Diablo® III

Analysis Of Sharpshooter Skill

After looking around the web ALOT, I realized that not too much analytical information was published about this remarkable and unique skill regarding its real impact on your Critical Hit Chance in particular, and your DPS in general.

I also found that most of the fan-published information is, while extremely interesting (including graphs, 2d color plots, and matrices), are based on various simulation techniques - and thus each publication has slightly different results and non of them are accurate "enough" for my analytic and somewhat crazy mind.

After some thought, I realized there is a gaping hole I can fill regarding the statistical analysis of this skill, utilizing 3 different courses in applied statistics I completed.

Warning, the following is NOT for non mathematical/statistical oriented minds. Here is the Statistical Analysis producing a real CHC value that is a function of initial CHC, and APS:
https://skydrive.live.com/redir?resid=F94AD530D6C3F80B!119&authkey=!AKL39o_bal0x1-U

Using my formulation, I also created a basic Excel sheet to demonstrate the calculation of the real CHC and the DPS gained by using SS:
https://skydrive.live.com/redir?resid=F94AD530D6C3F80B!117&authkey=!AMtfixjg0RYROuY

I would love to have your feedback.
Thank you,
Amit.
Edited by Amitbl#1196 on 7/5/2012 4:40 AM PDT
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the data in the excel file cannot be changed?
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Not while you view it from within my skydrive since i don't want anyone to change my calculation expressions. Plus, I intend to improve and add more features into that spreadsheet, can't do that if random people are messing with my sheet ;)
Download a copy if u wish to make changes to it. skydrive lets you do that without a problem.
Edited by Amitbl#1196 on 7/5/2012 6:36 AM PDT
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Very nice work. I've been waiting for someone to do this, but it's quite complicated. Not too much info is out there because averaged "dps" is impossible to quantify.. but here's a start, with your assumptions. And the result seems quite significant - 17% dps increase with your average 25%/200% crit/dmg stat, and that's not taking into account the length of a fight. Many people say sharpshooter dps is 'fake' dps but it's impossible to deny that it does increase your dps.
Your model makes sense - as your base crit increases, sharpshooter's effectiveness decreases.
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Thank you.
I'm glad you agree that this type of analysis had to be done. I've been poking around the web for weeks until I decided to pick up the gauntlet and just do this myself.

Apparently the averaged dps is possible to quantify - under certain assumptions.
As I started this - I set a goal to find a lower-bound computation for the SS gain, one that is very close to the real numbers - and I think that goal has definitely been reached.
Furthermore, some of my assumptions can be quantified and put into account in the formula aswell - and while I'm wondering whether I should inject them in there, It will turn this already hard to understand analysis into a complete statistical mess.
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It's interesting your little calculator on SS. A lot of people say that SS really drops off after about 25% crit chance.

According to your calculator, assuming 25% crit chance and using a 2hxbow, SS will offer 5.6% crit chance, with an overall dps increase of 8.5%. That's still pretty substantial.

For those of you too lazy to look at the spreadsheet: Assuming 1 attacks per second.

Critical Hit Chance-----Gained Critical Hit Chance-----Increased damage
5%-----------------------------------10.73%-----------------------------------16.09%
10%-----------------------------------9.12%-----------------------------------13.68%
15%-----------------------------------7.76%-----------------------------------11.64%
20%-----------------------------------6.61%-----------------------------------9.91%
25%-----------------------------------5.63%-----------------------------------8.44%
30%-----------------------------------4.8%-------------------------------------7.2%
35%-----------------------------------4.09%-----------------------------------6.13%
40%-----------------------------------3.48%-----------------------------------5.22%
45%-----------------------------------2.95%-----------------------------------4.43%
50%-----------------------------------2.49%-----------------------------------3.74%

We all know of course the following factors that can't really be calculated, which adds to the value of SS.
1. Time between packs ensures near 100% CC for front damage loading
2. The process of kiting itself lends to periods of time with no firing, which increases the effectiveness of SS dramatically for when you do fire.
3.The satisfaction you get as a player when you stare at your character sheet and see the DPS climb 5k at a time until it doubles! (That feeling can't be replaced)
Edited by Mattyboyhoy#1969 on 7/5/2012 11:24 AM PDT
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I somewhat agree with those people's observations. Stacking CHC has a negative impact on your relative DPS gained by SS, but not on your absolute DPS value. There should be an inflection point somewhere in 25-35% range of CHC (that point is also dependent on other parameters) where its impact on the SS gain gets so taxing that it the difference between the absolute dps without SS and asbolute dps with SS is small to the extent that it makes hunting for CHC items not worthwhile anymore.

That relation between absolute DPS and CHC when using SS will be my next little project btw, but I'm guessing its gonna be much, much harder to analyze.

that said, its important to understand that CHD is the variable with the strongest impact on the DPS increase (both relative, and absolute) when using SS.
Edited by Amitbl#1196 on 7/5/2012 11:46 AM PDT
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I haven't downloaded your sheet yet as I'm busy, but does it take into account that your crit remains at the stacked level for 1 second before reseting? If so visit this:

http://us.battle.net/d3/en/forum/topic/5835833998

Then contact me at hiredhit007@aol.com, I've been trying to do some much needed actual DPS impressions for realistic damage. However I will have to look over your math first.
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No it doesn't take into account that the crit chance is reset only after another shot or two are made
It also does not take under account that the first shot off is a crit 100%.

These two matters over-complicate things on an already complicated mathematical analysis.
the latter is fairly easy to add to the final dps gain.
the former is hard to extrapolate. I can try if that's what you need but I don't see the point in it.

The reason for my lack of interest - is that the really big impact is the wrong assumption that you stand still and shoot at enemies from the beginning of the fight to the end. SS benefits the most from moving around and kiting during fights (a thing that ALWAYS happens).
That is something that is downright impossible to analyze, and therefor I mentioned in the analysis that the best and easiest way to get a better estimate on the real-life CHC is to add 2-3% to the CHC gain.

Regardless, as I mentioned on my mathematical analysis, the longer the fights, the better the real CHC converge into the CHC predicted by the formula.
Edited by Amitbl#1196 on 7/6/2012 2:06 AM PDT
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I haven't downloaded your sheet yet as I'm busy, but does it take into account that your crit remains at the stacked level for 1 second before reseting? If so visit this:

http://us.battle.net/d3/en/forum/topic/5835833998

Then contact me at hiredhit007@aol.com, I've been trying to do some much needed actual DPS impressions for realistic damage. However I will have to look over your math first.

Don't ever take this guy seriously. Hes a kid who scammed me, using his "highly rated" topic as a proof that hes a safe guy to trade with.. guess what? I lost my set (500$)
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No it doesn't take into account that the crit chance is reset only after another shot or two are made
It also does not take under account that the first shot off is a crit 100%.

These two matters over-complicate things on an already complicated mathematical analysis.
the latter is fairly easy to add to the final dps gain.
the former is hard to extrapolate. I can try if that's what you need but I don't see the point in it.

The reason for my lack of interest - is that the really big impact is the wrong assumption that you stand still and shoot at enemies from the beginning of the fight to the end. SS benefits the most from moving around and kiting during fights (a thing that ALWAYS happens).
That is something that is downright impossible to analyze, and therefor I mentioned in the analysis that the best and easiest way to get a better estimate on the real-life CHC is to add 2-3% to the CHC gain.

Regardless, as I mentioned on my mathematical analysis, the longer the fights, the better the real CHC converge into the CHC predicted by the formula.


Yes but for those of us who farm in a group and can stand still it is important to take into account the 4 shots that will get 100% crit.

In the opening alone, let's say I shoot 4 Hungering arrows and then 2 Loaded for bears.

The following takes place:

HA #1 hits locking crit into place at 100% for 1 second
HA #2, 3, and 4 all hit for crits
Both Loaded for Bear shots also hit at nearly the same time due to travel speed of the skill and also therefor have 100% crit chance.

All of these actions would have 100% crit, not to mention if the HA pierced target and re-hit. It is VERY important that any formula used to predict real damage increase takes into account the 1 second of frozen crit % before the reset.
Edited by theK1ll577#1738 on 7/6/2012 9:09 AM PDT
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You seemed to ignore the fact that SS is worse in longer engagements and better in shorter ones, which is a huge deal. If you do high DPS and every engagement ends in 2 seconds, SS will gain value. How does your calculator account for this?

Additionally, point 4 under 'important points' is really, well, important.
Edited by Genome#1182 on 7/6/2012 9:21 AM PDT
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No it doesn't take into account that the crit chance is reset only after another shot or two are made
It also does not take under account that the first shot off is a crit 100%.

These two matters over-complicate things on an already complicated mathematical analysis.
the latter is fairly easy to add to the final dps gain.
the former is hard to extrapolate. I can try if that's what you need but I don't see the point in it.

The reason for my lack of interest - is that the really big impact is the wrong assumption that you stand still and shoot at enemies from the beginning of the fight to the end. SS benefits the most from moving around and kiting during fights (a thing that ALWAYS happens).
That is something that is downright impossible to analyze, and therefor I mentioned in the analysis that the best and easiest way to get a better estimate on the real-life CHC is to add 2-3% to the CHC gain.

Regardless, as I mentioned on my mathematical analysis, the longer the fights, the better the real CHC converge into the CHC predicted by the formula.


Yes but for those of us who farm in a group and can stand still it is important to take into account the 4 shots that will get 100% crit.

In the opening alone, let's say I shoot 4 Hungering arrows and then 2 Loaded for bears.

The following takes place:

HA #1 hits locking crit into place at 100% for 1 second
HA #2, 3, and 4 all hit for crits
Both Loaded for Bear shots also hit at nearly the same time due to travel speed of the skill and also therefor have 100% crit chance.

All of these actions would have 100% crit, not to mention if the HA pierced target and re-hit. It is VERY important that any formula used to predict real damage increase takes into account the 1 second of frozen crit % before the reset.


Well said, there is no point to do lots of technical staff just to get to a completely pointless calculation, you need to fit your model to reality.
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80 Blood Elf Warlock
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Posts: 243
The reason for my lack of interest - is that the really big impact is the wrong assumption that you stand still and shoot at enemies from the beginning of the fight to the end. SS benefits the most from moving around and kiting during fights (a thing that ALWAYS happens).
That is something that is downright impossible to analyze, and therefor I mentioned in the analysis that the best and easiest way to get a better estimate on the real-life CHC is to add 2-3% to the CHC gain.

Saying its impossible is silly. You have to define a lot of stuff like what abilities are being used, attack speed, etcetc, but that isn't 'impossible'. I don't disagree that it is unreasonable to expect you to work it in, but it is important to keep in mind when quantifying SS.

As far as practical analysis, it is hugely relevant. My opening 2 attacks in act 3 inferno can potentially 100-0 an entire elite pack if the stars align and 60-80% of their HP isn't particularly uncommon. The 1 second window is why. As someone else said, SS works best on short fights, and that means it also scales off your DPS as well as your kiting time.

Technical analysis aside, Sharpshooter is a ridiculously strong (overpowered) passive that anyone with a decent gear level and optimized spec should be using.
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Well said, there is no point to do lots of technical staff just to get to a completely pointless calculation, you need to fit your model to reality.

How is a very defined model for a low bound of the CHC and DPS gain "completely pointless"?
This gives you a very clear idea of what to expect AT THE VERY LEAST when using SS.

if you have read my analysis before fiddling around with the calculator i made, you'd have seen that this is a formula that I mathematically proven to be right. that makes it more reliable then anything else i've seen around the web - most of which is based on simulations (with extremely large variance in observations because of the nature of SS), or just absolutely wrong theory-making.

unless you have ideas on how to fit my model to be closer to reality - what was your point in this nonconstructive feedback?
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Saying its impossible is silly. You have to define a lot of stuff like what abilities are being used, attack speed, etcetc, but that isn't 'impossible'. I don't disagree that it is unreasonable to expect you to work it in, but it is important to keep in mind when quantifying SS.

As far as practical analysis, it is hugely relevant. My opening 2 attacks in act 3 inferno can potentially 100-0 an entire elite pack if the stars align and 60-80% of their HP isn't particularly uncommon. The 1 second window is why. As someone else said, SS works best on short fights, and that means it also scales off your DPS as well as your kiting time.

Technical analysis aside, Sharpshooter is a ridiculously strong (overpowered) passive that anyone with a decent gear level and optimized spec should be using.


you missed my point.
analyzing THE WAY people fight is impossible.
It's impossible to quantify how many times, and for how long the player kites. every person does this slightly differently, and also depending on their own gear, skill selection and the momentary state in the game (surrounded? in a corridor/open area? has a tank in the team or solo? and many many more)
furthermore - if you put 2 people in the EXACT same position, with same skill selection, gear, and game-state (monster and positioning-wise) - they might still do 2 completely different things to end that fight.

Analyzing this statistically/mathematically is just impossible - and given that SS benefits the most from kiting - different players and play styles will gain yield different gain in DPS when using SS, regardless of their skill selection.

that aside, I agree that SS works best on short fights.
my analysis lets you know how much at the very least you will gain in long fights. isn't that more important (especially in inferno)?
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I shoot and I kill.... so long as I don't do a Barny Fife ... I'm good to go... :)

thx for the information
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You seemed to ignore the fact that SS is worse in longer engagements and better in shorter ones, which is a huge deal. If you do high DPS and every engagement ends in 2 seconds, SS will gain value. How does your calculator account for this?

Additionally, point 4 under 'important points' is really, well, important.


yes I ignored that fact.
I chose willingly to quantify the SS gain from long engagements only - since those are the ones that will define what skills you use in the late game.

now you can know for sure, that in long engagements SS will render at the very least a X% gain in dps, and that is probably going to be enough to make a knowledgeable choice.
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