tl;dr: Spreadsheet to evaluate what value you'd get out of sharpshooter and how to improve your gear

I am probably not the first to make a spreadsheet to evaluate sharpshooter, but I made this for a friend and thought I might as well share it. The point is to answer the following questions: If I use sharpshooter and never stopped shooting at a target with infinite health (i.e. a spherical über chicken in a vacuum), then

1) what would be my effective crit chance?
2) by how much would my effective dps increase?
3) whats my real dps as compared to the insane number the game now displays?
4) what should I buy next, crit dmg or crit chance?

All you need to do is enter three numbers: crit chance, crit dmg and attack speed. The sheet then computes your effective damage as a multiple of the dps you'd have if you never ever critted. With and without sharpshooter. By comparing these numbers, one can say how much more dps you get from sharpshooter. In percent.

For the last question, I do not do three dimensional calculus, but simply compare the dps increase an additional 1% crit chance and an additional 10% crit dmg would give you.

I uploaded it to googledocs: https://docs.google....TTV3bjFOYWwxOFE
I think you need to download that as excel or open office to be able to enter your stats. Dont change any other cell except the three green ones.

The whole thing comfirms what is probably widely known anyway: Sharpshooter is only good if you have some increased crit dmg. And as you increase your attack speed and crit chance, it is worth less and less.
I.e. its a passive for low to medium gear. The spreadsheet just quantifies this.

For those interested to check my maths, here is what the columns do: Shots:
the number of shots fired without having had a crit before
Time passed
the time that took in seconds, given the attack speed
ss ticks
the number of sharpshooter ticks. Thats just the time rounded down to the next integer

The next columns always come in threes. The first uses sharpshooter, the second does not, the third uses sharpshooter and assumes 1% more crit chance.

Chance to crit on that shot:
The chance to crit on the given shot assuming that there had not been a crit before. This starts at the input value in the 1st and 2nd column and 1% more in the third. It stays constant in the 2nd column and increases in the 1st and third by 0.03 times the number of ss ticks.

Chance of not having had a crit before, i.e. chance to even get that far:
This is the probability of all previous shots failing to crit. The 1st and 3rd column hit zero at some point because the chance to crit hits 1. The 2nd row converges to 0.

Chance of critting on exactly this shot for the first time:
The previous probability multiplied by the current chance to crit

Chance of at least one crit so far, including the current shot:
This simply sums up the probabilities in the previous three columns. Its just here to check things, as all three columns should converge to 1. And happily, they do.

Expected number of shots until first crit
The expected value of the number of shots needed to get the 1st crit is the infinite sum over all intergers, each multiplied with the probability of the 1st crit occurring on exactly that number.
This is the important bit. The numbers are totally meaningless taken on their own. The only thing that matters is the value the columns converge to if the number of shots converge to infinity. Infinity being 500 for all practical intents and purposes.

Thus, the only three values that are used in the results are the last in the three columns to the right. They give the average number of shots needed to get one crit. From that, I compute the effective crit chance and from that the effective dmg.

To simplify things, here is a graph that expresses the effect of the sharpshooter passive in terms of extra crit chance.
Its kinda weird that the difference between attack speed of 1.4 and 1.5 does not matter much. I guess that is because of the way the attacks sync with the ticking of the seconds.

Nice table, and graph too. This is probably well known fact but it is always good to have a tool for starting DH.

Sharpshooter is great passive skill that greatly simplify gearing process for starting DH. It allows you to focus primarily CHD bonus, which is great DPS boost. It also allows players without funds to buy items with just single offensive stat (either CC or CHD), which is a whole lot cheaper than dual or tri-stats.

I think its safe to say that SS is getting less and less popular now that other passives are a must have for DH and also a lot of players have like over 40% CC which renders SS almost as a wasted passive.

What are those "must-have" passives you are talking about WizArt?

Average, and for sure starting, DH will use Archery and Steady Aim as pretty much given choices. There is very few other passive skills that have direct impact on your damage output--Sharpshooter being prime choice because it gives you a direct boost do damage and also allows for heavy damage front-loading, which works great with skills such as Impale: Grievous Wound or Cluster Arrow.

If you play less standard builds, you will choose different passive skills, however, majority of population will use very similar build including Hungering Arrow, Ball Lightning and set of defensive/tactical skills.

Once you reach certain gear level, I guess past 100k character sheet DPS, you can start making sacrifices in offensive passives for more utility based ones (Tactical advantage, Perfectionist or Night Stalker).

doesnt sharpshooter always give u at least 3% crit since its +3% per sec and bonus resets 1 sec after u crit

Meh. This is what happens if you dont actually read the tooltip carefully. My sheet assumes an immediate reset to base crit chance and thus undervalues the effect of sharpshooter.

With the extra crit chance sticking around for a second, some leftover crit bonus should be left over at the time of my n=1. How much depends on the average number of ticks until the first crit. Which unfortunately would lead to a circular reference in the excel sheet.

I guess I deserve that for trying to use Excel to weasel my way out of doing proper maths.

doesnt sharpshooter always give u at least 3% crit since its +3% per sec and bonus resets 1 sec after u crit

yes it does. however its still not what I would call an obvious choice once u get 35%+ CC. I personally like nightstalker, so that there is always discipline available for SS/Gloom. Perfectionist is also nice since the buff, 10% more hp, armor and resist

A problem with this analysis is that it's only assuming a single target. Unless I'm mistaken about the methodology, anyway.

Since most Demon Hunters are using abilities that hit many targets at a time (ball lightning), or at least have multiple attacks (devouring arrow), the critical chances per second is far higher than shots per second. This will drastically reduce how high Sharpshooter is allowed to stack before resetting. The model used here is only appropriate for modeling the effectiveness of Sharpshooter against a single target using a single damage source attack, such as impale, evasive fire, or multishot.

doesnt sharpshooter always give u at least 3% crit since its +3% per sec and bonus resets 1 sec after u crit

yes it does. however its still not what I would call an obvious choice once u get 35%+ CC. I personally like nightstalker, so that there is always discipline available for SS/Gloom. Perfectionist is also nice since the buff, 10% more hp, armor and resist

A problem with this analysis is that it's only assuming a single target. Unless I'm mistaken about the methodology, anyway. Since most Demon Hunters are using abilities that hit many targets at a time (ball lightning), or at least have multiple attacks (devouring arrow), the critical chances per second is far higher than shots per second. This will drastically reduce how high Sharpshooter is allowed to stack before resetting. The model used here is only appropriate for modeling the effectiveness of Sharpshooter against a single target using a single damage source attack, such as impale, evasive fire, or multishot.

I tested this by using SS on large, easy packs (Cemetry of the Forsaken) on MP10. Both of the above statements are 100% correct. While Sharpshooter's DPS bonus drops like a brick from the moment I start nuking a large pack (probably due to me getting far more crits per second than I would on a single target), it continues to grant a small DPS increase, probably from the minimum bonus of 3% crit it provides.

Without SS, I am at a 274k char screen DPS.
With SS, I was unable to drop my char screen DPS below 284k.

This means that, for my current gear setup, Sharpshooter provides roughly 10k sustained char screen DPS. That's still a nice bonus, but it's certainly lackluster compared to Nightstalker, Vengeance or Tactical Advantage.

The only big advantage of Sharpshooter, as far as I can see, is the way it makes sure your first hits will be crits. As such, it may be worthwhile when you are farming content that you are basically one-shotting with SS, with enough gaps in between packs to allow the SS bonus to ramp up a little.

Critical hit chance is just that, a chance of the crit, the dps goes up because you will be criting more, but the ingame damage remain the same unless you upgrade the critical hit damage.

Sharpshooter give you a boost dps because if you crit every shot, the damage per second will be huge, and real, but you will never crit every second. That is why attack speed and crit damage become more importan at certain level. Why would i want 3% more of cc after 40% i would prefer to shoot faster or to make more damage with my crit.
Sharpshooter is useless after that point, you dps upgrade is fake

Not true, L0k1_uy. The 3% extra crit damage is still a real upgrade to your DPS until you already have a natural 100% crit chance from gear (which is impossible).

You are right when you say that crit damage or attack speed are more important once you have more than 40% crit from gear. But there aren't any passives that give either crit damage or attack speed, so the point is irrelevant.

The real question is: how does a 3% crit boost compare to a Discipline on Crit or movement speed or defensive stat boost (Nightstalker, Tactical Advantage or Perfectionist) in actual gameplay? My guess is, not very well.

Nevi, that 3% extra crit is not a DPS boost since your crits will be the same, and you will be "criting" at the same rate.

You got it wrong, in your first and also 2nd post.

Every % of critical hit chance (CHC) is direct boost to you DPS because higher portion of your shot will be critical hit. Critical hit has a multiplier, ie. critical hit damage (CHD), attached to it, which cause each critical hit to be XXX% higher then normal hit. Base multiplier for critical hit is 50% damage bonus or 1.5 times your normal hit. Obviously, each critical hit will hit for more and you will hit more often as you get more crit chance.

CHC, CHD and IAS are stats that directly impact your DPS. Their relative contribution can change as your gear progress but they will most often oscillate amongst each other. No matter how much of each stat you have (bar the rare case when you are alraedy at 100% CHC), each next % will provide DPS boost to you.

So is or isn't it profitable to use sharpshooter when you have a 40% crit chance?

There is still that flat 3% crit bonus provided by SS to you at all times. 40% CHC is generally considered a breakpoint when you start looking for different passive. I would say that you can still use SS at 40% CHC as long as you have low attack speed (it is easy to get to 40% CHC even with entry level gear).
I liked SS also for its ability to frontload damage, which comes very handy with heavy hitters such as Cluster Arrow or Impale.

Hmmm my attack speed is currently 2.10 (or 2.something, whatever).
So you'd argue that with this att. speed I should go for something different if my crit chance is high enough?

If you want rock-solid answer, you have to use a spreadsheet or some DPS calculator on web. I have switched away from SS when I reached roughly 45% crit chance and started using Cluster Arrow, at which point I felt that Grenadier passive gives me more benefit. It will come down to a point where you have to evaluate if you have better passive to replace SS with--other option, the one Im using currently, is Tactical Advantage.

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I am probably not the first to make a spreadsheet to evaluate sharpshooter, but I made this for a friend and thought I might as well share it. The point is to answer the following questions: If I use sharpshooter and never stopped shooting at a target with infinite health (i.e. a spherical über chicken in a vacuum), then

1) what would be my effective crit chance?

2) by how much would my effective dps increase?

3) whats my real dps as compared to the insane number the game now displays?

4) what should I buy next, crit dmg or crit chance?

All you need to do is enter three numbers: crit chance, crit dmg and attack speed. The sheet then computes your effective damage as a multiple of the dps you'd have if you never ever critted. With and without sharpshooter. By comparing these numbers, one can say how much more dps you get from sharpshooter. In percent.

For the last question, I do not do three dimensional calculus, but simply compare the dps increase an additional 1% crit chance and an additional 10% crit dmg would give you.

I uploaded it to googledocs:

https://docs.google....TTV3bjFOYWwxOFE

I think you need to download that as excel or open office to be able to enter your stats. Dont change any other cell except the three green ones.

The whole thing comfirms what is probably widely known anyway: Sharpshooter is only good if you have some increased crit dmg. And as you increase your attack speed and crit chance, it is worth less and less.

I.e. its a passive for low to medium gear. The spreadsheet just quantifies this.

For those interested to check my maths, here is what the columns do:

Shots:

the number of shots fired without having had a crit before

Time passed

the time that took in seconds, given the attack speed

ss ticks

the number of sharpshooter ticks. Thats just the time rounded down to the next integer

The next columns always come in threes. The first uses sharpshooter, the second does not, the third uses sharpshooter and assumes 1% more crit chance.

Chance to crit on that shot:

The chance to crit on the given shot assuming that there had not been a crit before. This starts at the input value in the 1st and 2nd column and 1% more in the third. It stays constant in the 2nd column and increases in the 1st and third by 0.03 times the number of ss ticks.

Chance of not having had a crit before, i.e. chance to even get that far:

This is the probability of all previous shots failing to crit. The 1st and 3rd column hit zero at some point because the chance to crit hits 1. The 2nd row converges to 0.

Chance of critting on exactly this shot for the first time:

The previous probability multiplied by the current chance to crit

Chance of at least one crit so far, including the current shot:

This simply sums up the probabilities in the previous three columns. Its just here to check things, as all three columns should converge to 1. And happily, they do.

Expected number of shots until first crit

The expected value of the number of shots needed to get the 1st crit is the infinite sum over all intergers, each multiplied with the probability of the 1st crit occurring on exactly that number.

This is the important bit. The numbers are totally meaningless taken on their own. The only thing that matters is the value the columns converge to if the number of shots converge to infinity. Infinity being 500 for all practical intents and purposes.

Thus, the only three values that are used in the results are the last in the three columns to the right. They give the average number of shots needed to get one crit. From that, I compute the effective crit chance and from that the effective dmg.

Its kinda weird that the difference between attack speed of 1.4 and 1.5 does not matter much. I guess that is because of the way the attacks sync with the ticking of the seconds.

Sharpshooter is great passive skill that greatly simplify gearing process for starting DH. It allows you to focus primarily CHD bonus, which is great DPS boost. It also allows players without funds to buy items with just single offensive stat (either CC or CHD), which is a whole lot cheaper than dual or tri-stats.

Average, and for sure starting, DH will use Archery and Steady Aim as pretty much given choices. There is very few other passive skills that have direct impact on your damage output--Sharpshooter being prime choice because it gives you a direct boost do damage and also allows for heavy damage front-loading, which works great with skills such as Impale: Grievous Wound or Cluster Arrow.

If you play less standard builds, you will choose different passive skills, however, majority of population will use very similar build including Hungering Arrow, Ball Lightning and set of defensive/tactical skills.

Once you reach certain gear level, I guess past 100k character sheet DPS, you can start making sacrifices in offensive passives for more utility based ones (Tactical advantage, Perfectionist or Night Stalker).

Meh. This is what happens if you dont actually read the tooltip carefully. My sheet assumes an immediate reset to base crit chance and thus undervalues the effect of sharpshooter.

With the extra crit chance sticking around for a second, some leftover crit bonus should be left over at the time of my n=1. How much depends on the average number of ticks until the first crit. Which unfortunately would lead to a circular reference in the excel sheet.

I guess I deserve that for trying to use Excel to weasel my way out of doing proper maths.

Since most Demon Hunters are using abilities that hit many targets at a time (ball lightning), or at least have multiple attacks (devouring arrow), the critical chances per second is far higher than shots per second. This will drastically reduce how high Sharpshooter is allowed to stack before resetting. The model used here is only appropriate for modeling the effectiveness of Sharpshooter against a single target using a single damage source attack, such as impale, evasive fire, or multishot.

I tested this by using SS on large, easy packs (Cemetry of the Forsaken) on MP10. Both of the above statements are 100% correct. While Sharpshooter's DPS bonus drops like a brick from the moment I start nuking a large pack (probably due to me getting far more crits per second than I would on a single target), it continues to grant a small DPS increase, probably from the minimum bonus of 3% crit it provides.

Without SS, I am at a 274k char screen DPS.

With SS, I was unable to drop my char screen DPS below 284k.

This means that, for my current gear setup, Sharpshooter provides roughly 10k sustained char screen DPS. That's still a nice bonus, but it's certainly lackluster compared to Nightstalker, Vengeance or Tactical Advantage.

The only big advantage of Sharpshooter, as far as I can see, is the way it makes sure your first hits will be crits. As such, it may be worthwhile when you are farming content that you are basically one-shotting with SS, with enough gaps in between packs to allow the SS bonus to ramp up a little.

Sharpshooter give you a boost dps because if you crit every shot, the damage per second will be huge, and real, but you will never crit every second. That is why attack speed and crit damage become more importan at certain level. Why would i want 3% more of cc after 40% i would prefer to shoot faster or to make more damage with my crit.

Sharpshooter is useless after that point, you dps upgrade is fake

You are right when you say that crit damage or attack speed are more important once you have more than 40% crit from gear. But there aren't any passives that give either crit damage or attack speed, so the point is irrelevant.

The real question is: how does a 3% crit boost compare to a Discipline on Crit or movement speed or defensive stat boost (Nightstalker, Tactical Advantage or Perfectionist) in actual gameplay? My guess is, not very well.

Every % of critical hit chance (CHC) is direct boost to you DPS because higher portion of your shot will be critical hit. Critical hit has a multiplier, ie. critical hit damage (CHD), attached to it, which cause each critical hit to be XXX% higher then normal hit. Base multiplier for critical hit is 50% damage bonus or 1.5 times your normal hit. Obviously, each critical hit will hit for more and you will hit more often as you get more crit chance.

CHC, CHD and IAS are stats that directly impact your DPS. Their relative contribution can change as your gear progress but they will most often oscillate amongst each other. No matter how much of each stat you have (bar the rare case when you are alraedy at 100% CHC), each next % will provide DPS boost to you.

I liked SS also for its ability to frontload damage, which comes very handy with heavy hitters such as Cluster Arrow or Impale.

So you'd argue that with this att. speed I should go for something different if my crit chance is high enough?