Archer Attack Speed Basics

Elenacostel - Heavens Tear · January 2010

All of those examples agree with the math I posted:

0.648 => truncates to 0.64 => Rounds to 0.65 (up)
0.567 => truncates to 0.56 => Rounds to 0.55 (down)
0.4455 => truncates to 0.44 => Rounds to 0.45 (up)
0.5115 => truncates to 0.51 => Rounds to 0.50 (down)

None of these are counterexamples.

AndyNagato - Lost City · January 2010

except that when your decimal is < 5 you round down, not up. 1.14 would go to 1.10

Elenacostel - Heavens Tear · January 2010

Incarnata - Harshlands wrote: »

I would imagine that 1.15 seconds/attack was closer to 1.14 seconds/attack than 1.10 seconds/attack would be?

Oh wow, how did I miss that one?

Back to the drawing board...

EDIT: Here's the data I've collected so far. I am playing around with formulas such that I can get the resulting interval in-game.

Old       % Increase  Resulting   Resulting  Round    Round
Interval              Interval    Interval   Up/Down  Closest
                      Calculated  In Game
                      
1.10      30          0.7700      0.75       Down     Yes
1.30      12          1.1440      1.10       Down     No
1.45      12          1.2760      1.25       Down     No
0.55      25          0.4125      0.40       Down     Yes
0.55      30          0.3850      0.40       Up       Yes
0.80      19          0.6480      0.65       Up       Yes
0.70      19          0.5670      0.55       Down     Yes
0.55      19          0.4455      0.45       Up       Yes
0.55      07          0.5115      0.50       Down     Yes

Telarith - Sanctuary · January 2010

One way to track interval breakpoints, is dividing .05 by the percentage of the boost. This only works once one breakpoint is found, however.

25% is the easiest to track. Fists start at .7 interval, which is their breakpoint.

.7 * .75 = .525 While mathematically it is halfway between two intervals, the game rounds it down to .5 interval for an end attack rate of 2 per second.

Since the speed buff is 25%, or .25 faster, divide .05 by .25 to get .2 interval. Every -.2 interval, you reach the next breakpoint of 25% speed buff.

Each time a break point is reached though, your next -.05 interval has no actual effect while the speed buff is in effect. So .45 and .5 act the same under 25% speed buff, just like .65 and .7, etc. For every 4 units of -interval, your attack speed only changes 3 times. It repeats one of them twice.

Elenacostel - Heavens Tear · January 2010

Telarith - Sanctuary wrote: »

One way to track interval breakpoints, is dividing .05 by the percentage of the boost. This only works once one breakpoint is found, however.

25% is the easiest to track. Fists start at .7 interval, which is their breakpoint.

.7 * .75 = .525 While mathematically it is halfway between two intervals, the game rounds it down to .5 interval for an end attack rate of 2 per second.

Since the speed buff is 25%, or .25 faster, divide .05 by .25 to get .2 interval. Every -.2 interval, you reach the next breakpoint of 25% speed buff.

Each time a break point is reached though, your next -.05 interval has no actual effect while the speed buff is in effect. So .45 and .5 act the same under 25% speed buff, just like .65 and .7, etc. For every 4 units of -interval, your attack speed only changes 3 times. It repeats one of them twice.

My apologies, but you lost me there. I've tried understanding this for about 30 minutes, but I cannot comprehend what you are saying.

Telarith - Sanctuary · January 2010

Elenacostel - Heavens Tear wrote: »

My apologies, but you lost me there. I've tried understanding this for about 30 minutes, but I cannot comprehend what you are saying.

I added another quick way to check intervals, while answering a couple posts during it.

The game rounds to our benefit when a figure falls halfway between two intervals. Rounds down, giving us a lower interval in all cases.

The next I guess kinda has two parts. I'll leave out the first part, can cover it in second part I think.

First off, your existing -interval gives you your base, which is already known. -.2 interval on a .7 interval weapon gives you .5. Now speed buffs have a diminishing return when -interval comes into effect. The lower your interval, the smaller the change your speed buff affects. A 1.4 interval would have -.35 interval with 25% speed buff. A .6 interval would have -.15 with 25% speed buff.

For the effect it has on only moving 3 times for every 4 units of -interval (-.05), it's due to the rounding that is being done with the speed buffs. If you check the difference of your mathematical interval, and you'll get a clearer view. Each change with a 25% speed buff isn't .5; it's actually .0375 from .7 to .3 base interval. It won't be noticeable due to rounding, until you lose all remainders when you get four of them (4*.375 =1.5). There's other math that supports this, but it actually is much more confusing since it's more theory than formula. Proven theory, but unless already known doesn't help in explaining at all.

The interval loss is only in relation to the speed buff interval, not the base interval already modified by -interval gear. Only other thing I can think of to clarify.

EDIT: Added a 0 I missed to be .0375 (.05 * .75), and the .0375 from speed buff is consistent through all intervals in relation to 25% speed buff. Numbers change based off of speed buff number.

Elenacostel - Heavens Tear · January 2010

Can you demonstrate the steps to calculated a new attack interval, with the following set ups?

Old Interval: 1.30
% Increase: 12%

Old Interval: 0.55
% Increase: 25%

Old Interval: 0.55
% Increase: 30%

Legerity - Sanctuary · January 2010

I think Telarith's method might be able to explain why I ended up with an attack rate of 1.18a/s with a base of 1.2s/a (0.83a/s) using both demon QS and spark.

I noticed it was the same at that particular value but wasn't able to explain if even if I tried. I still don't fully comprehend Telarith's method but it sounds as though it may have the potential to be more accurate.

Now to wait for more clarification from Telarith.

Elenacostel - Heavens Tear · January 2010

Yeah, I think I might understand her better if she demonstrated it using an example. That's why I asked.

EDIT: Updated Table:

Old       % Increase  Resulting   Resulting  Round    Round    Source
Interval              Interval    Interval   Up/Down  Closest
                      Calculated  In Game
                      
1.10      30          0.7700      0.75       Down     Yes      Devoted
1.30      12          1.1440      1.10       Down     No       Elena Costel
1.45      12          1.2760      1.25       Down     No       Elena Costel
0.55      25          0.4125      0.40       Down     Yes      Cirdan
0.55      30          0.3850      0.40       Up       Yes      Cirdan
0.80      19          0.6480      0.65       Up       Yes      Kristoph
0.70      19          0.5670      0.55       Down     Yes      Kristoph
0.55      19          0.4455      0.45       Up       Yes      Kristoph
0.55      07          0.5115      0.50       Down     Yes      Kristoph
1.20      25          0.9000      0.85       Down++   No       Legerity
1.20      30          0.8400      0.85       Up       Yes      Legerity

Asterelle - Sanctuary_1381265973 · January 2010

I believe Telarith's argument is that the rounding operation is not distributive.

old interval = base interval from weapon - interval reduction from gear
interval decrease = 1 - attack speed increase

So one approach:

new interval = round(old interval * interval decrease)

An alternative approach:

new interval = round(base interval from weapon * interval decrease) - round(interval reduction from gear * interval decrease)

It is possible but calculating the first way seems more logical.

Personally I don't think any truncation to 2 decimal points is involved since that involves decimal arithmetic which is unnatural for modern computers and requires specialized data structures or hardware support. I only ever hear about decimal arithmetic used for financial calculations while normal programming is binary. It makes more sense for operations to be done in discrete units of .05 seconds so a 0.75 interval is stored more simply as a 15.

I've been looking at your data table.

Old       % Increase  Resulting   Resulting  Round    Round
Interval              Interval    Interval   Up/Down  Closest
                      Calculated  In Game
                      
1.10      30          0.7700      0.75       Down     Yes
1.30      12          1.1440      1.10       Down     No
1.45      12          1.2760      1.25       Down     No
0.55      25          0.4125      0.40       Down     Yes
0.55      30          0.3850      0.40       Up       Yes
0.80      19          0.6480      0.65       Up       Yes
0.70      19          0.5670      0.55       Down     Yes
0.55      19          0.4455      0.45       Up       Yes
0.55      07          0.5115      0.50       Down     Yes

The only data that look odd are the ones with 12% speed increase. To me it looks like that the "12%" part is incorrect and the skill is really doing something like 14% or 15% reduction. This is probably a skill description error or an error in adding the STR/DEX component of a genie skill.

EDIT: Ehh Legerity got weird numbers too.. maybe the second approach really is correct.

Elenacostel - Heavens Tear · January 2010

I was thinking the attack intervals are stored in an array, as follows:

[00] 0.00
[01] 0.05
[02] 0.10
[03] 0.15
[04] 0.20
....
[10] 0.50
[11] 0.55
etc...

Then, I figured that the array index is modified by the % value. To calculate the array index, you can divide the attack interval by 0.05, which results in a whole number (which is what Asterelle suggested).

But I have been experimenting in a spreadsheet, and unable to come up with a "formula" that generates the correct answer for all of them.

I've also tried normalizing vs. the minimum 0.20 seconds / attack, so that the array looks like this:

[00] 0.20
[01] 0.25
[02] 0.30
[03] 0.35
etc...

That did not work, either.

Incarnata - Harshlands wrote: »

I did not really follow Telarith's description either, but if we knew the weapon type (slingshot, bow, crossbow) for your various examples that would help us figure this out. (But that "12%" being wrong might also be enough.)

The 1.45 Interval came from Crimson Horn: Soulsmasher. No other gear.
The 1.30 Interval came from Wind and the Clouds. No other gear.

Legerity - Sanctuary · January 2010

Telarith - Sanctuary wrote: »

One way to track interval breakpoints, is dividing .05 by the percentage of the boost. This only works once one breakpoint is found, however.

25% is the easiest to track. Fists start at .7 interval, which is their breakpoint.

.7 * .75 = .525 While mathematically it is halfway between two intervals, the game rounds it down to .5 interval for an end attack rate of 2 per second.

Since the speed buff is 25%, or .25 faster, divide .05 by .25 to get .2 interval. Every -.2 interval, you reach the next breakpoint of 25% speed buff.

Each time a break point is reached though, your next -.05 interval has no actual effect while the speed buff is in effect. So .45 and .5 act the same under 25% speed buff, just like .65 and .7, etc. For every 4 units of -interval, your attack speed only changes 3 times. It repeats one of them twice.

I think I start to see this breakpoint phenomena.

My breakpoint interval for my old interval gear was 1.2 s/a.

With 25% speed increase

1.2*0.75 = 0.9 s/a

This means according to Telarith, my next unit after the breakpoint (0.9) is 0.85.

Which means 0.9 and 0.85 shares the same resulting interval ONLY if a speed increase is involved.

If no speed increase is involved, I believe Elena's rounding closest with the exception of exact half rounds down is valid.

...I think

edit: I'm playing around with the data provided by our fellow kin. I'll see what I can come up with.

Legerity - Sanctuary · January 2010

Legerity - Sanctuary wrote: »

I think Telarith's method might be able to explain why I ended up with an attack rate of 1.18a/s with a base of 1.2s/a (0.83a/s) using both demon QS and spark.

...

Wait a minute... I think I made a mistake here which may explain my odd values.

Unfortunately I do not have -0.1s interval bracers anymore so I cannot verify what I had remembered. Anyone willing to lend me a pair or test it themselves?

It had something to do with 0.8, 0.83, demon spark and QS which gave the same results of 1.18a/s.

I should be slapped for causing this much confusion. b:cry

edit: best to leave my 2 rows of "data" out for now. Will confirm when I can get wind and clouds or find -0.1s interval wrists to get a total of 1.2s/a interval.

Int_o	Inc	Int_c	Int_n	Int_a	Int_b	Change	Exact	Moves	Units
1.10	30%	0.7700	0.75	0.75	0.16667	0.0350	0.35	7	10
0.55	30%	0.3850	0.40	0.40	0.16667	0.0350	0.35	7	10
0.55	25%	0.4125	0.40	0.40	0.20000	0.0375	0.15	3	4
0.80	19%	0.6480	0.65	0.65	0.26316	0.0405	4.05	81	100
0.70	19%	0.5670	0.55	0.55	0.26316	0.0405	4.05	81	100
0.55	19%	0.4455	0.45	0.45	0.26316	0.0405	4.05	81	100
1.30	12%	1.1440	1.15	1.10	0.41667	0.0440	1.10	22	25
1.45	12%	1.2760	1.30	1.25	0.41667	0.0440	1.10	22	25
0.55	7%	0.5115	0.50	0.50	0.71429	0.0465	4.65	93	100

What I have so far:

Int_o is the original interval
Int_c is the calculated interval
Int_n is the nearest interval
Int_a is the actual in game interval
Int_b is the interval block of the increase in attack %
Change is Telarith's definition of change between intervals after inc%
Exact is the exact values of when there is no rounding occuring
Moves is how many value moves available for the unit cycle
Units is the amount of steps available where "x" moves occur

I still don't know how this ties in with the difference noticed in game so far. I need some time or clarification from Telarith.

Elenacostel - Heavens Tear · January 2010

Okay, so if we throw out Legerity's data, and assume my genie's 12% is just wrong, then we can all agree that "round to nearest" is the correct way to do things?

Smobo - Heavens Tear · January 2010

From the data I've seen, I think whatever the +12% was is buggy. It may also be the formula has some really small error, which makes it not work. More data for slower attacks may be needed to make sure its not just intervals which are larger (I think 1.25+ was stated).

Don't forget though:
"No amount of experimentation can ever prove me right; a single experiment can prove me wrong." - Albert Einstein

((Get back soon Elena, we all miss ya))

Legerity - Sanctuary · January 2010

Elenacostel - Heavens Tear wrote: »

Okay, so if we throw out Legerity's data, and assume my genie's 12% is just wrong, then we can all agree that "round to nearest" is the correct way to do things?

I still have a feeling my upcoming results will prove the method wrong. I explicitly remember unable to explain the silly 1.18a/s value.

Asterelle - Sanctuary_1381265973 · January 2010

Look how much of this topic is devoted to explaining a rare calculation discrepancy of one twentieth of a second.

Go archer forums! b:victory

Telarith - Sanctuary · January 2010

Oh, for just interval with a speed boost, it goes to the closest value near it, but if it is halfway between the two you round the value down. So after finding your adjusted interval could be done by dividing your end result by .05 and looking at the remainder to make it easier to see if needed.

Example 1.3 interval, 12% speed boost.

1.3 * .88 = 1.144.

Remove the part that is divisible by .05, and you're left with .044, which is closest to being round up. Any remainder that is .26 - .49 gets rounded up, any remained .01-.25 gets rounded down.

Tracking breakpoint is based solely off of the speed buff value itself, it won't change even with different weapons as long as the value of the speed buff is the same. 25% speed buff has a breakpoint every .2 intervals, which always falls on an odd number (i.e. .3, .5, .7, .9, etc.) This means the next time you get an extra -.05 interval added on, you will have a faster attack outside of speed buff, but with the speed buff you will have the exact same attack rate as you had without it. Because the speed buff loses one -.05 boost every .2 interval with a 25% speed boost.

For how often your interval break hits, you divide .05 (this is a constant in all of them) by the value of the speed buff. 25% gets you .2, 20% gets you .25, 12% gets you .4167, which is kinda unwieldy. Every time a breakpoint is reached, the next -interval will lose its benefit only when under a speed buff due to losing .05 from the speed buff bonus lowering.

It's essentially because of the fact that each speed buff leaves a certain portion of the interval behind. With 25%, 75% is left behind. 20%, 80% is left behind. 25% has 4 interval changes, but only 75% of that gets through. So 4 * .75 = 3, meaning only 3 times does in the speed buff, for every 4 changes out of the speed buff. 20% has 5 interval changes in between breakpoints, with only 80% of it counting in speed buff. Which gives .8 * 5 = 4, leaving 4 changes during speed buff for every 5 in base interval. Easiest way to see it, is finding the ending attack speed, vs. the -interval modifier the speed buff gives. Even there you will see the -interval modifier show up as often as the base interval, but in the actual attack column you'll see that one of those 5 is the same as the number above it.

Really wish I knew how to add tables in, I had made a table long ago for many of speed buff affects based off of the base interval for reference. Adding a table without it just kinda is a mess since they don't allow us to space it out on the post.

Asterelle - Sanctuary_1381265973 · January 2010

The breakpoint talk seems to be describing the effects of rounding over a range of initial intervals and is not an extra factor needed for any particular interval yes?

Ehh.. what this thread needs is a single person to record data over a wide range of intervals. Id do it if I had a computer... and if I wasn't abstaining from pwi <_<

Telarith - Sanctuary · January 2010

Asterelle - Sanctuary wrote: »

The breakpoint talk seems to be describing the effects of rounding over a range of initial intervals and is not an extra factor needed for any particular interval yes?

Ehh.. what this thread needs is a single person to record data over a wide range of intervals. Id do it if I had a computer... and if I wasn't abstaining from pwi <_<

Yep. All the rounding eventually hits the point where it doesn't round to our benefit after X number of times. Basically there's a bunch of different ways to find whichever particular value you want quickly; it all depends on what you want mostly. Came up with a bunch of different patterns when I did my chart for interval, and mostly just use them as needed. Hard to explain them, because I didn't use a formula to get them. That's why my posts seem kind of strange; I use math theory over formula, and end up having to figure out the formula to explain it. Doesn't always quite work though.

Elenacostel - Heavens Tear · January 2010

Telarith - Sanctuary wrote: »

Really wish I knew how to add tables in, I had made a table long ago for many of speed buff affects based off of the base interval for reference. Adding a table without it just kinda is a mess since they don't allow us to space it out on the post.

Use the [Code] tag, which allows you to space out everything manually.

Im_Grumpy - Dreamweaver · June 2010

Susaku - Heavens Tear wrote: »

Interval is So Offensive! Especially in PvP!
Slingshot FTW > Rest

against barbs & BMs, xbow ftw!

Zhadi - Archosaur · June 2010

Im_Grumpy - Dreamweaver wrote: »

against barbs & BMs, xbow ftw!

bow....
xbows have such a low min damage that makes breaking a heavy's charm a pain in the **** sometimes...

Iturothi - Heavens Tear · July 2010

Yet another great addition by Elenacostel, Danke. ^^

nxb · July 2010

Hello i am nood at interval. i think something mess up with my stuff
here is my story.

i am a sin 100 i have
Cape event =-0.5
tt 99 wrist and boot give me =-.15 because wrist -.1 and bonus from tt 99 gold
rank amor =-.5
and dagger lvl 80 with .-5
well my base speed is 2.0
spark is 2.86

then after i get my nir legging with -.5 invterval
my base speed goes from 2.00 to 2.22
however after i spark 2.86 still stay at 2.86 no change
do you know what happen ?

Legerity - Sanctuary · July 2010

nxb wrote: »

Hello i am nood at interval. i think something mess up with my stuff
here is my story.

i am a sin 100 i have
Cape event =-0.5
tt 99 wrist and boot give me =-.15 because wrist -.1 and bonus from tt 99 gold
rank amor =-.5
and dagger lvl 80 with .-5
well my base speed is 2.0
spark is 2.86

then after i get my nir legging with -.5 invterval
my base speed goes from 2.00 to 2.22
however after i spark 2.86 still stay at 2.86 no change
do you know what happen ?

Pre nirvana @ 2.0 means an interval of 0.5 s/attack. With spark this becomes 0.5*(0.75) = 0.375 s/att. Since it's exactly at the half mark, we round down to the benefit of the user so 0.35 s/att. This becomes 2.86 attacks per second.

With nirvana, your interval is now 0.45 s/attack. With spark this becomes 0.45*(0.75) = 0.3375 s/att which is rounded to 0.35 s/attack. This is the same result as above, resulting in an identical attack rate after demon spark.

Hope this helped.

nxb · July 2010

Well so is there anyway i can fix this. by getting the nirvinia dagger will change my speed?

Legerity - Sanctuary · July 2010

nxb wrote: »

Well so is there anyway i can fix this. by getting the nirvinia dagger will change my speed?

Getting an additional -0.05s interval will be an important breakpoint for you as you break the 2.86a/s and end up with 3.33a/s.

If you are lucky and manage an additional -0.1s interval, you will reach 4a/s.

How you go about getting the additional -interval is up to you. There are a few options but all are fairly expensive. The cheapest for your situation would be TT99 lionheart ornaments bonus of -0.05s, followed by a scroll of tome, followed by rank 8/nirvana dagger with -0.1 (depending on luck).

Dagger base speeds are the same regardless of which one you get so simply getting nirvana daggers won't "fix" your problem. You could always use fist/claws if you find the interval system unbearable in your situation.

Asterelle - Sanctuary_1381265973 · July 2010

Legerity - Sanctuary wrote: »

Dagger base speeds are the same regardless of which one you get so simply getting nirvana daggers won't "fix" your problem. You could always use fist/claws if you find the interval system unbearable in your situation.

Well the g13 nirvana dagger is the only one with -.1 interval I think.

nxb · July 2010

Thx a lot.
if i have nir dagger my speed will be 3.33
i am saving for it anyways

Archer Attack Speed Basics

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