CoT defense debuffs?

[shortguy on indom]

• STREAKBREAKER IS A SEPARATE ISSUE AND MECHANIC THAT IS APPLIED AFTER A MISS, SINCE IT'S APPLIED AFTER AN ATTACK MISS, IT INDEED DOES CHANGE THE NUMBERS OF ONE'S END CHANCE OF GETTING HIT.
• ...AND I RESPPECTFULLY DISAGREE WITH THAT CONCLUSION AND THE APPLICATION  OF STATING THAT FORMULA WORKS FINE FOR ALL ATTACK TYPES.
• GOING TO SHOW THE WHY IN OTHER THREAD.
• ONE DOES NOT GET HIT MULTIPLE TIMES IF THE ENEMY HITS YOU WITH AN AOE... JUST ONCE.

[Maelwys]

25 minutes ago, shortguy on indom said:

• ...AND I RESPPECTFULLY DISAGREE WITH THAT CONCLUSION AND THE APPLICATION  OF STATING THAT FORMULA WORKS FINE FOR ALL ATTACK TYPES.
• GOING TO SHOW THE WHY IN OTHER THREAD.

[shortguy on indom]

• SINCE I ALREADY HAVE IT HANDY... 😐
• IT BASICALLY STATISTICALLY IMPOSSIBLE BTW TO FOR THE GAME FOR 0.2 CHANCE TO HIT BECAUSE IT WOULD TAKE OVER 2,000,000 CONSECUTIVE ATTACKS ... 1 MILL SHOWN BELOW. 
• 
• 

[shortguy on indom]

• ...JUST WANTED TO SHOW IN THIS THREAD TO SHOW THAT EVEN WITH ONLY 5 CONSECUTIVE ATTACKS, THE CHANCE TO GET HIT IS MORE THAN THE CRAZY FORUMALS COME UP WITH ABOVE FOR 95% CHANCE TO HIT.....THIS EQUATES TO A +3/AV. (WHICH BY MATH = 95% ENEMY CHANCE TO HIT).
• STREAKBREAKER ADDS TO ENEMY CHANCE TO HIT IN THIS CASE.

WAITING OVER.

[shortguy on indom]

• FINALLY... TO SHOW THE MATH... IF I MUST TO SATISY THE MATH SCHOLARS ON STEROIDS...
• NATURAL LOG METHOD... USE AT WILL.
•  

defense losing streak calculator - Copy.ods

[shortguy on indom]

1 hour ago, aethereal said:

Any time someone mentions the Streakbreaker in a defense thread, you can safely assume they have no idea what they're talking about.

 

• YEP

Edited Thursday at 06:22 PM by shortguy on indom

[Maelwys]

3 hours ago, aethereal said:

Any time someone mentions the Streakbreaker in a defense thread, you can safely assume they have no idea what they're talking about.

I mean; the Devs outright told us exactly how it works twenty years ago.
WeirdBeard (original Dev team) was the one who gave us the full breakdown of exactly how it functions:
 

Quote

Final to-hit : misses allowed
>.9 : 1
.8-.9 : 2
.6-.8 : 3
.4-.6 : 4
.3-.4 : 6
.2-.3 : 8
0 -.2 : 100

You're correct, it's the final to-hit chance (in the range [0.05 .. 0.95]) of an actual executed attack against a specific target.

Auto-hit powers are not included in the system.

Critters get the benefits of the system as well.

The system does not track each power individually; instead it tracks every miss you make in a row, regardless of power (or target). Otherwise you could have nine different powers, each with a 0.95 to-hit, and if you executed them all in a row you could miss each attack (note a caveat at the bottom of the post regarding this).

AE attacks are considered distinct sequential attacks on indivudual targets for the purpose of the system (so if you AEd two targets and had 0.95 to-hit for both, you be guaranteed to hit one of them).

...

Something to note, for those inclined to note such things. Because we do the lookup based on your worst to-hit in the series, the streak breaker is a bit less aggressive about breaking streaks than it might initially appear from the table. If you miss an ill-advised attack with a final to-hit of 0.15, you would in fact be allowed to continue the miss series for another 99 attacks, even if all the followup attacks are of capped to-hit, should you be unlucky enough.

And these days you can even see this for yourself in the code (it's within entity/character_combat.c)

The Streakbreaker does indeed allow up to 100 misses in a row if an attack has <20% hit chance.

Sure; it's a bit wonky in practice because LOTS of things generate HitChecks and so sometimes it might actually make more sense to turn off your damage aura and queue up big splatty attacks. But most of the time it's not something the players need to be overly concerned about. Those first two numbers on the 6th line of code and the paragraph at the bottom of Weirdbeard's quote are the most important bits IMO.
 

Edited Thursday at 08:44 PM by Maelwys

[Maelwys]

3 hours ago, shortguy on indom said:

• 

So a toon with 10% defense versus 10 incoming single target attacks in a row... can expect 22 of those 10 attacks to hit them?
OK.



If we'd picked a slightly more sane traditional method:

HitChance = Clamp( AccMods × Clamp( BaseHitChance + ToHitMods – DefMods ) )
If the attacker is a +3 AV then their AccMods would be (1.0 [Attack base Accuracy] x 1.3 [Attacker is +3 to you] x 1.5 [Attacker is an AV]) = 1.95
And their BaseHitChance would be 50% [for a regular unbuffed PVE foe attacking a player]
Without any Defense Buffs, ToHit buffs or Defense Debuffs in play at all then that'd work out at:
Clamp (1.95 x Clamp (0.5 + 0 - 0)) = Clamp (0.975) = 0.95 = 95% chance to hit for each attack.

If the player they're attacking had 10% Defense then that'd instead work out at: 
Clamp(1.95 x Clamp (0.5 - 0.1)) = Clamp(0.78) = 0.78 = 78% chance to hit for each attack.

So with 10% Defense; against a stream of 10 identical such attacks the likelihood of being hit by at least one of them would be:
1-((1-0.78)*(1-0.78)*(1-0.78)*(1-0.78)*(1-0.78)*(1-0.78)*(1-0.78)*(1-0.78)*(1-0.78)*(1-0.78)) = 0.999999734 = 99.999%
And the likelihood of being hit by ALL of them would be:
((0.78)*(0.78)*(0.78)*(0.78)*(0.78)*(0.78)*(0.78)*(0.78)*(0.78)*(0.78)) = 0.083357758 = 8.336%
And the individual probability for each particular number of hits peaks at 8.



And like most theoretical estimations of cumulative probability; in practice it's about as useful as a fart in a hurricane.
But most people can understand that the attack has a 78% chance to hit them each time + they can be "lucky" or "unlucky".

[aethereal]

4 hours ago, Maelwys said:

I mean; the Devs outright told us exactly how it works twenty years ago.

Yes.  And the odds of 100 misses in a row at floored 5% miss chance are...  0.56%

 

On the off chance that any enemy actually makes 100 attacks against you, if the streakbreaker ever kicks in, it's because you've been extraordinarily lucky.

 

Streakbreaker has never once been a reason not to build defense.

 

Never.  Once.

[shortguy on indom]

5 hours ago, Maelwys said:

So a toon with 10% defense versus 10 incoming single target attacks in a row... can expect 22 of those 10 attacks to hit them?
OK.

• lolz... you know what its max can be, or you would not have mentioned it.  no need to put min maxes in there for clarity.

[Maelwys]

8 hours ago, aethereal said:

Yes.  And the odds of 100 misses in a row at floored 5% miss chance are...  0.56%

The formula to calculate the binomial distribution of a specific event is: 


 

where n is the number of trials, p is the probability of success on a single trial, and X is the number of successes.

Substituting in the stated values for this test case [ n=100, p=0.05, and X=0 ] and we get:



which reduces to: P(0)=0.005920529220334 = 0.592063% (a tiny smidge more than 0.56%; but close enough for government work)

However the problem is that the Streakbreaker doesn't care that all 100 misses in a row were at that floored 5% hit chance.
It cares that AT LEAST ONE of those attacks was at that floored 5% hit chance.

Read Weirdbeard's entire statement; noting the last paragraph:
"Because we do the lookup based on your worst to-hit in the series, the streak breaker is a bit less aggressive about breaking streaks than it might initially appear from the table. If you miss an ill-advised attack with a final to-hit of 0.15, you would in fact be allowed to continue the miss series for another 99 attacks, even if all the followup attacks are of capped to-hit, should you be unlucky enough."

But I certainly wholeheartedly agree with the implication that the Streakbreaker hardly ever matters for enemy attacks against you if you have a high enough defense buff.

...


All that said... I do however find it a bit dubious that in both this thread and the "new thread" @Shortguy is apparently repeatedly assuming that Enemy Hit Chance against you is always going to be reduced to 5%; because it's not.

If whatever attacking you is of a rank higher than minion, a level higher than +0 or is using an attack that possesses an inherent accuracy higher than 1.0 then their AccMods rises above 1.0... which will cause that 5% Hit Chance figure to become substantially higher. Realistically if the HitChance of an attack before applying Accmods was 5% then after applying Accmods it'll still not get above about ~10%; but those few percentage points still matter quite a lot whenever you're modelling a row of 100 such attacks; let alone 2,000,000.

 

Edited yesterday at 10:18 AM by Maelwys

[Maelwys]

@shortguy on indom - Hopefully after you correct the error in your AccMods clamping methodology (as mentioned in the other thread; AccMods only gets clamped *AFTER* you multiply it by the clamped product of that bracketed "BaseHitChance+ToHitMods-DefMods" bit on the right; not before!) then you should see that these lines:





are a big glaring issue as they're indicative of a fundamental error in the current formula you're using; which in turn is impacting the logic within the spreadsheet you uploaded.

The values for 45% Defense and 50% Defense should be identical here; providing that no other enemy ToHit buffs or player Defense debuffs are in play.
HitChance = Clamp( AccMods × Clamp( BaseHitChance + ToHitMods – DefMods ) )
CLAMP() imposes a minimum boundary of 0.05 and a maximum boundary of 0.95 on anything within its brackets.
So whenever the right hand side of the formula effectively reduces to CLAMP(0.5 - YourDefenceBuff) going beyond 0.45 (45%) defense will have zero effect.

If it was me, I'd probably use the "Possible Losing Streak" column to give an idea of how many total attacks on average within a given sample size are likely to miss... so for example cell C7 might be something like ROUNDUP(MEDIAN(0.05,(MEDIAN(0.05,(0.5-B6),0.95)*ACCMODS),0.95)*C$3,0) instead of ROUND(LN(C$3)/LN(1-B7)*-1,0)

CoX Forumites often (rightfully) argue about whether chasing 45% defense is worth it (because most PVE content doesn't require much mitigation in the first place and "killing stuff faster" is more fun; because hitting 45%+ defense solo on most toons inevitably requires some form of build compromise; and because without large swathes of Defense Debuff Resistance any defense you have can quickly be stripped off you just by a few unlucky hits from even-level mooks armed with swords or rifles, let alone an autohit Earthquake patch; etc. etc.) however if you can attain and keep 45% defense between yourself and the enemy after Defense Debuffs and ToHit Buffs have been factored in then you'll get the maximum level of mitigation from it and adding more defense on top simply won't matter.
 

Edited 22 hours ago by Maelwys

[Snarky]

17 hours ago, aethereal said:

Any time someone mentions the Streakbreaker in a defense thread, you can safely assume they have no idea what they're talking about.

Doesn't Streakbreaker simplify all the extreme cases and you do not need the maths?

[Maelwys]

5 minutes ago, Snarky said:

you do not need the maths

 

[Jacke]

47 minutes ago, Maelwys said:

 

 

First, do not encourage @Snarky.  He's more fun to watch that way.

 

Second....  Really.

 

"YEARS OF COUNTING yet NO REAL-WORLD USE FOUND for going higher than your FINGERS"

 

You must have never done anything with Logistics.  Or Pay.  Or sold anything written that was paid by word-count.  (BTW, that last one is rather tricky.)

 

Or done any electrical work or electronics design.  Or so many other examples.

 

Thank goodness for Mathematicians.  They have usually worked out whole areas of new Maths before they're actually needed.  Considering how hard that can be to get just right, that's really good for the rest of us.

 

 

[Uncle Shags]

Some people get mad at a derailment, but I am very much not!  My silly little earthquake mystery was resolved (mission accomplished) and I got useful info to help deal with it (bonus!). But now I get to host all this extra good stuff, including the glorious addition of an s at the end of math (super bonus!)! 

 

It's like hosting a small dinner party for coworkers that suddenly turns into a raging kegger. But the party is at the local pavilion, not my house, so I I don't have to clean up the mess. 

 

Who's up for a keg stand?! 

[Maelwys]

2 minutes ago, Jacke said:

Second....  Really.

Nah, not really.

_{I just needed a brief mental degauss after poking at functions in Excel for the last 30mins 🤮
(why you still have to jerry rig functions like Median() just to perform a simple Clamp() operation is beyond me...)}

[aethereal]

9 hours ago, Maelwys said:

which reduces to: P(0)=0.005920529220334 = 0.592063% (a tiny smidge more than 0.56%; but close enough for government work)

 

Sorry, you are of course correct, I turned the 9 into a 6 when looking at the number and transcribing it.

 

9 hours ago, Maelwys said:

However the problem is that the Streakbreaker doesn't care that all 100 misses in a row were at that floored 5% hit chance.
It cares that AT LEAST ONE of those attacks was at that floored 5% hit chance.

 

The odds of 100 misses in a row are even astronomically smaller if any of those attacks were at a higher hit chance than 5%.

 

The calculation of them being at a heterogeneous hit chance gets very complicated, but just to be clear, the odds of 100 misses in a row at 6% miss chance are 0.2%, so if there are some number of 6%s and some number of 5%s in the mix, then the odds are between 0.59% and 0.2%. 

 

This is all in a kind of insane world in which someone actually makes 100 attacks against you: I don't think that basically any enemy in the game attacks more than one time every two seconds for a long streak of attacks, so we're talking like more than three minutes of continuous battling -- plausible if you're say a tank fighting an AV solo, but almost no other situation.

 

9 hours ago, Maelwys said:

All that said... I do however find it a bit dubious that in both this thread and the "new thread" @Shortguy is apparently repeatedly assuming that Enemy Hit Chance against you is always going to be reduced to 5%; because it's not.

 

This is true, but makes the streak breaker even less relevant.

[shortguy on indom]

• MAYBE WE CAN WRITE THE AUTHOR OF THE FORMULA AT THE FINANACIAL INSTITUTION AND TELL THEM.
• THE SPREADSHEET IS SHOWING LOSING STREAKS, AND SHOWS WHAT IT SHOWS.  IF IT IS REALLY HARMING THE THREAD WILL REMOVE.

Edited 18 hours ago by shortguy on indom
more words

[shortguy on indom]

• FUN FUN.

[Maelwys]

  

33 minutes ago, aethereal said:

Sorry, you are of course correct, I turned the 9 into a 6 when looking at the number and transcribing it.

No worries. I think we're on the same page regarding the Streakbreaker's irrelevancy anyway. 



Whenever I said

23 hours ago, Maelwys said:

Also; the streakbreaker is largely irrelevant providing the final ToHitChance is 20% or below; as it'll only kick in after 100 misses as confirmed by Pohsyb and Castle years ago.

it was more a point of clarification that this: 

On 5/15/2025 at 4:35 PM, shortguy on indom said:

THE ABOVE TWO EXAMPLES IS LACKING THE EFFECT OF 'STREAKBREAKER.'

shouldn't have mattered; because the aforementioned two examples were only looking at 7-8 attacks in a row.

And then we started talking about attack sample sizes in the millions. Because of course that was where this conversation needed to go next.
_{(and I'm still uncertain if it happened in reaction to the Streakbreaker comments or if it was just a continuation of one of the earlier tangents. This is why we can't have nice things.)}

[Maelwys]

29 minutes ago, shortguy on indom said:

• FUN FUN.

'til 'er daddy takes the keyboard away?

 🏖️ 👦 👦
 

  

40 minutes ago, shortguy on indom said:

• MAYBE WE CAN WRITE THE AUTHOR OF THE FORMULA AT THE FINANACIAL INSTITUTION AND TELL THEM.
• THE SPREADSHEET IS SHOWING LOSING STREAKS, AND SHOWS WHAT IT SHOWS.  IF IT IS REALLY HARMING THE THREAD WILL REMOVE.

Or just; y'know, start using the brackets in the correct place and work from there.

It's HitChance = Clamp( AccMods × Clamp( BaseHitChance + ToHitMods – DefMods ) )
Not HitChance = Clamp( AccMods ) × Clamp( BaseHitChance + ToHitMods – DefMods ) 

so this bit: 

  

15 hours ago, shortguy on indom said:

Enemy AccMod = (enemy's power inherent Acc) X (enemy RankAcc) X (enemy LevelAcc)
    = 1 x 1.5 x 1.3                                      (note: these values taken from 'Attack Mechanics' wiki page).
    = 1.95
    = 0.95 due to clamping
New Enemy ChanceToHit = enemy AccMod x (enemy BaseHitChance - player's defense%)
    = 0.95 x (0.50 - 0.45)
    = 0.95 x (0.05)
    = 0.0475
    = 4.75%

 

Is throwing you off in every calculation you've made so far; including the derivative work in the spreadsheet.

Use an unclamped AccMod; multiply it by (enemy BaseHitChance - player's defense%) and THEN clamp the result.
And after that recheck your "45%" and "50%" defense figures again and by all means plug the correct figures into the spreadsheet.
But at the moment it's got a bad case of GIGO.

 

Edited 17 hours ago by Maelwys