Rokjin
05-14-2006, 12:13 AM
<DIV>I am cross posting this with the Combat Discussion forum, as the critical damage bonus calculations are applicable to all classes..</DIV> <DIV> </DIV> <DIV>Up until the math I did today, I had believed Crits were a straight 30% damage boost. Due to the parses I have gathered for another post, and Chix's information (<A href="http://eqiiforums.station.sony.com/eq2/board/message?board.id=33&message.id=11629" target=_blank>http://eqiiforums.station.sony.com/eq2/board/message?board.id=33&message.id=11629</A>) I have now been able to get the exact damage added due to crits. You can read the lengthy post below if your interested in my method and math, or just skip to the summary at the bottom, below the graphs.</DIV> <DIV> </DIV> <DIV>First I will cite the Parse info.</DIV> <DIV> </DIV> <DIV><STRONG>Methodology:</STRONG></DIV> <DIV> </DIV> <DIV>No AA's in effect except for stat boost ones. No Combat Abilities were used, no combat haste/dps modifiers, no procs of any kind. Used only Defensive Stance (effective 333 Slashing skill). STR was at 325 throughout entire test. The mobs used for the test were "a juvenile lava crawler" in Lavastorm, all level 43 and ^^^ ups, with no debuffs on them. No buffs affected me during any of the parsing. This provides a direct baseline comparison for 1H vs DW damage and the crits for both. Ripostes were removed from the parse due to them using a different formula then auto-attack.</DIV> <DIV> </DIV> <DIV>Weapons used were: indium assault axe and 2x indium spatha. Both vendor bought. The 1H axe has 31.9 DR, the DWs have 23.9 DR each, giving a total DR of 47.8. 1000 hits with each weapon, delay of all weapons used is 1.6. 2000 Hits were used for Dual-wield, since that is equivalent to 1000 hits of the 1H.</DIV> <DIV>Parsing was done with ACT version 1.81.</DIV> <DIV> </DIV> <DIV>Results from 1H (31.9 DR, 1.6 delay, 1000 hits) (Min-Max damage ratio on all weapons used is 1:3)</DIV> <DIV>Non-Crits:<BR>Min hit: 32<BR>Average Hit: 65<BR>Max Hit: 96</DIV> <DIV> </DIV> <DIV>Crits:<BR>Min hit: 97<BR>Average hit: 101<BR>Max hit: 125<BR># of Crits: 112</DIV> <DIV> </DIV> <DIV>Results from DW(23.9*2 DR (47.<img src="/smilies/b2eb59423fbf5fa39342041237025880.gif" border="0" alt="SMILEY" />, 1.6 delay, 2000 hits)</DIV> <DIV>Non-Crits:<BR>Min hit: 24<BR>Average Hit: 48<BR>Max Hit: 72</DIV> <DIV> </DIV> <DIV>Crits:<BR>Min hit: 73<BR>Average hit: 76<BR>Max hit: 94<BR># of Crits: 197</DIV> <DIV> </DIV> <DIV>From this we can see that on average, crits were on average ~55-58% higher then the average non-crit on auto-attack. However Crit rate seemed to be at ~10%. Considering I have nothing boosting it, it may just be an effect of the 15 level difference between me and the mob I did the parsing on. The Crit rate is irrelevant to this discussion though, as we are looking at the crit damage, not crit rate. We can also see that the damage ratio is 1:3 (72/24 = 3 for DW and 96/32 = 3 for 1H). For CAs you can just take the displayed max damage, divide it by the min damage, and get a decimal, multiply that by 10 to get a ratio of x:10. Then you can reduce it to 3:5 or 4:5 (which most CAs seem to be)</DIV> <DIV> </DIV> <DIV><STRONG>Calculations:</STRONG></DIV> <DIV> </DIV> <DIV>Now we can start looking at things analytically and verify whether this is expected.</DIV> <DIV><BR>Most melee weapons seem to have a damage range of x to 3x. This is confirmed with the weapons in the above test, as well as my Blade of the Bixies.</DIV> <DIV><BR>Using the crit formula Crit damage = Max damage +1 to Max Damage * 1.3, then this gives us a possible crit range of:</DIV> <DIV><BR>3x to 3x*1.3 = 3.9x</DIV> <DIV><BR>Taking x = 1 to simply things, we have the following figures:</DIV> <DIV>Normal damage range = 1-3<BR>Crit damage range = 3-3.9</DIV> <DIV> </DIV> <DIV>The key thing is that any damage roll that is a crit, ie: hit for 1, add 30% since it's a crit = 1.3, is adjusted up to 3. How can we quantify this? Any normal hit below 2.3 that crits, is adjusted up to 3. Assuming a linear spread of hits, then 65% of hits will be 2.3 or below. (1.3/2 = 0.65)</DIV> <DIV> </DIV> <DIV>Thus we have that 65% of crits will do 3 damage, while the other 35% will do 3 to 3.9, with an average of 3.45 ((3+3.9)/2 = 3.45).<BR>Thus the average crit will be = 65% * 3 + 35% * 3.45 = 3.1575 ~= 3.16.</DIV> <DIV>Then the damage boost from a crit is average crit damage / average damage = 58%. This corresponds to the parse data.</DIV> <DIV> </DIV> <DIV>From this then we can see that each 1% of crit, gives you 0.58% more auto-attack damage with a 1-3 ratio weapon. As far as I can determine, ALL MELEE WEAPONS are 1:3 Ratio. This means that for any melee weapon, you auto-attack damage will be increased by 0.58% per each point of Crit you raise your crit chance.</DIV> <DIV> </DIV> <DIV>Bows seem to be different, some having 1:5 ratio, others having 1:3 and other having even 1:9. The smaller the ratio, the more damage boost you get from crits, since a larger amount of 'low crits' will be adjusted up to the max damage of the weapon. For example for a 1:5 ratio weapon the math would give:</DIV> <DIV><BR>Damage range = 1-5, crit damage range = 5-6.5, average normal hit = 3. Any normal hit for less then ~3.85 will be adjusted up. This means that ~71% of all normal hits that crit will be adjusted up to max damage. so then average crit damage is 71% * 5 + 29% * 5.75 = ~5.22. Then damage boost from crit = 74%.</DIV> <DIV>This means that for a weapon with 1:5 Ratio, 1% of crit will add 0.74% more auto-attack damage.</DIV> <DIV> </DIV> <DIV>Now we can look at CAs. Most of my Swashbuckler CAs are 3-5 and 4-5 damage ratio. Let's take a look at 3-5 first.</DIV> <DIV><BR>Normal damage range = 3-5, crit damage range = 5-6.5, average normal hit = 4. Any normal hit for less then ~3.85 is against adjusted up. In this case this means only 42% (0.85/2) of all normal hits that crit are adjusted up to max damage. So Average crit damage is 42% * 5 + 58% * 5.75 = ~5.44, then damage boost from crit is 5.44/4 = 36%.</DIV> <DIV> </DIV> <DIV>SO for CAs, we get a 0.36% damage boost from each point of crit, quite a bit less then auto-attack, but still more then the 30% assumed before.</DIV> <DIV> </DIV> <DIV>Finally we have the 4:5 ratio, which I will cover because it is an interesting case. Normal damage range is 4-5, crit damage range is 5.2-6.5. Yes, the lowest possible crit is LARGER then max damage. That's because the lowest possible normal hit 4 * 30% = 5.2, which is already larger then max normal damage. This case is simple then since every hit will be adjusted up by a straight 30%.</DIV> <DIV> </DIV> <DIV>So for 4:5 CAs, the crit increase is a straight 0.30% per crit point.</DIV> <DIV> </DIV> <DIV>So, for any attack who's damage ratio is LARGER then ~3.85/5 = 77:100 ratio, the Crit increase is a straight 30%. For any attack with a damage ratio LOWER then that the crit increase is larger then 30%. A 1:10 damage ratio weapon would have a crit increase of nearly 0.9% per crit point. As the ratio gets smaller and smaller, the crit continues to increase, flattening out, to a maximum possible damage boost of ~1.07% per point of crit.</DIV> <DIV> </DIV> <DIV>The actual calculation for finding this is:<BR>f(max,min) = ((((max/1.3)-min)/(max-min))*(max)+(1-(((max/1.3)-min)/(mad-min)))*(1.15*max))/((max+min)/2)</DIV> <DIV> </DIV> <DIV>Where max and min are the max and min damage ratios. IE: For most melee weapons, max = 3, min = 1. As a note, this equation is only valid<BR>for max > = 1.3 * min. When max is less then 1.3 * min, then every single possible critical will be above maximum damage, and the ratio that is used in the function will blow up. In those cases, it's easy to see that Crit increase is exactly 0.3% per point.</DIV> <DIV> </DIV> <DIV>To break this function down, the first part: ((max/1.3)-min)/(max-min))*(max) determines what percentage of your crits will hit for max damage + 1 (~max damage) and multiplies that by the max damage. This is the (max damage + 1) part of the average crit damage.</DIV> <DIV> </DIV> <DIV>The second part: (1-(((max/1.3)-min)/(mad-min)))*(1.15*max)) is the other percentage of crits that will hit for the average crit damage (ie: (max damage + max damage * 1.3)/2 = 1.15 * max damage.</DIV> <DIV> </DIV> <DIV>The third part ((max+min)/2) is just the average damage of the weapon's normal hits, which we divide the sum of the first two parts by to get the damage boost (assuming 100% crit).</DIV> <DIV><BR> </DIV> <DIV>I have graphed this function for min damage = 1, where y = the damage multiplier from 100% crit. x = max damage. You can see as the min:max ratio gets larger, so does the damage multiplier, though it tapers off, and if I continued the graph up to 1:100 Ratio, you would see it flatten out:</DIV> <DIV> </DIV> <DIV><IMG src="http://matkun.googlepages.com/critgraph.png"></DIV> <DIV> </DIV> <DIV>As you go across the bottom, the ratio increases from 1:1.3 up to 1:10.. This graph is good for Melee Weapons.</DIV> <DIV> </DIV> <DIV>Another graph that may be useful is for CAs. Since most seem to have a base of 5 Max damage, I created another graph, with Max damage kept constant at 5, and Min damage varying.</DIV> <DIV> </DIV> <DIV><IMG src="http://matkun.googlepages.com/critgraph2.png"></DIV> <DIV> </DIV> <DIV>As you go across the bottom, you can see the damage goes flat at 3.85:5, and beyond that it's just a 30% damage bonus. The lowest ratio on here is 1:5, with ~75% damage bonus. This graph is good for CAs.</DIV> <DIV><BR><STRONG><FONT size=5>Summary:</FONT></STRONG></DIV> <DIV> </DIV> <DIV>Raising your crit rate gives varying bonuses dependent on the Min:Max Damage ratio of your attack. Most Weapons are 1:3 Ratio, giving a ~0.58% damage increase per point of crit. Most CA's (atleast as a Swashbuckler) have a 3:5 Ratio, and get ~36% boost per crit.</DIV> <DIV> </DIV> <DIV>For any attack with a ratio of 1:X, you can use the first graph to determine the damage boost you get by looking at the X axis for the MAX Damage part of the ratio.</DIV> <DIV> </DIV> <DIV>For any attack with a ratio of X:5, you can use the second graph to determine the damage boost you get by looking at the X axis for the MIN Damage part of the ratio.</DIV> <DIV> </DIV> <DIV>Now looking at Blackguard's Luck, using a standard Swashbuckler 33/66 auto-attack to CA damage ratio, the ~14% crit we get gives us an ~8.1% damage boost for auto-attack, and a ~5.1% damage boost for CAs, which gives us a total of ~6% damage increase. Going to a 50/50 ratio gives ~6.6% damage increase, and 20/80 gives ~5.7% damage increase.</DIV> <DIV> </DIV> <DIV>So, depending on your auto-attack to CA ratio, 8 points of Blackguard's Luck will directly increase your damage ~5-7%.</DIV> <DIV> </DIV> <DIV>Comparing this to the Wisdom Double Attack boost, which gives a straight ~13.5% damage boost to auto-attack, then Double Attack currently boosts damage less then the crit boost if your auto-attack damage is less then 50% of your damage. This does not factor in Inspiration, burst damage boosts from Double Attack (for example with a bow), or other 'side' benefits of Double Attack. This means that with the nerf of procs on Double Attack (It seems now only things with 100% chance to proc (like Inspiration) hit on a double attack), the 'key' Wisdom Line DPS Booster is a bit weaker than Blackguard's Luck.</DIV> <DIV> </DIV> <DIV>When comparing STR and WIS lines though, if you are looking for DPS, keep in mind that the extra ripostes from Freehand Reversal, the skill boosts from Coule and the damage from Lunge Reversal all also add to DPS. Looking purely at Short-term CA damage though, STR line is superior in that regard.</DIV> <DIV> </DIV> <DIV>Please post any comments/questions/feedback below. I am not sure if this deserves a sticky, but if the mods feel like it or if the people of this forum feel it should be stickied, then go ahead.</DIV> <DIV> </DIV> <P><SPAN class=time_text>-edit: fixed spelling mistakes</SPAN></P> <P><SPAN class=time_text></SPAN><SPAN class=time_text>-edit2: fixed up graphs so you can actually read off the multiplier easier now.. reload the page if it's still showing the ones without gridlines</SPAN></P> <P><SPAN class=time_text>-edit3: ammended crit % part with corrections from readers, ~10% crit rate was observed in the parse, most likely due to level difference between me and the mob</SPAN></P><p>Message Edited by Rokjin on <span class=date_text>05-14-2006</span> <span class=time_text>07:33 AM</span>