yukichigai
New member
- Joined
- Nov 28, 2012
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Alright, so, this is a sort of complicated one, and from an unlikely source too. I'm not entirely sure where this belongs, since it includes a statistical component, but since I'm virtually certain this will involve an infinite series I decided it should go in here.
So, some background. First off, the question I'm asking concerns a video game. That might put some of you off, but I PROMISE, there's interesting math involved. The game in question, if it matters, is Borderlands 2. The bulk of the game content doesn't matter; what does matter is that weapon damage output is stated numerically, and can be tracked. Right now several of us are attempting to figure out the mathematical ins and outs of weapon damage, but we've come up against something that has us stumped.
The BASIC level of weapon damage is pretty easy: weapon has a fire rate of X shots per second, each shot does Y damage, ergo the Damage Per Second (DPS) is X*Y. Easy. So far, so good.
Where the REAL complication comes in is that each element has a chance to generate an independent damage-over-time event, called a status effect. The status effect lasts for a set duration, and deals damage based on a separate variable (call it A) which represents the status effect's DPS. The percentage chance that this will happen (call it B) is listed on the weapon, but can vary. The DURATION of the status effect (call it C) also varies depending on the element: either 2 seconds (Shock), 6 seconds (Fire), or 8 seconds (Corrosive) long. If a status effect triggers from a shot while it is active, the time limit is reset, i.e. the stop time on the effect is now 2/6/8 seconds from that moment.
What we're trying to figure out is the effective average DPS for a weapon based on its damage, fire rate, chance to cause a status effect, status effect duration, and status effect damage per second. Obviously immediate results will differ, but over the long term by how much? Obviously, the status effect with the shortest duration will do less in the long run, but is it statistically significant, or will it be a difference of a few tens of points when the weapon deals damage in the thousands?
If anyone actually decides to take a crack at this, we've been using some hypothetical example weapons which have a damage (X) of 1000, a fire rate (Y) of 8, a status effect DPS (A) of 1000, and a percent chance (B) of 12.5%. Since we're comparing the three elements, we're using three versions with different durations (C): 2, 6, and 8. These are simplified some, but if it matters actual weapons with values VERY close to these do exist.
In terms of range, there's a LOT of variety in all of the values, depending on the weapon type. EDIT: Except the duration, which is ONLY 2, 6, or 8. Generally the high chance is limited to the lower fire rate weapons, but not always. I can't actually give you any ranges, and there are also complicating factors like reload time, magazine size, etc. etc. I have no idea how to even incorporate those elements, and I think this problem is enough of a head-scratcher already.
Anywho, I hope this piques someone's interest. If not, it's not like anyone's going to die regretting that they never figured it out. On the other hand, if you do decide to take a crack at this you'll find a forum's worth of people over at the Gearbox forums who are rather appreciative of the effort.
So, some background. First off, the question I'm asking concerns a video game. That might put some of you off, but I PROMISE, there's interesting math involved. The game in question, if it matters, is Borderlands 2. The bulk of the game content doesn't matter; what does matter is that weapon damage output is stated numerically, and can be tracked. Right now several of us are attempting to figure out the mathematical ins and outs of weapon damage, but we've come up against something that has us stumped.
The BASIC level of weapon damage is pretty easy: weapon has a fire rate of X shots per second, each shot does Y damage, ergo the Damage Per Second (DPS) is X*Y. Easy. So far, so good.
Where the REAL complication comes in is that each element has a chance to generate an independent damage-over-time event, called a status effect. The status effect lasts for a set duration, and deals damage based on a separate variable (call it A) which represents the status effect's DPS. The percentage chance that this will happen (call it B) is listed on the weapon, but can vary. The DURATION of the status effect (call it C) also varies depending on the element: either 2 seconds (Shock), 6 seconds (Fire), or 8 seconds (Corrosive) long. If a status effect triggers from a shot while it is active, the time limit is reset, i.e. the stop time on the effect is now 2/6/8 seconds from that moment.
What we're trying to figure out is the effective average DPS for a weapon based on its damage, fire rate, chance to cause a status effect, status effect duration, and status effect damage per second. Obviously immediate results will differ, but over the long term by how much? Obviously, the status effect with the shortest duration will do less in the long run, but is it statistically significant, or will it be a difference of a few tens of points when the weapon deals damage in the thousands?
If anyone actually decides to take a crack at this, we've been using some hypothetical example weapons which have a damage (X) of 1000, a fire rate (Y) of 8, a status effect DPS (A) of 1000, and a percent chance (B) of 12.5%. Since we're comparing the three elements, we're using three versions with different durations (C): 2, 6, and 8. These are simplified some, but if it matters actual weapons with values VERY close to these do exist.
In terms of range, there's a LOT of variety in all of the values, depending on the weapon type. EDIT: Except the duration, which is ONLY 2, 6, or 8. Generally the high chance is limited to the lower fire rate weapons, but not always. I can't actually give you any ranges, and there are also complicating factors like reload time, magazine size, etc. etc. I have no idea how to even incorporate those elements, and I think this problem is enough of a head-scratcher already.
Anywho, I hope this piques someone's interest. If not, it's not like anyone's going to die regretting that they never figured it out. On the other hand, if you do decide to take a crack at this you'll find a forum's worth of people over at the Gearbox forums who are rather appreciative of the effort.