Balance Proposal: Universal Weapon Power Equation

[Oggdo Bogdo]

Hello, I am not on the development team and I have no say in the current equation nor do I believe that efficiency should be the great equalizer between all guns, but I am a snub PvPer and I have a background in mathematical optimization. I think this is a good effort, but I want to explain some of the reasons why this model as it is, shouldn't be applied to snub PvP. I think your calculations are sound, but there must be some consideration for the context to make the model better. Particularly the context of snub duels.

The reason why range should not be of equal weight (or a weight at all) to gun velocity in snub PvP is because the effective range of a gun against other snubs in both 1v1 and group fights is currently almost entirely dependent on the gun velocity, and this effective range is already lower than the current range values. If a projectile requires too much time to connect with a target, the probability of scoring a hit falls off because there is more time to react to it. You're weighting a value that has an impact of close to 0 equally with a value that is crucial to snub balance. In a cap fight, this is less true because the larger size of cap hitboxes increases the probability that a projectile at long range will hit. In a snub fight, the probability of a hit at maximum range is very close to 0 and therefore is negligible. In other words, you would be over-penalizing players for choosing slightly longer ranged guns on their snub, which provide them almost no value. This leads either to a re-working of range values to make the numbers suitable, or with these longer ranged weapons being discarded entirely, neither of which I presume is what you want. I also don't really think this is your fault because snub range values aren't very consistent in vanilla because of flavor, and they are mostly an afterthought in discovery.

If you want the model to have range as a weight, I would suggest thinking about range in terms of what the range value is able to accomplish. For example, there is no functional difference between a snub gun with 560 range and 480 range and there should be no difference in calculation for energy. However if you put the range at 800 metres for example, you might be able to start boxing caps, and that would start to add significant value to the gun.

A small point, but you solved for the calibration coefficient using a Vengeance MK IV as your base case. There is no reason for you to believe this is a good choice if you consider that the model that you are lifting numbers from might already be flawed, which in turn leads to balancing every gun on a flawed case. I think you might find a lot of snub players are NOT happy with this in-game value of 89.

Additionally, hull and shield damage values are not independent, so you can simply rewrite D_h + D_s as simply 1.5* D_h. I want to note that in vanilla, ship shield and hull values were almost equal, just that shields essentially reduced incoming damage from non-pulses by half. In discovery, at least for snubs, ship hull values are retained but both hull and thus shield damage numbers are scaled down by 2.5 and ship shield values down by 2.5, so it might not be accurate to think of all damage as having equal weight.

A more important point: by ignoring DPS, you essentially guarantee that some guns will perform strictly better than others. Two guns that only differ with refire rate have the same efficiency and energy cost per shot. Then there is no reason for players to pick the gun that has a lower refire, because the gun with the higher DPS will outperform the lower DPS one in a duel where ship powercore is much less of a factor, but both guns will have equal performance in a group fight. This situation actually does exist in the game with the Nomad Laser Type II and the Lesser Nomad Laser Type I, albeit they are at different classes. You will however notice that apart from the rarely flown Labraid and Nomad LF the other Nomad ships don't have a problem mounting full class 3s. What currently stops players from doing this is the difference in efficiency values. If not, they would always choose the higher DPS Nomad Laser Type II. There are probably much better examples than this, but I just want to illustrate why accounting for this would make the model better at giving players more choices to play with.

DPS isn't even the full picture. Because duels are entirely about recurring short passes between the ships, there is limited time to fire, and a lot of time during which players are not facing each other and thus won't fire. This means that it's very likely that powercores will never even fully drain, and players have room to play around the mechanic of lower powercores if needed. The damage per hit in combination with DPS is thus what makes lower refires very strong in duels. For simplicity, let's say every duel only has passes that last 1 second. Let's take an example from the game with the EXCALIBUR and the THUNDERWAVE that both have the same DPS, speed and range. Which weapon actually performs better in terms of damage in this situation? It's the 2.00. Because the first shot of the pass isn't on cooldown, you actually get 3 shots from the EXCALIBUR and 9.33 shots from the THUNDERWAVE. That's 1800 damage from the EXCALIBUR and 1344 from the THUNDERWAVE in that 1 second pass. With your current model, you get an efficiency of 1.64 with both guns. However, one outperforms the other by 33% more damage in duels. You can thus see that the model gives an unfair advantage to weapons that have lower refires. Since efficiency doesn't matter with duels, why does this matter? Because with the same level of accuracy with both guns in group fights, the EXCALIBUR breaks even because of equivalent efficiencies. Which means you again have a clear winner that does one branch of snub PvP better and the other branch equally well.

Personally, the problem with the in-game equation is over-weighting of a lot of things by allowing all kinds of junk weapons into the game that range from fundamentally unfun to interact with and use, to being outright utterly useless, and accommodating these outliers has really skewed the efficiency of more standard and vanilla-style guns to being extremely unfun to play with. Arguably, the solution is to actually look at what is viable in the game and recalculate the efficiencies based on what the guns are actually capable of, since they either utterly fail or are unreasonably effective at certain tasks. A more general model like this that relies entirely on realism doesn't account at all for player decisions and interactions in practical situations. Realistically, if a weapons designer was to design weapons based on your model, they would simply apply optimization techniques to find the optimal range and speed to ensure their guns have the highest expected efficiencies (range should be high enough to do its job and not more, speeds should not be too low that they have low probabilities of hitting, and not too high to yield diminishing returns). However, we have the ranges and speeds in advance and we are designing the efficiency after the fact to suit these combinations. This means that there will be a lot of guns that are going to be suboptimal, and that you would end up with a range/speed combination that is a clear winner.

tl;dr Ranges aren't as important as the model claims it to be for snubs. Not all guns with the same range and speed are equal, nor should they be treated equally. Refires, DPS and alpha damage are important but not factored in. The model prescribes a clear winner based on the context of snub PvP. I am however, interested and hopeful for any change that is better than what we currently have. There are many snub players who are extremely discontent with the in-game efficiency values.

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