War Weariness

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War Weariness depicts how distraught is your population by your involvement -and losses- in recent wars of aggresion (not defensive, as determined by the Sphere of Influence). It is one of the more important regulating mechanics in Evosolaria, making mindless and constant warfare between players non-beneficial, and even more so against weaker or new players. It doesn't aim to prohibit war at all, but only make players think (and weigh the risks and the rewards) before committing attacks, and discourage especially long-drawn campaigns or permanent occupations of planets. In other words, under the war weariness mechanic, succesful warfare can be defined as cycles of short, brief periods of highly profitable engagements, followed by "recovery" periods of relative peace and rebuilding.

Calculating War Weariness
War Weariness is in fact a ratio -expressed in %- of a factor derived from losses in combat (inciting factor) divided by a factor derived from your population (mitigating factor). It is also very important to note that War Weariness is also affected by time, as it tends to return to 0% provided there is no further conflict.
 * Inciting Factor: War Weariness increases every time fleet is lost in combat taking place strictly outside your Sphere of Influence (only). War Weariness doesn't increase at all when combat takes place within your borders (Sphere of Influence), as such engagements are considered defensive wars. Note that War Weariness also only increases from combat with other Players, not with NPC Factions. Also, for civilizations with very low Support & Discipline Social Factors (both of them required), War Weariness can occur simply by the presence of (significant) fleet outside the player's Sphere of Influence. Finally, the Inciting Factor is naturally diminished by the passing of time. In particular, regarding all of the above:
 * The Inciting Factor of War Weariness increases by combat events (not-time-based factors):
 * +0.003*(x)*log(x/100)*HR, where x is a unit of cost of your fleet that is destroyed in a combat event where you are the attacker, (example: if you attack and lose fleet costing 100,000 metal, the inciting factor will be increased by 0.003*100,000*log10(100000) = 1500) and HR is the Honor/Reason factor which equals to:
 * max [1, (level of higher level player/level of lower level player) - 0.25) ]
 * which means that if the lower level player in that combat has more than 80% of the higher level player's strength, war weariness remains as it is, but is gradually increased the higher the level difference becomes (it starts becoming an important factor if the lower level player has less than 60% of the higher level player's strength). This discourages high level players from picking on low level ones (but note that is also discourages low level ones from making senseless attacks against players of much higher level than they are). "Honor" stands for the fact that the citizens are either against their leaders "bullying" too weak civilizations (idealistic motives) or they simply consider fighting - and losing fleet - against "primitives" to be beneath them/insulting (prideful/vanity motives). "Reason" stands for the fact that the citizens are against their leaders behaving without reason and starting an offensive fight with enemies who are way out of their league.
 * Note: The HR factor is greater or equal to 1, so it either increases war weariness, or it does nothing, it can never decrease it.
 * +0.001*(x)*log(x/100)*RP* HR, where x is a unit of cost of enemy (player's) fleet that is destroyed in a combat event event where you are the attacker, HR is the Honor/Reason factor again, and RP is the Relative Population Factor which equals to:
 * max [1, 0.5*(Your Total Population/Enemy Total Population) ], if YTP>ETP
 * min [1, 2.0*(Your Total Population/Enemy Total Population) ], if YTP<ETP
 * this modification is there as one more way to discourage attacks against the weak - much lower population - players, especially a type of attack that would otherwise cause negligible war weariness for a high level player: an attack with seemingly little losses for both combatants, but where the term "little" is only accurate from the point of view of the high level player, while being at the same time "huge" losses (a significant part of his fleet) for the low level player. This multiplier also makes war (weariness) a little more "fair" for those who choose to develop low population civilizations, given the importance of total population in the war weariness mitigation factor, as seen below (still, civilizations with a larger population will be naturally more resistant to war weariness, as they should be). Note that there is no modification if the higher population is less than double of the lower one, and it starts becoming an important factor if the higher population player has more than 4 times the population compared to the lower population player.
 * Note: the Relative Population factor can either increase war weariness (if your population is the large one) or even decrease it (if your population is the small one).
 * +0.002*(x)*log(x/100), where x is a unit of cost of your fleet that is destroyed in a battle where you are the defender.
 * Note that the presence of "log(x/100)" (that is the common, decadic - with base 10 - logarithm, btw) means that losing (or killing) the same amount of fleet all in one combat event incites greater war weariness than losing it in many consequent events. For example, losing 2*Y fleet in one battle causes about 30% more weariness than losing Y+Y (=2*Y) fleet in two combat events. 4*Y is 60% more weariness that Y+Y+Y+Y, etc. For obvious reasons, a loss of fleet less than 100 (which is the cost of 2 Fighters) would give a negative result, so all instances of "log10(x/100)" should be treated as "max [0, log(x/100)]" instead.
 * The Inciting Factor of War Weariness increases by the following time-based factor:
 * +0.001*D*(Y) per hour, where:
 * D is a factor taking values from 0 to 1 according to the value of the Discipline Social Factor
 * Y = max [0, (F-S*TP)]
 * F is the amount of fleet (in units of cost) currently outside your sphere of influence
 * TP is the player's Total Population
 * S is a factor taking values equal or greater to 0 [...add here...] according to the value of the Support Social Factor
 * The Inciting Factor decreases with time until finally reaching 0 in the following way:
 * -1%*(current inciting factor) - (% of Fleet inside Sphere of Influence)*max[0, (Total Population - 0.5*Occupied Population)^0.8] per Hour (rounding UP to the closest integer).
 * The above means that, even if you keep all of your fleet outside your Borders, or have so many -and big- occupations that their population exceeds the population of your colonies by a factor of 2 at least, (and of course provided you don't engage in any new combat event), the inciting factor will still decrease by 1% per hour (decreasing less each hour, as the 1% is applied to a lower inciting factor each time), which means that it will be halved in about 70 hours and be 1/4th of its initial value in around 140 hours. However, if you also pull back most of your fleet behind your borders and have a large population - with few occupations - the war weariness decrease can be significantly greater.
 * Mitigating Factor: As mentioned already, the mitigating factor for war weariness is your population, since a large nation can afford to sustain bigger losses before the population becomes fatigued of warfare. Thus, the value of the Mitigating Factor is:
 * 100*max[1, (Total Population - 0.5*Occupied Population)^0.8]
 * From the above equation we can deduce the following:
 * A large population equals less war weariness, assuming the same losses in combat (inciting factor). However, as indicated by the fact that the Population factor is raised to the power of 0.8, this relationship isn't linear (doubling the population doesn't exactly equal half war weariness, but a bit more than half - about 7% more; or vice versa, to achieve half war weariness you need double the original population PLUS about 19% more population over that)

[Potential War Weariness ... ]

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