| The fundamental is question: when does AR do more damage than CS? | |||||||||||||||
| Assumptions: | |||||||||||||||
| a) assume players and bows are otherwise identical | |||||||||||||||
| 1 | b) calculate both for DAP/DFC and D Elemental ammunition | ||||||||||||||
| Methodology: | |||||||||||||||
| 2-5 | a) calculate ΔDoTCS -- i.e. "how much more" damage a CS bow versus a non-imbued bow? Calculate for a number of different bow skills. | ||||||||||||||
| 6-7 | b) given each bow skill in (a), calculate AR_mod -- the percentage of armor is ignored by a similar AR bow. | ||||||||||||||
| 8-11 | c) calculate ΔDoTAR, which is the ratio of damage reduction (%red(AL)) for the original (AL) and modified (AL ') armor levels | ||||||||||||||
| 12-14 | d) for each bow skill, calculate the Equivalent Armor Level (EAL) at which ΔDoTAR results in a damage increase equal to ΔDoTCS | ||||||||||||||
| 15 | e) conclude that CS is more effective for MOBs with an AL lower than EAL, and AR more effective for MOBs with an AL greater than EAL. | ||||||||||||||
| DAP | D ELEM | ||||||||||||||
| 1 | Arrow Max | 30 | 26 | ||||||||||||
| Arrow Min | 24 | 19 | |||||||||||||
| Variance | 80.0% | 73.1% | |||||||||||||
| 2 | Critical Strike: (base bow - 60)/600 = %chance of crits | ||||||||||||||
| 3 | DoTCS(crit%) = (crit% * (MAX * 2)) +( (1- crit %) * (MAX (Var + 1) /2) ) | ||||||||||||||
| 4 | ΔDoTCS = ( DoTCS(crit' ) / DoTCS(10%) ) -1 | ||||||||||||||
| FOR DAP | ΔDoTCS | FOR D ELEM | ΔDoTCS | ||||||||||||
| bow | % crit | dam (crit) | dam (norm) | total dam | % increase | bow | % crit | dam (crit) | dam (norm) | total dam | % increase | ||||
| 5 | 120 | 10% | 6.00 | 24.30 | 30.30 | 0.0% | 5a | 120 | 10% | 5.20 | 20.25 | 25.45 | 0.0% | ||
| 180 | 20% | 12.00 | 21.60 | 33.60 | 10.9% | 180 | 20% | 10.40 | 18.00 | 28.40 | 11.6% | ||||
| 240 | 30% | 18.00 | 18.90 | 36.90 | 21.8% | 240 | 30% | 15.60 | 15.75 | 31.35 | 23.2% | ||||
| 300 | 40% | 24.00 | 16.20 | 40.20 | 32.7% | 300 | 40% | 20.80 | 13.50 | 34.30 | 34.8% | ||||
| 360 | 50% | 30.00 | 13.50 | 43.50 | 43.6% | 360 | 50% | 26.00 | 11.25 | 37.25 | 46.4% | ||||
| ==> this is pretty intuitive … your increased DoT is linear with the number of criticals you score. | |||||||||||||||
| the only real trick to the calculation is to make sure a crit is 2X MAX damage … | |||||||||||||||
| … whereas a normal hit must be adjusted for variance. | |||||||||||||||
| ==> so from the above, table, a bow skill of 300 geta a 40% crit rate, which does 32.7% more DoT than an unimbued (10% crit rate) bow when using DAP | |||||||||||||||
| 6 | AR_mod = % of AL ignored = (base bow - 120) / 400 | ||||||||||||||
| bow | AR_mod | ||||||||||||||
| 7 | 120 | 0% | |||||||||||||
| 180 | 15% | ||||||||||||||
| 240 | 30% | ||||||||||||||
| 300 | 45% | ||||||||||||||
| 360 | 60% | ||||||||||||||
| 8 | %red(AL) = | 1 | |||||||||||||
| (1 + AL / (200/3)) | |||||||||||||||
| ==> %red(AL) is the amount of damage reduction that a given AL provides | |||||||||||||||
| AL | %reduction | ||||||||||||||
| 9 | 0 | 100.0% | |||||||||||||
| 67 | 49.9% | ||||||||||||||
| 200 | 25.0% | ||||||||||||||
| 450 | 12.9% | ||||||||||||||
| 1000 | 6.3% | ||||||||||||||
| 11 | AL' = AL * (1 - AR_Mod) | ||||||||||||||
| 10 | ΔDoTAR = %red(AL' ) / %red(AL) | ||||||||||||||
| 12 | ==> so we need to solve for AL, where ΔDoTAR = ΔDoTCS for any given bow skill. | ||||||||||||||
| 13 | EAL = | ΔDoTCS * (200/3) | |||||||||||||
| ( ( ΔDoTCS +1 ) * ( 1 - AR_mod) ) - 1 | |||||||||||||||
| FOR DAP | FOR D ELEM | ||||||||||||||
| bow | CS crit % | ΔDoTCS | AR_mod | EAL | bow | CS crit % | ΔDoTCS | AR_mod | EAL | ||||||
| 14 | 120 | 10% | 0.0% | 0% | n/a | 14a | 120 | 10% | 0.0% | 0% | n/a | ||||
| 180 | 20% | 10.9% | 15% | 126 | 180 | 20% | 11.6% | 15% | 150 | ||||||
| 240 | 30% | 21.8% | 30% | 98 | 240 | 30% | 23.2% | 30% | 112 | ||||||
| 300 | 40% | 32.7% | 45% | 81 | 300 | 40% | 34.8% | 45% | 90 | ||||||
| 360 | 50% | 43.6% | 60% | 68 | 360 | 50% | 46.4% | 60% | 75 | ||||||
| 15 | Conclusion: | ||||||||||||||
| So there we have it: | |||||||||||||||
| "At a bow skill of 300 base, AR is better than CS for targets greater than AL81 using DAP | |||||||||||||||
| or AL90 using DFire." | |||||||||||||||
| How you apply this information to the critters in front of you is up to you. | |||||||||||||||