Triangular numbers are a common pattern in RPGs, whether overt or covert. You may not know what triangular numbers are but as soon as I show the pattern, you’ll probably recognise it.
The triangle of 1 is 1 (1 = 1)
The triangle of 2 is 3 (1+2 = 3)
The triangle of 3 is 6 (1+2+3=6)
The triangle of 4 is 10 (1+2+3+4=10)
The triangle of 5 is 15 (1+2+3+4+5=15)
As an example, you can multiply this pattern by 1000 and you get the basic scheme for experience in early versions of D&D (modified a bit on eother side to account for the benefits and weaknesses of different classes).
I’m thinking that factions in a LARP could easily follow the same triangular structure. One player can’t form a faction (Individual = L1), Three players can form the most basic faction (Circle = L2), Six players can form the next level of faction (Squad = L3), Ten players are needed for the next level (Order = L4), Fifteen to progress further…etc.
Being in a faction provides benefits to the members, and those benefits are capped by the faction level. Such bonuses might include automatic increases to influence actions, availability of equipment or allies, security, etc. Factions would have player characters as leaders, so larger factions would have a higher number of players under the control of a single individual, but there would always be the option that players could defect or break-away. A faction operating near full strength for its size would need to be good to its members, otherwise a decent breakaway might reduce the membership below a level threshold.
For example: An Order (Level 4) might contain 12 members (an order requires 10 members), but hypothetically it might offend a small group of its members who decide to break away. If three members leave, the larger group drops below the numbers required for an order (now at 9). The new break-away faction is a circle (Level 2 = 3 players), and the old faction drops back to level 3. The old faction needs to find a new player to resume its former status (preferably during the same game in which the break-away occurred, so that word doesn’t spread to other groups about their weakened state).
Why use a triangular system? It’s actually pretty simple, and works for a few reasons. Firstly, it’s an intuitive system with easy numbers to work with. Secondly it allows for fairly rapid progression at lower levels while gradually slowing down with its benefits as the numbers get larger (this means that bigger factions, with more members, tend to have higher potential benefits for their membership, but they aren’t so overwhelmingly powerful that there is no point to starting up a new smaller faction).
Also note that I’m using this system to cap potential benefits.
I like the idea of having characters spend some kind of currency to gain benefits for their faction. It basically works the same as spending XP to gain benefits for their character. If we use influence actions as the basic unit of expenditure for factions, then we can use them to build strongholds or headquarters (which provide security, healing benefits and possibly things like training grounds for the characters), battle standards (which provide benefits to morale on the battlefield), back-up troops, or a wide range of other potential items that could be used to benefit the faction’s members.
Such benefits would have to be bought, but could only be bought up to the level of the faction. It might be an idea to also add an upkeep cost on certain items (let’s say a quarter of the original value, otherwise it degrades by a level).
Example 1: A Stronghold
A stronghold might cost twelve influence points per level, so a level 3 stronghold might cost a total of 36 influence points to build and 9 influence points per month to maintain. If the upkeep cost wasn’t maintained, it would drop to a level 2 stronghold. Increasing an existing building would cost the monthly upkeep cost, plus the extra 12 points to increase the building’s level status. This level 3 stronghold would require a minimum level 3 faction, and therefore a minimum of 6 players. The nine points of influence would basically cost 1 to 2 influence actions per player to maintain. If everyone spends 2 influence actions to upkeep the stronghold, the remainder could be banked for potential growth in future.
Example 2: A Battle Standard
A battle standard might cost four influence points per level, so a level 5 battle standard would cost 20 influence points to build and 4 points per month to maintain. I have no idea what a level 5 battle standard would do at this stage, but it would be pretty damned impressive (maybe a morale bonus to all fighters within 3 metres per level of the standard). A level 5 battle standard would require a minimum faction level of 5, and therefore a minimum of 15 players. Only a few characters would need to pay a single point each for the upkeep cost on the standard, these characters might belong to the factions “honour guard”, or maybe a single character takes on the role of standard bearer and earns a special point of factional status in exchange for looking after the flag.
Some factional benefits would simply be bought, and would then become permanent attributes of the faction. It might cost 30 points to gain a speciality sphere of influence; once bought, every member of the faction automatically gains an extra level in this particular sphere (a faction might be able to buy 1 level in a sphere of influence per factional level). This adds a degree of specialisation and interest to the factions, beyond the mere colour of designing factional emblems, house mottoes and battlecries. A GM could create a few factions initially populated by NPCs for characters to join, rise through, and eventually lead, or they could allows players to develop their own factions from scratch.