FYI: 100 APM Rounding

[Aio]

Evening,

Got me thinking today in a separate thread about reload buffs on tools/faps not just weapons.

I used a 100apm knife (Imp7) to show that reload buffs have an effect not just on guns, but melee too.

It got me thinking... how is the extra cost truly factored in. So I did a little decay testing:

First, to confirm the Imp7 decay as 12.600pec:

Initial TT: 499.44 + 399 Nova = 499.44602.

1 Use TT: 499.32 + 999 Nova = 499.32002.

Diff: 0.12600. Perfect. (It's an ancient weapon so having rounded decay is fairly normal). Now, using an (L) Ares + Thorifoid hat I get 4% + 5% reload buff, so 9% overall.

Theoretically, as the APM is 100, this would give 109 APM. But we know that we can't exceed 100APM, and it is compensated in extra damage (the initial linked thread proves this). So, the additional damage should be (thanks to the nice and simple 100APM) 9%:

Old Max: 42 DMG

42*0.09 = 3.78

New Max: 45.78 DMG

However, when testing the decay using the reload buffs above:

Initial TT: 499.58 + 553 Nova = 499.58448.

1 Use TT: 499.44 + 399 Nova = 499.44602.

Decay: 0.13846. (13.846 pec).

Expected decay should be: 12.6*1.09 = 13.734.

So there is a mis-match of 0.112 pec... or an overall increase of 13.846/12.6 = 1.09888*%.

Where's the extra decay coming from? Is it a rounding error? If I set the max dmg as 46, then the %dmg increase is 46/42 = 1.0952%. 1.09888% gives 46.1533*.

It's really odd. So to make it a bit more complex, I tested the overall decay on Imp7 T5 (5x DMG) + Melee Trauma IV:

Expected (unbuff) decay: Knife*1.5 +Amp = 12.6*1.5 + 4.444 = 23.34400.
Expected (buff) decay: (Knife*1.5 + Amp) * 1.09 = (12.6*1.5 +4.444)*1.09 = 25.44496 (25.4450)


Tested decay (with Buff, 9%):

Amp Initial TT: 179.95 + 885 Nova = 179.95116
Knife Initial TT: 499.79 + 774 Nova = 499.79227


Amp 1 Use TT: 179.90 + 770 Nova = 179.90331
Knife 1 Use TT: 499.58 + 553 Nova = 499.58448


Amp Decay: 0.04785 (4.785pec)
Knife Decay: 0.20779 (20.779pec)

Overall Decay: 25.564

Again, higher than the expected (25.4450). %wise, that's 1.0951% increase.

Now to throw a spanner in the works.. Expected max dmg from the knife, enhancers, amp and buff is:

(42*1.5 + 20) * 1.09 = 90.47.

However, I have stoichastically tested the damage, and received (text) outputs of 91.0 damage. If this was the case, then the damage increase is in percentage, 91/83 = 1.09639%. Using this percentage, the expected decay is: 25.594 pec.

So:

Expected (90.47 dmg) decay: 25.445
Tested decay: 25.564
Correct (91.0 dmg) decay: 25.594.

_______________________________________________

Can anyone work out how/where MA or I have got the rounding wrong? It seems that in some cases, you will make yourself less economical by buffing past 100 APM (naked knife >100 costs more than it should), and in other cases you will make yourself more economical (amped, enhanced knife costs less than it should).

Apologies in advance for all the numbers

 

[SirAzzah]

Was 45.78 the highest max damage you saw during use or maybe you will see extra damage too?
Thanks for taking the time to do the test! Interested to see the results ?

 

[Aio]

Was 45.78 the highest max damage you saw during use or maybe you will see extra damage too?
Thanks for taking the time to do the test! Interested to see the results ?

I don't use the knife much naked, usually with max enhancers + amp.

Interestingly, I just got a 91.2 dmg. Theoretically it should be 83*1.09 = 90.47.

At 91.2, that is a % increase on max dmg = 91.2/83 = 1.0988. Suspiciously close to 1.10...

 

[Aio]

OK, you ready for it to get real freaky?

I just tried out the T5 Imp7 + Amp with:

Ares (L) +4%, Thorifoid Helmet +5%, and X2 pill +16%.

Overall, +25% reload. Max damage = 83, so my expected max damage is 83*1.25 = 103.75.

I am getting recorded damages of 110.7. That's a 33.37% damage increase.

I have a feeling that the compensation mechanism is either seriously bugged (in my favour ) or is doubly compensating for extra critical hits:

If you have a 5% CH rate on 100APM, that means 5 crits per min. If you have a 5% CH rate on 125APM, that's 6.25 crits per min. But - the crit increase should already be compensated by the initial extra damage...

(Incidentally, this means I'm reaching 185 old-school DPS at tier 5 with this knife...)

 

[krogfan]

OK, you ready for it to get real freaky?

I just tried out the T5 Imp7 + Amp with:

Ares (L) +4%, Thorifoid Helmet +5%, and X2 pill +16%.

Overall, +25% reload. Max damage = 83, so my expected max damage is 83*1.25 = 103.75.

I am getting recorded damages of 110.7. That's a 33.37% damage increase.

I have a feeling that the compensation mechanism is either seriously bugged (in my favour ) or is doubly compensating for extra critical hits:

If you have a 5% CH rate on 100APM, that means 5 crits per min. If you have a 5% CH rate on 125APM, that's 6.25 crits per min. But - the crit increase should already be compensated by the initial extra damage...

(Incidentally, this means I'm reaching 185 old-school DPS at tier 5 with this knife...)

110,7 x 0,75.......both ways are % just that one way seems to match out ome but allso seem wrong

 

[Aio]

110,7 x 0,75.......both ways are % just that one way seems to match out ome but allso seem wrong

Interesting... looks like MA are using a bizarre way of working percentages.

Instead of adding and multiplying, they are subtracting and dividing:

Correct:

(100+25)/100 = 1.25 * 83 = 103.75.

Incorrect:

(100-25)/100 = 0.75

83/0.75 = 110.7.

Also works with the 9% reload:

(100+9)/100 = 1.09 * 83 = 90.47

(100-9)/100 = 0.91

83/0.91 = 91.2

_____________

At 30% I would expect:

83/0.7 = 118.57

rather than

83*1.3 = 107.9

Anyone got Xmas Ring, Perf Ares and Thorifoid helmet to test?

 

[Darth Revan]

So you are getting higher dps and higher decay?
If so, what does the dmg/pec now equal? do you get a better result? does it equal out? or are you worse off?
This is all very interesting and shows how an easy mistake in code can cause unexpected outcomes!

 

[Aio]

So you are getting higher dps and higher decay?
If so, what does the dmg/pec now equal? do you get a better result? does it equal out? or are you worse off?
This is all very interesting and shows how an easy mistake in code can cause unexpected outcomes!

Looking at the data, it confirms that MA are using an incorrect way of adding damage. However, they use the same modifier for both damage and decay, so economically it is the same.

In effect, you will get a greater benefit the farther above 100 APM you can reach, for your DPS (but your DPP will stay static).

If you have 100 APM base (as I have) the calculations are simple:

New Max Damage = Old Max Damage / ((100-%ReloadBuff)/100)

New Decay = Old Decay / ((100-%ReloadBuff)/100)

Now, to see what would happen when you start below 100 APM and buff above it (probably the most useful for those mod merc users).

I used a Mir-1 fist (4.0 max damage) and buffed to 21% reload. Mir-1 has a 92 base reload. Max recorded damage was 4.8, which is a 20% increase or 0.83* using MA's logic.

Now, I can see what they are doing.

First, you find the new APM (with MA's backwards calculation):

92 / ((100-21)/100) = 116.5 (Your new APM, so a 16.5% reload buff effective).

Then, you do as before:

4.0 / ((100-16.5)/100) = 4.8.

Obviously there is a lot of rounding here but if someone could give me max damages (and buff%) using a mod merc that would involve 1 more degree of accuracy I think I may have cracked it though.

Overall formula (which works for any weapon):

New Max Damage = Old Max Damage / ((100-((APM/(100-BUFF)/100)-100))/100).

If the bolded section is less than zero, then the equation is not used (you are below 100APM even with buffs).

Worked example with Mod Merc & 30% reload buff:

67/((100-((87/(100-30)/100)-100))/100) = 88.5 new max damage. (which is a 32% dmg increase...)

Make sense?

 

[krogfan]

Looking at the data, it confirms that MA are using an incorrect way of adding damage. However, they use the same modifier for both damage and decay, so economically it is the same.

In effect, you will get a greater benefit the farther above 100 APM you can reach, for your DPS (but your DPP will stay static).

If you have 100 APM base (as I have) the calculations are simple:

New Max Damage = Old Max Damage / ((100-%ReloadBuff)/100)

New Decay = Old Decay / ((100-%ReloadBuff)/100)

Now, to see what would happen when you start below 100 APM and buff above it (probably the most useful for those mod merc users).

I used a Mir-1 fist (4.0 max damage) and buffed to 21% reload. Mir-1 has a 92 base reload. Max recorded damage was 4.8, which is a 20% increase or 0.83* using MA's logic.

Now, I can see what they are doing.

First, you find the new APM (with MA's backwards calculation):

92 / ((100-21)/100) = 116.5 (Your new APM, so a 16.5% reload buff effective).

Then, you do as before:

4.0 / ((100-16.5)/100) = 4.8.

Obviously there is a lot of rounding here but if someone could give me max damages (and buff%) using a mod merc that would involve 1 more degree of accuracy I think I may have cracked it though.

Overall formula (which works for any weapon):

New Max Damage = Old Max Damage / ((100-((APM/(100-BUFF)/100)-100))/100).

If the bolded section is less than zero, then the equation is not used (you are below 100APM even with buffs).

Worked example with Mod Merc & 30% reload buff:

67/((100-((87/(100-30)/100)-100))/100) = 88.5 new max damage. (which is a 32% dmg increase...)

Make sense?

Mod merc has been altered, its working the way its "supposed" to work, probably the most crucial fix since it has impact in events. For you others it has no real financial impact since you pay for the damage you get.

//Linz

 

[Aio]

Mod merc has been altered, its working the way its "supposed" to work, probably the most crucial fix since it has impact in events. For you others it has no real financial impact since you pay for the damage you get.

//Linz

But has it been altered, as it should (via the above formula) or by some other way? Care to post your max dmg and decay?

 

[krogfan]

But has it been altered, as it should (via the above formula) or by some other way? Care to post your max dmg and decay?

Lent the merc to a friend atm but its the reverse way of counting % compared to your way

In the old way it became a too strong tool for events, hemce the change. Actuallya bit interesting that they changed only for this weapon but not for other

 

[Piotr]

Too many numbers in this thread for me to comb through but here's stuff about MM:

I think ur math is right cause when MM was bugged, with 30% buff it was easy to see that actual gain was 42,8%+- which corralates with ur formula (100/0.7=142.85).

Atm MM with 28% speed buff (~38,8% increase) gives extra 19.044% decay n ammo usage which again corralates with numbers mentioned above (86apm*1.388=119.368 so pretty close)

 

[Aio]

Lent the merc to a friend atm but its the reverse way of counting % compared to your way

In the old way it became a too strong tool for events, hemce the change. Actuallya bit interesting that they changed only for this weapon but not for other

Too many numbers in this thread for me to comb through but here's stuff about MM:

I think ur math is right cause when MM was bugged, with 30% buff it was easy to see that actual gain was 42,8%+- which corralates with ur formula (100/0.7=142.85).

Atm MM with 28% speed buff (~38,8% increase) gives extra 19.044% decay n ammo usage which again corralates with numbers mentioned above (86apm*1.388=119.368 so pretty close)

So MA know about the issue with their calculation, but only changed it for mod merc.

What goes through their minds!

 

[Piotr]

So MA know about the issue with their calculation, but only changed it for mod merc.

What goes through their minds!

It was changed for all weps as it was not a weapon specific issue, all weps gets same boost from faster reload (% wise).
The fix was because before that with 30% buff, u got the extra 42.8% dmg AND u got ur attack speed up to 100. Now all works fine

 

[Aio]

It was changed for all weps as it was not a weapon specific issue, all weps gets same boost from faster reload (% wise).
The fix was because before that with 30% buff, u got the extra 42.8% dmg AND u got ur attack speed up to 100. Now all works fine

Mod Merc (apparently) works fine.

But as I've shown, with Imp7 I'm receiving too much damage because the mathematics are wrong.

MA are using subtract, divide (as it were before) when they should be adding, multiplying (as apparently they are now with Mod Merc).