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I use this term in games pretty frequently so I thought it would be worthwhile to explain what I mean by trajectory here. Although I have used the term in mafia since long before I started playing at MS, I never really explained what I meant prior to a newbie game that I replaced into on late day 1.
"Re Player X and posts that I liked I'll start by saying it was the trajectory of his posts. He homed in on several posts that also caught my eye and asked probing questions. I could see his reasoning - how he reached the decision to vote Player A, and I agreed with it. Same thing with his trajectory on Player B. People good at playing scum absolutely can create that sort of trajectory with their posts, but it usually doesn't come off completely effortless and unforced and it can involve more emphasis on dots and less emphasis on connections because there's a layer of self-consciousness involved that is not easy to turn off. Player X is good at avoiding that tendency for more dots and the layer of self-consciousness. But, I've seen that his trajectory sometimes doesn't make as much sense when he's scum.
Trajectory isn't a naturally smooth thing in posts - we react to what other people post and sometimes a line of questioning gets left in the dust due to a change in the game's landscape. Town players reactions are pretty un-self-conscious. Scum are more likely to try to maintain a consistency in stance in the face of in-thread changes, the effort sometimes looks forced, or they freeze up a little and wait to see what town makes of things before committing."
Looking at the trajectory toward votes can be particularly helpful. What post or game event caught the player's eye? How did they react? What did they ask? How quickly did they go from interest or suspicion to vote, FoS or town read? Trajectory analysis is not purely objective. The more you know about a player's style the better you can evaluate trajectory. Some players tend to telegraph their thoughts and suspicions well in advance of voting/unvoting, etc. Some player keep a poker face until their minds are made up and then make a sudden and unexpected move, in which case their reasons for the change may come after they make their move. Some players do a little of from Column A and a little from Column B.
In generic terms, scum players often try to dot their i's and cross their t's when it comes to FoSing or unFoSing, voting or unvoting, etc. The trajectory looks good directionally, but may seem overdone compared to their town behaviors. Sometimes scum players are more inconsistent than town, or their trajectories look out of step with the direction town players seem to be headed. They react more slowly to game events, or they react to things that other players ignore and vice versa. These sorts of trajectory inconsistencies may trip up players who aren't really comfortable in scum roles, while experienced scum who enjoy scum roles may be able to emulate town behaviors, and even predict where town will head and get there first.
Models are tools for understanding reactions and relationships and/or for predicting outcomes. This is true of models in general, not just models for mafia.
We develop mental simulacra of players that we play with frequently or on whom we do detailed meta analysis. I often read something to the effect that it's not a meta tell if a player does something as both town and as scum. While it's true that something a player does only as scum is a nice find that you don't want to let the player know about, that's actually a pretty crude model of how the player behaves. It's not just what players do as town or scum, it's how or when they do things when they do them as any alignment.
This gets to what I mean when I talk about scum-PlayerName and town-PlayerName models. When an event occurs or the game state changes, what array of behaviors do I expect from the player if they are town? What array of behaviors do I expect if they are scum? And what subleties and nuances do I expect from behaviors that could be town or scum?
If I don't have enough information about a player to predict behaviors based on their past play, then I will attempt a more generic or combinatorial model.
win condition + role + strengths/weakenesses and longterm objectives --> motivation --> in-thread behaviors
As town or scum, this algorithm is useful. As town, you are trying to find and eliminate scum, identify other town you can work with, and protect your PRs. As scum, you are trying to get town eliminated, identify the town PRs, and come off as town to town while working toward your win condition. Writing a post flows from win condition through to motivation. Discerning wincon and role is an exercise in reverse engineering. One size doesn't fit all, and familiarity with players' personalities, how they approach the game and any changes they are trying to implement in their play style can help in discerning motivation and from there detangling role and personality modifiers to win condition.
Albert P. Rampage's excellent write-up on Alignment Discovery looks like a great resource for figuring out motivation from in-thread behaviors.