receive yourself, and you can take plenty of hits. Heavy item dependency, Broken. Dead Kobold Transit Teleports 98 squares a turn, and can bring someone along for the ride. Not fully built, so i can't judge the power Psilent Guardian Protect your allies, while being invisible. Overpowered, possibly broken Unnamed Avenger|Runepriest/Hammer of Vengance Do lot's of damage while boosting your teams. Strong to slightly overpowered. Charedent BarrageA charging ardent. Fine in a normal team, overpowered if there are 2 together, and easily broken in teams of 5. Super Knight A tough, sticky, high damage knight. Strong. Super Duper Knight Basically the same as super knight, only far more broken. Mora, the unkillable avenger Solid damage, while being neigh indestuctable. Overpowered, but not broken. Swordburst Maximus At-Will Close Burst 3 that slide and prones. Protects allies with off actions. Strong, possibly over powered with the right party.
If it's after you see the result (ala Heroic Effort), then I like the +X once per encounter better, provided X is sufficiently large (around 4ish would make me happy). If it's before you attack, then I'll take the permanent +1 every time.
Same goes for defenses. I'd rather have +4 to AC once per encounter when I know I can negate a hit, than +1 to AC all the time.
I just want to justify my bias toward always on boosts...
As you get more powerful as a party, the response of most DMs will to throw more powerfull stuff at you. You'll increasingly hit higher-than-CR challenges. Those combats will run longer, because you have to hit more times to drop a monster. The longer the combat runs, the more always-on outperforms one-time.
(Also: AoE blasters really crank up the attack count. So blasters will want always-on boosts more than single-target strikers will. Controllers really crank up the difference between attacks, so controllers want situational larger boosts more than always-on boosts)
"Nice assumptions. Completely wrong assumptions, but by jove if being incorrect stopped people from making idiotic statements, we wouldn't have modern internet subculture." Kerrus
Practical gameplay runs by neither RAW or RAI, but rather "A Compromise Between The Gist Of The Rule As I Recall Getting The Impression Of It That One Time I Read It And What Jerry Says He Remembers, Whatever, We'll Look It Up Later If Any Of Us Still Give A Damn." Erachima
I didn't know how to write the formula, but I figured a simple excel simulation might help. I ran 100,000 encounters each encounter assuming 10 attacks, with two characters. One character at +11 attack vs 16 defense. and the other at +10 attack, with an encounter bonus of +2 to hit.
For x = 1 To encounters For i = 1 To attacks roll = Rnd * 20 If roll + attack >= defense Then hits = hits + 1 End If If roll + attack = defense - 1 Then StaticHits = StaticHits + 1 'Static bonus hits End If If roll + attack < defense Then If dbonusAttacks > 0 Then If roll + attack + Dbonus >= defense Then dbonusAttacks = dbonusAttacks - 1 dhits = dhits + 1 'Dynamic bonus hits End If End If End If roll = 0 Next dbonusAttacks = dbonusAttacksMax Next
I didn't know how to write the formula, but I figured a simple excel simulation might help. I ran 100,000 encounters each encounter assuming 10 attacks, with two characters. One character at +11 attack vs 16 defense. and the other at +10 attack, with an encounter bonus of +2 to hit.
F-111 Interdictor Long (200+ squares) distance ally teleporter. With some warlord stuff. Broken in a plot way, not a power way. Thought Switch Higher level build that grants upto 14 attacks on turn 1. If your allies play along, it's broken. Elven Critters Crit op with crit generation. 5 of these will end anything. Broken. King Fisher Does an excellent job at keeping an enemy disabled in a few ways. Strong. Boominator Fun catch-22 booming blade build with either strong or completely broken damage depending on your reading. Very Distracting Warlock Lot's of dazing and major penalties to hit. Overpowered. Pocket Protector Pixie Stealth Knight. Maximizing the defender's aura by being in an ally's/enemy's square. Yakuza NinjIntimiAdin: Perma-stealth Striker that offers a little protection for ally's, and can intimidate bloodied enemies. Very Strong. Chargeburgler with cheese Ranged attacks at the end of a charge along with perma-stealth. Solid, could be overpowered if tweaked. Void Defender Defends giving a penalty to hit anyone but him, then removing himself from play. Can get somewhat broken in epic. Scry and Die Attacking from around corners, while staying hidden. Moderate to broken, depending on the situation. Skimisher Fly in, attack, and fly away. Also prevents enemies from coming close. Moderate to Broken depending on the enemy, but shouldn't make the game un-fun, as the rest of your team is at risk, and you have enough weaknesses. Indestructible Simply won't die, even if you sleep though combat. Sir Robin (Bravely Charge Away) He automatically slows and pushes an enemy (5 squares), while charging away. Hard to rate it's power level, since it's terrain dependent. Death's Gatekeeper A fun twist on a healic, making your party "unkillable". Overpowered to Broken, but shouldn't actually make the game un-fun, just TPK proof. Death's Gatekeeper mk2, (Stealth Edition) Make your party "unkillable", and you hidden, while doing solid damage. Stronger then the above, but also easier for a DM to shut down. Broken, until your DM get's enough of it. Domination and Death Dominate everything then kill them quickly. Only works @ 30, but is broken multiple ways. Battlemind Mc Prone-Daze Protecting your allies by keeping enemies away. Quite powerful. The Retaliator Getting hit deals more damage to the enemy then you receive yourself, and you can take plenty of hits. Heavy item dependency, Broken. Dead Kobold Transit Teleports 98 squares a turn, and can bring someone along for the ride. Not fully built, so i can't judge the power Psilent Guardian Protect your allies, while being invisible. Overpowered, possibly broken Unnamed Avenger|Runepriest/Hammer of Vengance Do lot's of damage while boosting your teams. Strong to slightly overpowered. Charedent BarrageA charging ardent. Fine in a normal team, overpowered if there are 2 together, and easily broken in teams of 5. Super Knight A tough, sticky, high damage knight. Strong. Super Duper Knight Basically the same as super knight, only far more broken. Mora, the unkillable avenger Solid damage, while being neigh indestuctable. Overpowered, but not broken. Swordburst Maximus At-Will Close Burst 3 that slide and prones. Protects allies with off actions. Strong, possibly over powered with the right party.
I didn't know how to write the formula, but I figured a simple excel simulation might help. I ran 100,000 encounters each encounter assuming 10 attacks, with two characters. One character at +11 attack vs 16 defense. and the other at +10 attack, with an encounter bonus of +2 to hit.
Character 1 (Static +1) Static bonus hits: 49,989 (5.00%)
Character 2 (Dynamic +2, once per encounter) Dynamic bonus hits: 52,824 (5.28%)
So Mellored is correct that a dynamic +2 bonus to hit is better than a static +1 to hit over 10 attacks per encounter.
Interestingly the break even point is 11 attacks. They are exactly equal at 11 attacks, and the +1 pulls ahead begining at 12 attacks per encounter.
Maybe I'm missing something, but those results seem wrong to me. I'm seeing Case 1 as a base 80% to hit (miss on 1-4), and Case 2 as a base 75% with a one time 85% hit percentage. Your hit results should be around 750,00-800,000.
Maybe I'm missing something, but those results seem wrong to me. I'm seeing Case 1 as a base 80% to hit (miss on 1-4), and Case 2 as a base 75% with a one time 85% hit percentage. Your hit results should be around 750,00-800,000.
Not me then.
Mabey he used a d12 instead of d20 for attack rolls...
F-111 Interdictor Long (200+ squares) distance ally teleporter. With some warlord stuff. Broken in a plot way, not a power way. Thought Switch Higher level build that grants upto 14 attacks on turn 1. If your allies play along, it's broken. Elven Critters Crit op with crit generation. 5 of these will end anything. Broken. King Fisher Does an excellent job at keeping an enemy disabled in a few ways. Strong. Boominator Fun catch-22 booming blade build with either strong or completely broken damage depending on your reading. Very Distracting Warlock Lot's of dazing and major penalties to hit. Overpowered. Pocket Protector Pixie Stealth Knight. Maximizing the defender's aura by being in an ally's/enemy's square. Yakuza NinjIntimiAdin: Perma-stealth Striker that offers a little protection for ally's, and can intimidate bloodied enemies. Very Strong. Chargeburgler with cheese Ranged attacks at the end of a charge along with perma-stealth. Solid, could be overpowered if tweaked. Void Defender Defends giving a penalty to hit anyone but him, then removing himself from play. Can get somewhat broken in epic. Scry and Die Attacking from around corners, while staying hidden. Moderate to broken, depending on the situation. Skimisher Fly in, attack, and fly away. Also prevents enemies from coming close. Moderate to Broken depending on the enemy, but shouldn't make the game un-fun, as the rest of your team is at risk, and you have enough weaknesses. Indestructible Simply won't die, even if you sleep though combat. Sir Robin (Bravely Charge Away) He automatically slows and pushes an enemy (5 squares), while charging away. Hard to rate it's power level, since it's terrain dependent. Death's Gatekeeper A fun twist on a healic, making your party "unkillable". Overpowered to Broken, but shouldn't actually make the game un-fun, just TPK proof. Death's Gatekeeper mk2, (Stealth Edition) Make your party "unkillable", and you hidden, while doing solid damage. Stronger then the above, but also easier for a DM to shut down. Broken, until your DM get's enough of it. Domination and Death Dominate everything then kill them quickly. Only works @ 30, but is broken multiple ways. Battlemind Mc Prone-Daze Protecting your allies by keeping enemies away. Quite powerful. The Retaliator Getting hit deals more damage to the enemy then you receive yourself, and you can take plenty of hits. Heavy item dependency, Broken. Dead Kobold Transit Teleports 98 squares a turn, and can bring someone along for the ride. Not fully built, so i can't judge the power Psilent Guardian Protect your allies, while being invisible. Overpowered, possibly broken Unnamed Avenger|Runepriest/Hammer of Vengance Do lot's of damage while boosting your teams. Strong to slightly overpowered. Charedent BarrageA charging ardent. Fine in a normal team, overpowered if there are 2 together, and easily broken in teams of 5. Super Knight A tough, sticky, high damage knight. Strong. Super Duper Knight Basically the same as super knight, only far more broken. Mora, the unkillable avenger Solid damage, while being neigh indestuctable. Overpowered, but not broken. Swordburst Maximus At-Will Close Burst 3 that slide and prones. Protects allies with off actions. Strong, possibly over powered with the right party.
It's also worth considering that sometimes landing that big single attack is what sets up following attacks. If you hit with something like like Lead the Attack or Knockout, the next hit (or hits) is pretty much guaranteed. Even things like Righteous Brand have consequences that might favor the one-time bonuses when you're setting up your teammate for a nova.
Didn't this come up a while back when people were arguing Elf Acc vs. Heroic Effort? It wasn't the main topic, but I thought it was mentioned.
Just to avoid confusion, probably good to explain what your dynamic bonus to hit means. Based on your formula, it means you get to CHOOSE when to apply that +X bonus, so the power of when to use it is in your hands. If you get a +X bonus on your next attack BEFORE you roll it, then this kind of bonus is much less helpful. If instead, you get a "floating" +X bonus you can apply to your attack AFTER you roll it, which means you only use it when it matters (makes you hit), then this is much more powerful. This may help some who are trying to run excel files on this
Since you only have 2 variables (X, Y) you could plot this on a 3D graph with the X axis number of attacks and the Y axis bonus to hit and the Z axis being the result. In case someone wants to plot this in 3D that is...
I'll have to agree, a 1/encounter +2 to-hit will usually outperform a static +1 to-hit. Assuming you can apply it after the roll, and hear by how much you've missed. It's easy to see why:
Assumption: You need to roll a 10 to hit a monster without the bonus (it holds for any number between 4 and 20, though).
A static +1 to-hit has an exact chance of 5% to turn any missed attack roll into a hit, since you have to roll exactly 9 for the bonus to turn a miss into a hit.
An activated +2 to-hit has an exact chance of 10% chance to turn a missed attack roll into a hit, since you can turn a miss into a hit on the roll of 8 or 9. However, only one missed attack per encounter can be turned into a hit.
So, as long as we roll exactly one 9 during an encounter, the two are equal in terms of how often you hit (regardless of how often we roll 8). If we roll an 8, but not a 9, the 1/enc bonus wins out. Rolling two nines puts the static bonus ahead.
But there's a really big selling point for the +2 once per encounter: It can turn an 8 into a 10. This matters when you activate a powerful encounter or daily power early in a fight. Average chance to hit means squat for nova rounds - you need your best attacks to hit, and you need it now, not on the at-will you use in round four. Same goes for those insane daily control powers you use to lock down that nasty elite.
And even if you're using only MBAs, the once/encounter bonus has a selling point: Its effect is frontloaded. Your first ten attacks have a higher chance to hit, meaning your first opponent will drop faster, on average.
The same idea goes for defensive bonuses, by the way. My late heroic avenger/swordmage may be sitting on a passive 26 AC, it takes a total attack roll of 32 to hit her outright (courtesy of Shield and Cloak of Displacement, with a Githzerai racial and some proactive defense bonuses for backup). Which is a nice and fuzzy safe feeling (were it not for the DM and Murphy conspiring - so far about half his d20s against me turned up 17+).
Not me then.
