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Even if you rock, 4 Templars don't stop 100 hydralisks

or.. Starcraft Economics 101 by Professor Zileas

One thing that even the best players often overlook is the simple fact that technique and tactical skills can only bridge so much of a gap. With all things being equal, good techinque wins.  But, as I was painfully reminded when I lost to Fistantilus not too long ago, 2:1 kill ratios, even between identical units, wont matter if they have a much stronger economy.

Understanding when you are winning and when you are losing is very important. Generally speaking, You could mathematically generalize this something like this:  (ill put it in plain english)

Zileas' Theorem of Starcraft Economics

If your kill ratio multiplied by the ratio of your production to their production is less than 1, you are losing. If their economy is gaining speed, and yours is stationary, and this number is close to but over 1, you are still probabaly losing.

When I say kill ratio I do not mean units killed/units lost; I mean RESOURCES killed/RESOURCES lost both in terms of unit production, miscellaneous upkeep costs (scarabs) and building production/loss.  Buildings also carry a lot higher cost in some cases when they cost them time -- especially when the time prevents them from making cost-effective advanced units (i.e. killing a greater spire, killing templar archives).  For example.  Zerg X has 3 expansions, and has an income of say 75 mineral/second, 30 gas/second. I have 1 expansion and an income of 15 gas/second, and 40 minerals/second. I take one templar and kill 2 mutalisks, losing the templar.  I destroyed 200/200.  I lost 50/150.  I actually lost here because although the actual cost of the units may seem "Advantageous" to me, I'm actually overall behind on production such that this is a loss.   You need to realize what you can and cannot afford to do.  When i have the upper hand I throw away units a LOT more (i.e. sacrifice 4 zealots to kill a hatchery on island expansions, etc), which leads me on to another point...

The Importance of Time, as Well as Opportunity Costs and Opportunity Denial

Time is so so very key in starcraft.  Delaying your opponents ability to expand by a few minutes, or striking away the capacity to produce advanced units for a while is CRIPPLING at times.  Not only will this often force them to produce cost-inefficient low tech units (zealots, wraiths, hydras (in late game)), but it will put them on the defensive.  Also you need to think in terms of opportunity costs and opportunity denial.  For instance: If you delay someone from expanding for 2 minutes, youve not only killed their new command center/nexus/hatchery, but youve ALSO stripped them of 2 more minutes of mining minerals at that point, effectively killing 2 minutes worth of mining worth of troops. Moreover, youve also given yourself the opportunity to build up for 2 additional minutes, which makes this benefit even more.  Time is extremely valuable. Killing large numbers of overlords, or supply depots is very very crippling at times, particularly in an early game, as these structures/creatures take quite some time to replace, as well as costing resources.  Just as a side note, KGOR/Maynard who is one of the few players I fear, does this thing where he almost constantly builds probes/drones/scvs so that when he expands, he instantly has full scvs/probes/drones on the expansion...This strat has costs, but its a wise idea, especially later on...  A great player for sure :)

Conversely, there is a resource cost associated with attacking, especially with larger attacks.  When you attack someone, if you are just beating on their troops, you are effectively wasting your time unless you are doing insane ammounts of damage in terms of the resources formula I was talking about earlier.  There are hidden costs associated with this. The biggest cost is the money you COULDVE spent on expanding instead of those combat troops (assuming you maintained a reserve in your base). Attacking to break their concentration though, in addition to killing their units may be worthwhile... Which leads me to the ULTIMATE hidden resource: Concentration.

The Third Resource: Concentration

Minerals and Gas are the resources that most players think in terms of.  Although these are central to the game, you also need to think in terms of concentration.  I define concentration as time that a player has to spend focusing on a task during the game.  Expanding is a high concentration task, especially if you are protoss.  Attacking certainly has a high concentration level, and the more concentration you put into an attack, the higher the effect.  Even scouting carries a high associated cost.  One big difference between "Someone who is really good" and someone who is #1 is knowing when you need to watch a battle, and when you dont, and recognizing that your opponent also has a finite ammount of concentration to draw from.  There are a number of techniques for minimizing concentration costs (i.e. hotkeying buildings, using magic spell hot keys, queing attacks, etc.), but every thing you do has some intangible concentration cost.  I would argue that as you get better at starcraft, you go into a match with a larger innate concentration income/second :P  It is very possible when doing multiple cooridinated attacks at different locations to use your superior concentration reserve (if you have it) to decimate an enemy who is tied with you in terms of unit control and tangible resources. Although I'm sorry to say this, concentration is basically talent.  Playing a lot of games slowly raises it, but its something some people have a lot of and some people dont.  Its kinda like fast sprint ability in running: You can train up and become a great long distance runner, but for sprinting, theres always that talent based barrier -- you can slowly improve it, but everyone has a limit.  Im sure that someone will push me off #1 who has more innate talent, along with the same skills...

The best way to train concentration, as Visage has reminded me just now over MIT chat, is to play 2 on 1s and 3 on 1s (multiple opponents vs you). I can often pull 3 on 1s, and certainly 2 on 1s, and really the only reason I can do this is my ability to multitask.  Also, team melee is an interesting game as it involves doubled concentration reserves on both sides... well almost doubled since its not one mind thinking at once and they have to communicate...