League of Legends: Attack Damage vs Attack Speed

Game Theory, League of Legends Add comments

Jul 142011

A carry champion can be built in many ways, the most obvious ones being focusing on attack damage and attack speed. Which one is better? Is a combination of both feasible or is it better to have a pure build? What happens if we add critical hits? With some numbers and calculations it’s possible to get an answer and to, at least, have some backup theory for building a carry.

For the first part of the analysis let’s ignore critical hits or assume that they don’t happen; probability = 0. Under such assumption the following table shows how the average damage per second (ADPS) is modified by attack damage and speed.

Table 1:

AS\AD	50	100	150	200	250	300	350	400	450	500	550	600	650	700	750	800	850	900	950	1000
0.1	5	10	15	20	25	30	35	40	45	50	55	60	65	70	75	80	85	90	95	100
0.2	10	20	30	40	50	60	70	80	90	100	110	120	130	140	150	160	170	180	190	200
0.3	15	30	45	60	75	90	105	120	135	150	165	180	195	210	225	240	255	270	285	300
0.4	20	40	60	80	100	120	140	160	180	200	220	240	260	280	300	320	340	360	380	400
0.5	25	50	75	100	125	150	175	200	225	250	275	300	325	350	375	400	425	450	475	500
0.6	30	60	90	120	150	180	210	240	270	300	330	360	390	420	450	480	510	540	570	600
0.7	35	70	105	140	175	210	245	280	315	350	385	420	455	490	525	560	595	630	665	700
0.8	40	80	120	160	200	240	280	320	360	400	440	480	520	560	600	640	680	720	760	800
0.9	45	90	135	180	225	270	315	360	405	450	495	540	585	630	675	720	765	810	855	900
1.0	50	100	150	200	250	300	350	400	450	500	550	600	650	700	750	800	850	900	950	1000
1.1	55	110	165	220	275	330	385	440	495	550	605	660	715	770	825	880	935	990	1045	1100
1.2	60	120	180	240	300	360	420	480	540	600	660	720	780	840	900	960	1020	1080	1140	1200
1.3	65	130	195	260	325	390	455	520	585	650	715	780	845	910	975	1040	1105	1170	1235	1300
1.4	70	140	210	280	350	420	490	560	630	700	770	840	910	980	1050	1120	1190	1260	1330	1400
1.5	75	150	225	300	375	450	525	600	675	750	825	900	975	1050	1125	1200	1275	1350	1425	1500
1.6	80	160	240	320	400	480	560	640	720	800	880	960	1040	1120	1200	1280	1360	1440	1520	1600
1.7	85	170	255	340	425	510	595	680	765	850	935	1020	1105	1190	1275	1360	1445	1530	1615	1700
1.8	90	180	270	360	450	540	630	720	810	900	990	1080	1170	1260	1350	1440	1530	1620	1710	1800
1.9	95	190	285	380	475	570	665	760	855	950	1045	1140	1235	1330	1425	1520	1615	1710	1805	1900
2.0	100	200	300	400	500	600	700	800	900	1000	1100	1200	1300	1400	1500	1600	1700	1800	1900	2000
2.1	105	210	315	420	525	630	735	840	945	1050	1155	1260	1365	1470	1575	1680	1785	1890	1995	2100
2.2	110	220	330	440	550	660	770	880	990	1100	1210	1320	1430	1540	1650	1760	1870	1980	2090	2200
2.3	115	230	345	460	575	690	805	920	1035	1150	1265	1380	1495	1610	1725	1840	1955	2070	2185	2300
2.4	120	240	360	480	600	720	840	960	1080	1200	1320	1440	1560	1680	1800	1920	2040	2160	2280	2400
2.5	125	250	375	500	625	750	875	1000	1125	1250	1375	1500	1625	1750	1875	2000	2125	2250	2375	2500

The distribution of values provides some interesting information that is better seen on a graph.

Graph 1:

The graph shows that by boosting only attack damage or attack speed it isn’t possible to reach an average damage per second of 500, it is necessary to improve the other stat. The circular shape of the bands also indicates that the fastest way to reach an ADPS of 500 is by evenly boosting both stats. Moreover, as ADPS increases, the benefit of increasing both stats diminishes; which is indicated by the curves being less pronounced.

The conclusion we arrive is that while a pure attack damage or attack speed is a viable strategy it isn’t optimal. The best way to maximize ADPS is to improve both attack damage and attack speed simultaneously. For that, Table 1 can be used as a guide for the best buy path for items according to the boost they provide.

In another article we’ll see the effect of critical hits on maximizing ADPS. If you have any questions, suggestions or advice please leave a comment; we love the feedback.

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