Attack Speeds and (Est) DPS

[Squishy]

Useless Preamble:
So I am admittedly pretty terrible at this game. After a hideous bout of matches where I got rolled by M&M I thought maybe my time would be better spent, for now anyway, looking more at the mechanics of the game.

At any rate, one thing that bugged me is I was noticing that all attack speeds are not created equal, and It made it harder to assess units without just throwing em in and seeing em go. The forums weren't much better because for every "1 unit X kills 8 of my unit Y" someone else claims they killed 12 unit X's with only 2 unit Y's. So I decided to test it myself and make a comparison of all the attack speeds and estimated dps. Hopefully this will help the discussions move away from anecdote a little.

Method:
All times and dps are estimated via watching replays at "slower" speed so as to minimize effect of human error. For each unit I recorded the time to 20th attack after first with splits at every 5. I timed based on when damage was done to the target not the animations even though they did seem to sync properly. I would assume a ± 0.1 on all attack speeds. Faster speeds are, of course, more prone to error.

A typical match at "faster" appears to be roughly 2.2 times faster than these tests at "slower".

Added two comparison categories:

HP*DPS: Simple really just a (HP + shields)*DPSv0. If using these numbers for balance consideration keep in mind that armor does not affect damage to shields so these stats will be weighted slightly in favor of Protoss.

DPS/Cost:Created a cost metric for individual units. This is a weighted estimation of creation cost using minerals + 3.3*gas. This, of course, does not take into consideration cost to tech to the unit, only the cost to produce it. 3.3 is based on the relative value of gas assuming that a player, at saturation, would have 16 miners and 6 gas collectors.


Legend:
# - Number of attacks
AS - Attack Speed (time in seconds between each attack or volley)
DPSv0 - The estimated DPS versus a target with 0 armor
DPSv3 - The estimated DPS versus a target with 3 armor
Cost - Unit build cost (minerals + (gas)3.3)
DPS/Cost - 100*DPS/Cost (made numbers simpler)

If there is a way to see the actual attack speed that I am missing, please let me know. Even if it does mean I wasted a good chunk of my Sunday :p

If you think this is useful, let me know and I will try to keep it updated with the patches.

An EU thread worth checking out: http://forums.battle.net/thread.html?topicId=23425636662&sid=5010
Little less of a comparison model and more of a database, but along with SC2armory, has the largest depth of info I have seen. Only listing I am aware of that has quantified movement speeds. Kudos to Thrios.

[Squishy]

TERRAN:

<pre>TERRAN:

Name Dmg # AS DPSv0 DPSv3 HP Shield Min Gas Cost DPS*Hp DPS/cost

Fortress 40 1 3.4 11.76 10.88 1500 550 150 1045 17647.06 1.13
Missile Turret 7 2 1.5 9.33 5.33 250 100 100 2333.33 9.33
v. Armor 14 2 1.5 18.67 14.67 250 100 100 4666.67 18.67
SCV 5 1 2.6 1.92 0.77 60 50 50 115.38 3.85
Marine 6 1 1.5 4.00 2.00 45 50 50 180.00 8.00
Reaper 4 2 1.9 4.21 1.05 50 50 50 215 210.53 1.96
v. Light 9 2 1.9 9.47 6.32 50 50 50 215 473.68 4.41
v. Struct 30 1 3.5 8.57 7.71 50 50 50 215 428.57 3.99
Marauder 10 1 2.5 4.00 2.80 125 100 25 182.5 500.00 2.19
v. Armor 20 1 2.5 8.00 6.80 125 100 25 182.5 1000.00 4.38
Ghost 10 1 2.5 4.00 2.80 100 100 200 760 400.00 0.53
v. Light 20 1 2.5 8.00 6.80 100 100 200 760 800.00 1.05
Hellion 8 1 4 2.00 1.25 90 100 100 180.00 2.00
v. Light 14 1 4 3.50 2.75 90 100 100 315.00 3.50
Tank 15 1 1.8 8.33 6.67 150 150 125 562.5 1250.00 1.48
v. Armor 25 1 1.8 13.89 12.22 150 150 125 562.5 2083.33 2.47
siege 60 1 5 12.00 11.40 150 150 125 562.5 1800.00 2.13
Thor
v. ground 45 2 3.25 27.69 25.85 400 300 200 960 11076.92 2.88
v. air 10 4 5 8.00 5.60 400 300 200 960 3200.00 0.83
v. air(light) 16 4 5 12.80 10.40 400 300 200 960 5120.00 1.33
Viking
v. ground 14 1 1.7 8.24 6.47 125 125 100 455 1029.41 1.81
v. air 10 2 3.4 5.88 4.12 125 125 100 455 735.29 1.29
v. air (armor) 14 2 3.4 8.24 6.47 125 125 100 455 1029.41 1.81
Banshee 12 2 2.15 11.16 8.37 130 150 100 480 1451.16 2.33
Raven (turret) 8 1 1.4 5.71 3.57 140 100 200 760 800.00 0.75
Cruiser
v. ground 10 1 0.5 20.00 14.00 550 400 300 1390 11000.00 1.44
v. air 6 1 0.5 12.00 6.00 550 400 300 1390 6600.00 0.86

</pre>

[Squishy]

ZERG:

<pre>Name Dmg attacks AS DPSv0 DPSv3 HP Shield Min Gas Cost DPS*Hp DPS/cost

Drone 5 1 2.6 1.92 0.77 40 50 50 76.92 3.85
Zergling 5 1 1.2 4.17 1.67 35 25 25 145.83 16.67
Queen
v. ground 4 2 1.7 4.71 1.18 175 150 150 823.53 3.14
v. air 9 1 1.7 5.29 3.53 175 150 150 926.47 3.53
Roach 16 1 3.4 4.71 3.82 145 75 25 157.5 682.35 2.99
Spore Crawler 15 1 1.5 10.00 8.00 400 150 150 4000.00 6.67
Spine Crawler 20 1 3.7 5.41 4.59 300 150 150 1621.62 3.60
v. Armor 30 1 3.7 8.11 7.30 300 150 150 2432.43 5.41
Infestor(IT) 5 1 1.5 3.33 1.33 120 100 150 595 400.00 0.56
Hydralisk 12 1 1.45 8.28 6.21 90 100 50 265 744.83 3.12
Mutalisk 9 1 2.6 3.46 2.31 120 100 100 430 415.38 0.81
Corruptor 12 1 3.2 3.75 2.81 200 150 100 480 750.00 0.78
v. massive 22 1 3.2 6.88 5.94 200 150 100 480 1375.00 1.43
Ultralisk 18 1 1.4 12.86 10.71 600 300 200 960 7714.29 1.34
v. Struct 60 1 2.8 21.43 20.36 600 300 200 960 12857.14 2.23
*Broodlord 25 1 4.2 5.95 5.24 275 300 250 1125 4936.90 1.60
`broodlings 4 1 1 4.00 1.00 </pre>

*Because of the nature of the broodlord's attack, it is difficult to get an accurate assessment of an independent broodling's speed. For the purposes of comparison, though, this should be close enough.

[Squishy]

PROTOSS:

<pre>Name Dmg attacks AS DPSv0 DPSv3 HP Shield Min Gas Cost DPS*Hp DPS/cost

Probe 5 1 2.6 1.92 0.77 20 20 50 50 76.92 3.85
Zealot 8 2 2 8.00 5.00 100 50 100 100 1200.00 8.00
Cannon 20 1 2.1 9.52 8.10 125 125 150 150 2380.95 6.35
Stalker 8 1 2.4 3.33 2.08 80 80 125 50 290 533.33 1.15
v. Armor 14 1 2.4 5.83 4.58 80 80 125 50 290 933.33 2.01
Sentry 8 1 1.6 5.00 3.13 40 40 50 100 380 400.00 1.32
Immortal 20 1 2.4 8.33 7.08 200 100 250 100 580 2500.00 1.44
v. Armor 50 1 2.4 20.83 19.58 200 100 250 100 580 6250.00 3.59
D. Templar 45 1 2.9 15.52 14.48 80 40 125 125 537.5 1862.07 2.89
Archon 25 1 3 8.33 7.33 10 350 250 250 1075 3000.00 0.78
v. Bio 35 1 3 11.67 10.67 10 350 250 250 1075 4200.00 1.09
Colossus 23 2 3.8 12.11 10.53 200 150 300 200 960 4236.84 1.26
Phoenix 5 2 1.9 5.26 2.11 120 60 150 100 480 947.37 1.10
v. Light 10 2 1.9 10.53 7.37 120 60 150 100 480 1894.74 2.19
Void Ray 2 1 1 2.00 0.00 150 100 200 150 695 500.00 0.29
v.Armor 6 1 1 6.00 3.00 150 100 200 150 695 1500.00 0.86
Beam 2 4 1 1 4.00 1.00 150 100 200 150 695 1000.00 0.58
v.Armor 12 1 1 12.00 9.00 150 100 200 150 695 3000.00 1.73
Beam 3 8 1 1 8.00 5.00 150 100 200 150 695 2000.00 1.15
v.Armor 24 1 1 24.00 21.00 150 100 200 150 695 6000.00 3.45
Carrier(int) 5 2 5 2.00 0.80 300 150 450 250 1275 7200.00 1.25
Mothership 6 6 3.8 9.47 4.74 350 350 400 400 1720 6631.58 0.55
</pre>

[Tiamazzo]

See? Whoever said Roaches do more damage then Hydras can eat there words.

[Squishy]

Updated:
Corrected gatherer speed (data wasn't consistant)
Added all air only attacks
Added stationary defense units
updated Reaper and Thor with non-building attack speeds and damage.


That should be all the units with a relevant attack speed. If you see anything I missed, please let me know.

[Krios]

tagging for later review
thanks!

[Squishy]

Updated with Planetary Fortress

Added some new comparison models (just mathy stuff):
HP*Dps and Dps/Cost

Gas is very inflated in the cost analysis. I assumed that at saturation you would have 16 miners and 6 gas collectors. That's 37.5% of mineral miner total on gas. Additionaly since gas collects at 4 vs 5 that makes it 80% as efficient to collect. Therefore, compared to minerals, gas collects at a rate of (0.8)(.375) = 0.3. Or gas is 3.3 times more valuable than minerals.

I am not sure how much I like this level of inflation for gas, but it's just a metric to compare units. If someone can think of a reason why a different number is more appropriate, I would be glad to adjust the scale.

[Nick]

Oh my god I love you. Bookmarked.

[Metallic]

Hydras are only 50 gas I believe, not 150 as listed.

[Squishy]

Hydras are only 50 gas I believe, not 150 as listed.
Fixed

Thank you, good catch.

[Xenozergie]

Although there are obviously a lot of mitigating circumstances making it so that you can't compare units straight across (special abilities, upgrades, ability to hit air, etc.) this is still a good baseline for estimating their cost effectiveness. Nice job!

I think one of the most interesting things is how low the dps per cost is for most air units. The devs must consider the mobility of air to be much more useful than their straight damage.

EDIT: Oh hey, I just noticed you don't have Banelings! Only Zerg unit iirc that deals extra damage to light.

[Comtrav]

Was wondering how Marines and Marauders stacked up against each other for damage output...seems they're the same against (non-armored) targets. Good to know.

[Mekhazzio]

EDIT: Oh hey, I just noticed you don't have Banelings! Only Zerg unit iirc that deals extra damage to light.A Baneling has undefined DPS, since it can only ever attack once. Division by infinity!

[Squishy]

Updated for patch 3:
adjusted zealot shields and hp*dps score.

[Squishy]

A reply to Tirios.Asthar on the EU boards.

Comments on Attack Values
You will see that his attack-times are 1.5-1.7 times longer than mine, for which I think different time-frames are the reason. As I said I used the in-game-timer, making my times completely dependant on that but independent of the game speed (which I timed separately with a watch). If he used a manual stop watch (more precise than the in-game-timer) to measure his values at slowest speed it would explain the discrepancy.
He used samples of 20 attacks, starting timer and counter after the first - statistically stabilizing these against error by making 4 samples of 5 attacks of those. I on the other hand used as single value time to kill a certain amount of HP: For that I took a map barrier or very stable building, wrote down the damage of a single attack movement (consisting of a number of attacks) and start-time of continuous attack. I then calculated numbers of attacks to kill and rounded that down (removing the first attack, which doesn't have a cooldown). Then I wrote down the time when the alloted amount of HP was done (the map barrier broke), divided the in-game time difference in seconds by number of attacks and got my attack time in that way.
My method has the advantage to be very precise for fast low-damage attacks (huge sample size), and is reasonable precise for the high damage attacks (like Thor) with >20 continuous attacks. The disadvantage of my method is a rather substantial chance for a calculation or measurement error, which I hope didn't happen (and from the comparison with Squishy's data hasn't happened (everything is connected with a factor around 1.6)).
(Missile Turret is missing in his list, attack speed is 0.9 in my measure, should be 1.5 in his)
I already laid down my reasons for not including DPS data here, which should always be used knowing its limitations. (I have the DPS values in the open office table, together with some even more derived values, but I wouldn't want to use it before verifying the usefulness of those).
I mentioned DPS/Health as guideline for target priority, but Squishy's use of DPS*HP escapes my understanding at the moment. It seems like the mixing of two different and independent statistics, creating a value not explaining anything.
Problems are:
-The values jump three orders of magnitude (in which way is a Battlecruiser comparable to more than 60 marines?).
-They will vary strongly with only minute changes (1 Carrier Weapon Upgrade or enemy Armor Upgrade = +/-1200 HP*DPS and that for each carrier).
-As for their use as a general quality criterium: A hypothetical unit dealing 5 DPS with 20Hitpoints has the same value as a 20HP unit dealing 5DPS and for those units range, damage and attack time would be absolutely critical in evaluating their respective strength.
All in all the value tells me nothing, if somebody knows what it can tell me, I would be happy to hear it.

I have thought that I should expand on the testing method, but not too many people were really asking about it so I didn't bother. I did, in fact, use a stopwatch at slower speed. 20 iterations was the minimum number of tests I did and in cases where the overall timing didn't match up with split times I redid the test over longer periods. Some units I basically soloed a rock formation to try and get a consistant data set. I expect some attack times are in the hundredths of seconds and just not matching up as well as I like, but since the data will all come out eventually via Galaxy Editor or data extraction I didn't see the need to get it more precise.

As for the HP*DPS category, I made it strictly as its own comparison model. I saw many threads where people were saying, "this unit does more damage than that, but it doesn't have as many hit points." One major weakness of the metric, of course, is that it ignores armor. It is probably better used purely as a ranking model than to extend beyond that but if you want to know how it applies:

Trying to find "Time to Kill" the stronger unit a: TtK(a) = hp(a) / n*dps (b) . Additionally TtK (b) = hp (b) / dps (a). setting TtK (a) = TtK (b) and ultimately solve for n..... n= hp(a) * dps(a) / hp (a) * dps (a). So hp * dps becomes the natural unit for ratio comparisons of time to kill.

So, to simplify, the numbers I have displayed, when used as a ratio, would show the number of units needed in order for each side to kill only one of the other. In the case of the cruiser, it would take roughly 61 marines (11000/180) to kill an unarmored cruiser in the same amount of time that it takes the cruiser to kill 1 marine.

Now admittedly, people would probably find it more useful to see the number of marines it takes so that the cruiser and all the marines die at once (equivalence). The problem is that that is a much more complicated formula because the dps of the weaker unit would diminish in increments. I just didn't feel, as a tool for comparis

[Squishy]

Bah cut me off:

didn't feel as a tool for comparison that it added anything over the much simpler hp*dps model. Also, it's been forever since I had to do math like that and I have completely forgotten the appropriate formula =).

If people would like an easy estimate for equivalence, however, taking the square root of the ratio and increasing it by about 41% should give a good figure. Again, using the cruiser vs. marine scenario: 1.41 * √61≈11.02. So 11 marines would probably just get beat out by an unarmored cruiser. If you want a more precise estimate of real game situation, the cruiser starts with 3 armor and the marines, conveniantly have half dps at 3 armor so: 1.41 √122 ≈ 15.5. So 16 marines are probably a close match for a battle cruiser in the game.


Edit: I have been pretty busy the last couple of days, but I will try to get the missile turret data up in a day or so.

[Azureflames]

I didn't read all the posts in detail so maybe this was mentioned, can you include stimmed stats for terran?

[Squishy]

I didn't read all the posts in detail so maybe this was mentioned, can you include stimmed stats for terran?

Short answer: Stimped marine AS is 1.0, marauder is 1.7 (50% attack speed increase).

This was a comparison of baseline units, which is why stimps weren't included. I am working on buffed and maxxed units atm, but have been pretty busy so it won't likely be up till after the weekend.

[Beta]

Ignore this post.

[Beta]

I think the only thing left to add is DPS*HP/cost

[Wyvern]

This is all really great information. I wish the in-game interface showed attack speed as an actual number and not a vague generality...a lot of units are a lot stronger or weaker than they look. I mean, check out Hydralisks versus Roaches. I knew Hydralisks were somewhat more damaging, but I never would have guessed it was by so much.

I only have two suggestions. First, it would be nice to list their range in there somewhere...there's no way to factor it directly into the DPS values, but it's an important number to know in order to be able to judge actual combat effectiveness. Also, major upgrades should probably be accounted for, like how much a Marine's DPS*HP increases with combat shields, or a Hellion's upgraded damage versus light targets.

Also, I think we should all stop for a moment to laugh at Stalkers, who do less DPS against non-armored targets than unstimmed Marines one-for-one at well over triple the cost.

[Squishy]

*Updated for patch 5 - Hydralisk numbers corrected for new attack speed:
- to get more accurate numbers I killed 3 rock formations via the Hydralisk. 1 at melee range, 1 at max range and 1 mid range (all variants tested the same). Tested times versus complete rock destruction as well as my previous method of split timings up to 40 attacks now.

Of note, after multiple tests I am getting an attack speed based on the in game clock of 0.86 (assuming error in favor of shortest time, best possible was 0.85). The patch notes say this should be 0.83. Noting it here and will mention in bug forum as this is my first chance to test against real numbers listed by blizzard. Unfortunately normal is not an option in replay so barring some more comprehensive tests I can't verify this as an error in attack speed of a single unit, all units or just an error in the replay clock (will come back to it).


I think the only thing left to add is DPS*HP/cost

The reason I don't do this is because by estimating the value of cost I have made an effectively arbitrary metric. Couple this with the fact that I don't have an idea of the "budget" value of damag vs HP and you would get a very biased statistic. I can tell you already that in its current form it would be heavily weighted to favor HP over damage and I don't think for these purposes that would serve to offer any new info. A subjective view of the data will give as much comparison value as that statistic would.

[Aeon]

Just a thought, I think most players have more then 16 workers mining crystal. I think most keep around 20-24, this might effect the weight of gas to crystal

[Squishy]

Just a thought, I think most players have more then 16 workers mining crystal. I think most keep around 20-24, this might effect the weight of gas to crystal

I realize this and there are 2 reasons I kept it at 16:

1) Up to 16 workers every unit adds an equally increasing amount of minerals to your supply. Above that number, the mineral to worker ratio starts to decrease ever so slightly. This makes the comparison between mineral and gas rates a little more complex from a "how many collectors are doing the job" perspective.

2) I felt, even though it seems rationally sound, that even 3.3 seemed a bit high. Adding more mineral consumption only inflates that number further. If you look at the cost analysis as it is, any unit that uses gas is way undervalued compared to ones that are pure mineral. One could argue that it is a correct assessment as gas seems way too slow right now given how quick many games are as well as the relative popularity of tier 1 units. But that should be its own discussion =)

Edit: Still if pepole would like the additional comparison, I will, for the time being, try and find the mineral info again and include a modifier value to the original post.