Attack Speed Bonus Math

[Kahiera]

hi, i want to know how to find out the desired attack speed percent for an item i want to get a specific cooldown rate.

for example, my heros have a cooldown of 2.00 seconds. i have an item that has 1.00 damage per second. and a cooldown of 2.00 seconds. so to find the attack speed bonus for it. what is the formula for finding my item's attack speed (yes i know it would be 0.00% bonus)

for the equation, let:
a = hero cooldown
b = item's damage per second
c = item's cooldown rate
d = item's attack speed % modifier

i'm using gloves of haste for this

 

[Danis[h]]

so.. your problem is, what exactly?

 

[Kahiera]

i have damage per second, my desired attack speed, but i don't know the mathematical formula to get the attack speed bonus to put in my gloves of haste item.

what i'm trying to get is the % for the attack speed bonus

 

[meOme]

like this?

a = your hero's normal attack cooldown
b = your hero's normal attack speed
c = the item's attack speed bonus in %
d = your hero's attack speed with bonus
e = cooldown of your hero's attack with bonus

b = 1/a
d = b * (1 + c/100)
e = 1/d

==>

e = 1/(1/a * (1 + c/100))
e = a / (1 + c/100)

Or if you know base atk cooldown (a) and the resulting cooldown (e) and want to know the speed bonus you need (c):

c = (a/e - 1) * 100

Example:
You have a base cooldown of 2.0, and want the item to give the hero a cooldown of 0.8. --> a = 2.0, e = 0.8

c = (2.0/0.8 -1) * 100 = 150

--> you would need a 150% atk speed bonus.

 

[Kahiera]

in my map agility won't increase attack speed.

what's the difference between

a = your hero's normal attack cooldown
b = your hero's normal attack speed

i don't see the dps implemented anywhere

 

[NetherHawk]

what do you want to do with the damage per second? How does it fit into the context of the equation. You are asking for attack speed? Damage per second increases as your attack speed increases.

 

[emootootoo]

i was actually using that exact same 2.00 cd in one of my maps with the same idea and i still have the list i made...

so here:
it shows % attack speed and resulting cooldown assuming the hero has a base cooldown of 2.0 and has no other attack speed modifiers such as agility bonuses

and 10 is the highest you can get and 0.4 is the lowest you can get (since 400% increase is the max)

-80%	10
-79%	9.52381
-78%	9.09091
-77%	8.69565
-76%	8.33333
-75%	8
-74%	7.69231
-73%	7.40741
-72%	7.14286
-71%	6.89655
-70%	6.66667
-69%	6.45161
-68%	6.25
-67%	6.06061
-66%	5.88235
-65%	5.71429
-64%	5.55556
-63%	5.40541
-62%	5.26316
-61%	5.12821
-60%	5
-59%	4.87805
-58%	4.7619
-57%	4.65116
-56%	4.54545
-55%	4.44444
-54%	4.34783
-53%	4.25532
-52%	4.16667
-51%	4.08163
-50%	4
-49%	3.92157
-48%	3.84615
-47%	3.77358
-46%	3.7037
-45%	3.63636
-44%	3.57143
-43%	3.50877
-42%	3.44828
-41%	3.38983
-40%	3.33333
-39%	3.27869
-38%	3.22581
-37%	3.1746
-36%	3.125
-35%	3.07692
-34%	3.0303
-33%	2.98507
-32%	2.94118
-31%	2.89855
-30%	2.85714
-29%	2.8169
-28%	2.77778
-27%	2.73973
-26%	2.7027
-25%	2.66667
-24%	2.63158
-23%	2.5974
-22%	2.5641
-21%	2.53165
-20%	2.5
-19%	2.46914
-18%	2.43902
-17%	2.40964
-16%	2.38095
-15%	2.35294
-14%	2.32558
-13%	2.29885
-12%	2.27273
-11%	2.24719
-10%	2.22222
-9%	2.1978
-8%	2.17391
-7%	2.15054
-6%	2.12766
-5%	2.10526
-4%	2.08333
-3%	2.06186
-2%	2.04082
-1%	2.0202
0%	2
1%	1.9802
2%	1.96078
3%	1.94175
4%	1.92308
5%	1.90476
6%	1.88679
7%	1.86916
8%	1.85185
9%	1.83486
10%	1.81818
11%	1.8018
12%	1.78571
13%	1.76991
14%	1.75439
15%	1.73913
16%	1.72414
17%	1.7094
18%	1.69492
19%	1.68067
20%	1.66667
21%	1.65289
22%	1.63934
23%	1.62602
24%	1.6129
25%	1.6
26%	1.5873
27%	1.5748
28%	1.5625
29%	1.55039
30%	1.53846
31%	1.52672
32%	1.51515
33%	1.50376
34%	1.49254
35%	1.48148
36%	1.47059
37%	1.45985
38%	1.44928
39%	1.43885
40%	1.42857
41%	1.41844
42%	1.40845
43%	1.3986
44%	1.38889
45%	1.37931
46%	1.36986
47%	1.36054
48%	1.35135
49%	1.34228
50%	1.33333
51%	1.3245
52%	1.31579
53%	1.30719
54%	1.2987
55%	1.29032
56%	1.28205
57%	1.27389
58%	1.26582
59%	1.25786
60%	1.25
61%	1.24224
62%	1.23457
63%	1.22699
64%	1.21951
65%	1.21212
66%	1.20482
67%	1.1976
68%	1.19048
69%	1.18343
70%	1.17647
71%	1.16959
72%	1.16279
73%	1.15607
74%	1.14943
75%	1.14286
76%	1.13636
77%	1.12994
78%	1.1236
79%	1.11732
80%	1.11111
81%	1.10497
82%	1.0989
83%	1.0929
84%	1.08696
85%	1.08108
86%	1.07527
87%	1.06952
88%	1.06383
89%	1.0582
90%	1.05263
91%	1.04712
92%	1.04167
93%	1.03627
94%	1.03093
95%	1.02564
96%	1.02041
97%	1.01523
98%	1.0101
99%	1.00503
100%	1
101%	0.995025
102%	0.990099
103%	0.985222
104%	0.980392
105%	0.97561
106%	0.970874
107%	0.966184
108%	0.961538
109%	0.956938
110%	0.952381
111%	0.947867
112%	0.943396
113%	0.938967
114%	0.934579
115%	0.930233
116%	0.925926
117%	0.921659
118%	0.917431
119%	0.913242
120%	0.909091
121%	0.904977
122%	0.900901
123%	0.896861
124%	0.892857
125%	0.888889
126%	0.884956
127%	0.881057
128%	0.877193
129%	0.873362
130%	0.869565
131%	0.865801
132%	0.862069
133%	0.858369
134%	0.854701
135%	0.851064
136%	0.847458
137%	0.843882
138%	0.840336
139%	0.83682
140%	0.833333
141%	0.829876
142%	0.826446
143%	0.823045
144%	0.819672
145%	0.816327
146%	0.813008
147%	0.809717
148%	0.806452
149%	0.803213
150%	0.8
151%	0.796813
152%	0.793651
153%	0.790514
154%	0.787402
155%	0.784314
156%	0.78125
157%	0.77821
158%	0.775194
159%	0.772201
160%	0.769231
161%	0.766284
162%	0.763359
163%	0.760456
164%	0.757576
165%	0.754717
166%	0.75188
167%	0.749064
168%	0.746269
169%	0.743494
170%	0.740741
171%	0.738007
172%	0.735294
173%	0.732601
174%	0.729927
175%	0.727273
176%	0.724638
177%	0.722022
178%	0.719424
179%	0.716846
180%	0.714286
181%	0.711744
182%	0.70922
183%	0.706714
184%	0.704225
185%	0.701754
186%	0.699301
187%	0.696864
188%	0.694444
189%	0.692042
190%	0.689655
191%	0.687285
192%	0.684932
193%	0.682594
194%	0.680272
195%	0.677966
196%	0.675676
197%	0.673401
198%	0.671141
199%	0.668896
200%	0.666667
201%	0.664452
202%	0.662252
203%	0.660066
204%	0.657895
205%	0.655738
206%	0.653595
207%	0.651466
208%	0.649351
209%	0.647249
210%	0.645161
211%	0.643087
212%	0.641026
213%	0.638978
214%	0.636943
215%	0.634921
216%	0.632911
217%	0.630915
218%	0.628931
219%	0.626959
220%	0.625
221%	0.623053
222%	0.621118
223%	0.619195
224%	0.617284
225%	0.615385
226%	0.613497
227%	0.611621
228%	0.609756
229%	0.607903
230%	0.606061
231%	0.60423
232%	0.60241
233%	0.600601
234%	0.598802
235%	0.597015
236%	0.595238
237%	0.593472
238%	0.591716
239%	0.589971
240%	0.588235
241%	0.58651
242%	0.584795
243%	0.58309
244%	0.581395
245%	0.57971
246%	0.578035
247%	0.576369
248%	0.574713
249%	0.573066
250%	0.571429
251%	0.569801
252%	0.568182
253%	0.566572
254%	0.564972
255%	0.56338
256%	0.561798
257%	0.560224
258%	0.558659
259%	0.557103
260%	0.555556
261%	0.554017
262%	0.552486
263%	0.550964
264%	0.549451
265%	0.547945
266%	0.546448
267%	0.544959
268%	0.543478
269%	0.542005
270%	0.540541
271%	0.539084
272%	0.537634
273%	0.536193
274%	0.534759
275%	0.533333
276%	0.531915
277%	0.530504
278%	0.529101
279%	0.527704
280%	0.526316
281%	0.524934
282%	0.52356
283%	0.522193
284%	0.520833
285%	0.519481
286%	0.518135
287%	0.516796
288%	0.515464
289%	0.514139
290%	0.512821
291%	0.511509
292%	0.510204
293%	0.508906
294%	0.507614
295%	0.506329
296%	0.50505
297%	0.503778
298%	0.502513
299%	0.501253
300%	0.5
301%	0.498753
302%	0.497512
303%	0.496278
304%	0.49505
305%	0.493827
306%	0.492611
307%	0.4914
308%	0.490196
309%	0.488998
310%	0.487805
311%	0.486618
312%	0.485437
313%	0.484262
314%	0.483092
315%	0.481928
316%	0.480769
317%	0.479616
318%	0.478469
319%	0.477327
320%	0.47619
321%	0.475059
322%	0.473934
323%	0.472813
324%	0.471698
325%	0.470588
326%	0.469484
327%	0.468384
328%	0.46729
329%	0.4662
330%	0.465116
331%	0.464037
332%	0.462963
333%	0.461894
334%	0.460829
335%	0.45977
336%	0.458716
337%	0.457666
338%	0.456621
339%	0.455581
340%	0.454545
341%	0.453515
342%	0.452489
343%	0.451467
344%	0.45045
345%	0.449438
346%	0.44843
347%	0.447427
348%	0.446429
349%	0.445434
350%	0.444444
351%	0.443459
352%	0.442478
353%	0.441501
354%	0.440529
355%	0.43956
356%	0.438596
357%	0.437637
358%	0.436681
359%	0.43573
360%	0.434783
361%	0.433839
362%	0.4329
363%	0.431965
364%	0.431034
365%	0.430108
366%	0.429185
367%	0.428266
368%	0.42735
369%	0.426439
370%	0.425532
371%	0.424628
372%	0.423729
373%	0.422833
374%	0.421941
375%	0.421053
376%	0.420168
377%	0.419287
378%	0.41841
379%	0.417537
380%	0.416667
381%	0.4158
382%	0.414938
383%	0.414079
384%	0.413223
385%	0.412371
386%	0.411523
387%	0.410678
388%	0.409836
389%	0.408998
390%	0.408163
391%	0.407332
392%	0.406504
393%	0.40568
394%	0.404858
395%	0.40404
396%	0.403226
397%	0.402415
398%	0.401606
399%	0.400802
400%	0.4

edit:
and dps is just damage/cooldown

so if you have a weapon with 100 damage and a 0.4 second cooldown (400% attack speed bonus)

it is 100/0.4 = 250 dps

 

[Kahiera]

so according to your list, if i wanted my item to set my attack speed to 1.6, under the Gloves of Haste ability i would set it to .25 for 25% right?

 

[emootootoo]

yeah