EPTLinkage:
Definitions
- HP+Shield = combined for practicality and consistency. Keep in mind the drawbacks: Protoss remains slightly stronger than the data suggests.
- Total resources = minerals + gas, combined for practicality and consistency. youngminii points out that gas is actually more valuable than minerals since they take longer to harvest. So bear in mind, gas-dependent units are weaker than the data suggests.
- Total damage = what the unit inflicts, in total, after each cooldown
- Cooldown = the time between "hits"
- Damage/second = (total damage/cooldown), or DPS, the average inflicted damage per second, over the long run. DPS is a very revealing statistic. A hit that does 60 damage may appear strong, but it is actually very weak if it must wait a whole minute before hitting again. DPS reconciles damage with cooldown, giving us a way to easily compare how fast each unit can kill. AssuredVacancy warns us not to overestimate DPS, "If there was a unit that did 1 damage at 20 hits per second, its dps would be quite high; realistically though its damage output is not high at all as most units in the game have armor." So: units who hit more frequently have an inflated DPS. tetracycloide says, "In a real world comparison the best conclusion to draw is that high damage slow refire rate units are the best damage dealers with only short windows do deal damage in while low damage high refire rate units with high DPS are best for sustained engagements."
- Thors, Battlecruisers, Ultralisks, and Void Rays (long) (in that order), do the best. Hellions, all three workers, and Mutalisks do the worse, here.
- DPS/R = (Damage/cooldown)/(minerals+gas), or "DPS per dollar." This is even more revealing than DPS. Say "Doodaas" inflict 40DPS and cost 80 in resources, and "Diddlies" inflict 20DPS and cost 30 in resources. Doodaas do 0.50 DPS per dollar and Diddlies do 0.67. That means even though Doodaas have a higher DPS, I'm better off buying Diddlies, since I can buy more and get higher overall damage throughput with them per dollar.
- Missile Turrets and Spore Crawlers are a great value here. For units, Zerglings, Reapers, Marines, and Zealots rate the best (in that order). Ghost, Void Ray (short), Thor (vs air), and Mothership perform the worse here.
- H/R = (HP + Shields)/(Minerals + Gas), or "brawn per buck." This simply says how much health you're getting per resource.
- Stationary attackers (like Photon Cannons) get the best value here. For units, Zealots, Roaches, and Zerglings rate the highest, while Ghosts, Dark Templars, and Reapers rate the lowest.
- ((H/R)*(D/R))*1000 =(((Damage/cooldown)/(minerals+gas))*((HP+shields)/(minerals+gas)))*1000, or cost-effectiveness: DPS over the course of a battling unit's life per dollar. I multiply here because every unit of life means another unit of time that a unit can actuate DPS. I multiply it all by 1000 only to make the numbers more readable. This is the meat and gravy. It thoroughly reconciles the costs (resources) with the benefits (damage, cooldown, and health).
- ((H/(S+R))*(D/(S+R)))*1000 = (((Damage/cooldown)/((minerals+gas)+((supply cost/8)*100)))*((HP+shields)/((minerals+gas)+((supply cost/8)*100)))*1000, or cost-effectiveness which accounts for supply: This is useful in the early game. In the later game when in battle, players often simply need to replace units that die. In this case, a player needn't buy supply, and this formula wouldn't be appropriate. The values correlate almost perfectly anyway, with the exceptions of stationary attackers (Photon Cannon) that, of course, don't require supply.
Unaccounted-for costs and benefits
Things not included, nor would I like to attempt to include in a quantitative way.
- Unit sizes
- Splash
- How well a unit is suited towards map elements
- Tier restrictions and tech tree climbing costs
- Spells
- Range
- Speed
- Flight
- Cliff-climbing
- Able to attack air (or ground)
Observations and inferences
If you disagree with any of these, please post which ones specifically and a detailed explanation of why. I will update with your insight and credit you.
General
- The archetypal starter units for each race are each extremely reasonably priced (Zealot, Zergling, and Marine). Chronocide adds, "never stop making tier 1 units. They're just too efficient to bypass completely."
- "Counter" bonuses against armor are almost always an excellent bargain (Marauders, Immortals, and Ultralisks). This isn't to say that their non-bonus counterparts aren't any good, as Chronocide indicates, "this spreadsheet would lead people to believe that they shouldn't use a unit unless they intend to exploit it's bonus damage, which leads to patently false ideas such as "Colossi are bad against Marauders")."
- Non-unit attackers (Missile Turrets, Photon cannon, Spore crawler, etc) are dirt cheap per DPS, likely because of their immobility.
- You're an absolute sucker if you make casters and don't capitalize on their abilities. Some casters are incredibly cost-ineffective without them (namely Ghost, Sentry, Mothership, and Corruptor).
Protoss
- Immortals and/or Void Rays are very worthwhile when many armored units are in play. Calamity reminds us to be wary of Ghosts' EMP.
- Zealots have excellent cost-effectiveness, but, as Chronocide points out, "only if you can utilize them. Can they surround? Does your opponent have anti-light or AOE units?" Furthermore, you will increase their utility, and thus cost-effectiveness by upgrading to Charge.
- When not exploiting Dark Templars' invisibility, they're basically over-priced Zealots. Ryuu314 speculates that after full upgrades, this may not be true. Once I have time to calculate that, we'll find out for sure.
- Stalkers appear like a much more reasonable answer to air than Pheonixes. Calamity adds that Stalkers don't require a Stargate and the player can warpgate them in--all an added benefit.
- When range and mobility don't matter, consider the very cost-effective Zealots instead of Colossi. PlaGuE_R points out that Colossi do however have splash damage, which can wipe out armies faster.
Zerg
- When not expecting an air threat, favor Roaches to Hydralisks? Meff adds that not only air, but also anti-armor units such as Marauders, Immortals or Ultralisks. Chronocide says, "Hydras have a much better range which means in ANY practical conflict they will do more damage than roaches. I think the conclusion to draw is that you might consider adding more roaches to your roach/hydra mix than you were expecting, but even that is dependent on factors well beyond the scope of this study."
- Mutalisks appear rather costly, throughput-wise. Chronocide adds, "The strength of the muta lies in it's mobility."
- Adrenal Glands boosts Zerglings' cost-effectiveness up almost 30%!
Terran
- Missile Turrets, out of all the units, give you the best bang for your buck, by far. Perhaps this is because of their minuscule demand. Chronocide explains, "Most missle turrets never fire more than 1-2 shots in a game."
- Marines are the most cost-effective mobile Terran unit. Despite this, Chronocide warn us of possible Banelings, Colossi, or Hellions.
- Marauders pay off best against armored units. Elsewise, they're so-so.
- Stim Pack is well worth the damage sacrifice. Marines get an 11% increase in cost-effectiveness. Marauders get a 20% increase (almost 30% when vs. armored).
- Be very wary before introducing Thors into an air-dominated game.
- When facing armored units at a closer range, get those tanks out of Seige? According to Cyanure, perhaps not since this does not take splash into account. However, seven added DPS seems like a good enough incentive to me. Chronocide advices, "it takes 3.5417 seconds to change from siege mode to tank mode. But there are indeed situations where tank mode is the better route to go, but only very early when unit counts are low (such as one tank + a handful of marines vs a few stalkers or marauders)."
Revisions
7/24/10 - Updated formula to take into account its quadratic nature (thanks MasterOfChaos). Added Missile Turrets, Planetary Fortress, and updated a couple of stats (thanks lololol). H/R added. Changed how the formula is presented (same values different look) per d3_crescentia's advice. Modified observation section per Chronocide's post. Added stim pack info. Created a column which accounts for supply costs. Fixed the confusing Vikings.
7/25/10 - Updated with Meff's comment. Added a description of the "cost-effectiveness with supply" formula.
7/26/10 - Added High Templar values. Added upper bound figure Colossus.
I'm pretty happy with my spreadsheet right now; however, if you would like something added, first calculate it yourself and I'll copy and paste it in and give you credit (e.g. Carriers, armor, upgrades, etc.).
