In this scenario, assume everything aside from damage and rate of fire is the same and that accuracy is completely dependent on the user, no random cone of fire or recoil.
All participants have 100 points of health and outside of headshots, there are no damage modifiers to specific body parts as with nearly every shootan gaem with masheen guns.
Damage Per Second is an ineffective method of measuring and balancing these weapons.
The green weapon has the lowest rate of fire yet the highest damage. It can kill in three shots.
Red is the mean between the two - four shots.
Blue in five shots and with double the bullets in the amount of the time the green fires.
If you just multiply damage and ROF, you'd see that Red would be ahead in Damage per whatever.
BUT that doesn't actually tell you anything. It doesn't tell you exactly how swiftly you can eliminate an enemy.
There are two way more important things to take into account.
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1. First is the absolute way of measuring balance in power or "Time to Kill".
Since these are guns, the shot is going to be almost instant hit, so obviously the first shot is at 0 seconds and the delay takes place after.
That means there is no delay after the lethal shot, it is left out.
Other delays or time related events like latency and bullet travel time are also left out as it would be assumed they are the same. If there is some deliberate speed (dis)advantage such as an SMG sighting faster, then that's a thing based on range and different weapon types and the advantage in time would be in that way rather than pure TTK.
Green weapon fires a shot every 0.15 seconds. Three shots to kill = the third (lethal) shot at 0.3 seconds.
Red fires every 0.1 seconds. Four shots = 0.3 seconds.
Blue fires every 0.075 seconds. Five shots = 0.3 seconds.
All three are 100% equal... only when they meet their ideal time to kill with no misses. That's where 2 comes in.
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2. The second thing is then the player factor. A player is completely unpredictable, inconsistent and can not be equated in balance.
There is an incredibly low chance of an encounter where every shot lands.
Therefore the only way to involve a player in the process is in Missed Shots.
With any missed shot, the other weapons win instantly. So the balance process must also include that every weapon misses a shot.
If Green misses a shot, he has to add 0.15 seconds to his Killing Time.
If Blue misses a shot, he only adds 0.075 seconds.
For every shot Green misses, Blue can miss TWO shots (which it would need since it needs two more shots to kill).
For every shot Green misses, Red inches ahead by 0.05 seconds.
For every shot Red misses, Blue inches ahead by 0.025 seconds.
One miss:
Green = 0.45
Red = 0.4
Blue = 0.375
With every miss, they grow further apart with the higher ROF getting the benefit. With that, there is a duality.
Green requires a player to be accurate or else the other weapons gain the advantage in killing speed, however he is given leniency in the number of shots necessary.
It requires the least shots, but every miss is a heavy penalty.
Blue requires the player to be accurate because he needs to land more shots, however he is given leniency for that with less penalty in time for missing.
It requires more shots, but each miss has a shorter time penalty.
Red is in the middle, it doesn't get the same level of benefit in power or speed that Green gets over Blue / Blue gets over Green.
It has double the benefit in time advantage over Green than blue has over it, but only half the benefit over Green in shot leniency than Blue's benefit over Green.
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The three are a perfectly ideal trio of guns with nothing to interfere with their potential.
But that's not all that makes the weapon in these games.
If the rate of fire were slightly different, other, rougher measures must be taken. Including inaccuracy and recoil and range.
If you go comparing a rifle and an SMG, there's another layer of balance (though rather simple) to be had. The SMG has an advantage in Time to Kill at point blank range either through Power or Speed while it has a disadvantage to the rifle at a distance.
If three guns killed in five shots, but were different in Rate of Fire by only 50 RPM, the fastest one would be the best, right?
750 - 0.08
800 - 0.075
850 - 0.07
There's no math that can make these weapons with equal shots to kill 100% balanced. The moment you enter random possibilities like recoil or a cone of fire as a deliberate force (the only way to deal with this scenario), the weapons run a tightrope that can topple over either way.
You could think that the 750 would have the least recoil and 850 the most. That sounds the most simple and usually is the best solution. However if one had just too little or too much recoil, that alone would make it superior (rendering the other two obsolete (even if it is the slow one)) or inferior (rendering it obsolete in the face of the other two (even if it is the fast one)).
The balance of Speed versus Power leading to Killing Potential can be elementary.
The balance of Accuracy versus Killing Potential is a whole new ballgame. One that has to be put into practice and not just run on paper.
Anyway.
Time to Kill is a measurement of ideal killing potential for
weapons of the same type and only a part of the weapon's power.
Balance of weapons isn't a "Guy A versus Guy B".
Balance is "
You with Gun A versus
You with Gun B".
When you can't choose a weapon based on the fact that it is "better" than the rest, and instead you choose any gun based on the style it offers and how you like the feel of it, there's a good balance.