NewbScum Greeting Tell

[mhsmith0]

Subject: Newbie 1714 (Game Over)

Hey all! Took a quick skim through the thread but want to spend more time before really developing opinions. I'll try to have something more useful to say by tonight.

(fortunately we still won tho )

then again
Subject: Newbie 1691 - Game Over

Hey kaag and everyone else! It's a bit after midnight my time so I'm not at my analytical best, so probably not any real content from me tonight.

This is my second online mafia game, first one here. For the curious, my first was 8/2/1 where scum+3p got a sweep (I was town). I really hope to do better this time around.

Ps a mechanical question (I promise eventually this slot will do more than that): is there a quick/easy way to link to posts? Like if I wanted to, I dunno, link post #3 or the like.

was my newbtown post so...

[Something_Smart]

Were the stats only for the original holder of the slot?

I bet the tell is way less effective with replacements.

[Jingle]

HOWEVER, 37.3% (P[wolf|greeting]) +59.3% (P[town|greeting]) != 100.0%, so something's off but I'm not sure off the cuff what it would be, and I'm too lazy to really rethink my math

Standard wolf frequency should be irrelevant. You just need to weight your sample groups (coefficient) so that the observed percentages are equal.

So, from the OP, you adjust the scum sample to be ~57.1/100. Then the P that any particular newbgreeting is scum is 57.1/(57.1+26) or ~69%, assuming the sample size is statistically significant.

Your probabilities are the ones that are useful to look at when a greeting actually happens. If you want the probability to sum to 1 and be useful for tell validity you drop all games with no greeting at all (as they don't have useful evidence) and have to decide how you're treating games where both town and scum do it. If you want the probability that there is a wolf greeting in a particular game.

Also

VOTE: fuzzybutternnut for having some really entertaining games. I'm sorry to anyone else with entertaining games, I got sidetracked while looking up his meta.

Subverted.

[Krazy]

You were discussing meta in your first post of your first scum game lol

[Jingle]

First game period, actually.

[mhsmith0]

Standard wolf frequency should be irrelevant. You just need to weight your sample groups (coefficient) so that the observed percentages are equal.

So, from the OP, you adjust the scum sample to be ~57.1/100. Then the P that any particular newbgreeting is scum is 57.1/(57.1+26) or ~69%, assuming the sample size is statistically significant.

Your probabilities are the ones that are useful to look at when a greeting actually happens. If you want the probability to sum to 1 and be useful for tell validity you drop all games with no greeting at all (as they don't have useful evidence) and have to decide how you're treating games where both town and scum do it. If you want the probability that there is a wolf greeting in a particular game.

fwiw...

Standard wolf frequency IS relevant, in the sense that the observed sample is biased (which it is). To take an extreme example: let's say that in this sample of game, ONLY newbies randed wolf (and also to be lazy, let's assume that all such games were 5 newbies / 4 SE's)

A sample of 20/46 "tells" being by wolves wouldn't really be relevant at all, because that'd be just barely off of the actual distribution of wolf rands (20/50, or whatever fits into the actual game count, but it'd still be 40%).

Obviously the bias here is far less ridiculously extreme, but a similar concept applies. All that said, the # of tells committed by newbscum players was 20/46 (43.5%), and that very simple calculation really doesn't get you all that far away from the answer. The true probability of a random tell being given by newbscum would be a bit less than that since the sample was overrepresented by newbscum in the first place, but not a whole lot less since the sample wasn't *THAT* skewed. I'm just too lazy to think through all of the math. "Somewhere in the 37%-43%" range is "good enough" anyway i think *shrugs*

[mhsmith0]

PS a "true" bayesian analysis would involve both a prior and a posterior distribution getting some kind of semi-arbitrary mutual weighting. Presumably the prior would be 2/9 = 22.2% (odds of a player randing wolf, also essentially the null hypothesis of the tell being meaningless), and then the weighting is based on w/e you think is appropriate, and I'm much, much, MUCH too lazy to even attempt to lay out the logic involved in that decision making process
(but tldr the "true" answer is "something less than 43.5%, and it's somewhat arbitrary exactly how much closer you get to 22.% vs 43.5%")

[Jingle]

assuming the sample size is statistically significant.

All of that falls under this. An assumption that the information gathered is relevant.

[Jingle]

What you're looking at is the odds that a scum player will greet, which is largely meaningless, btw. If you want a comparison that will add up to 100% probability there, you need to take the odds that a scum player will not greet as the counterpoint.

The important distinction isn't whether there is a greeting in the game, but which alignment a greeting is likely to be, which our data suggests is the case 69% of the time. Whether the data is significant is a point for debate, but the relevant data is 100% the P(Alignment) given event(Greeting). All event(!Greeting) cases are irrelevant.

[mhsmith0]

The observed probability that a given newbscum player will greet is 57.1% (=20/35)
The observed probability that a given newbie greeting will come from a newbscum player is 43.5% (20/46)
I think you're conflating the two of those things somewhat in your analysis, presuming I'm reading you correctly

[Jingle]

Ah, I got 57.1 as an extrapolation. Out of an imagined 100 scum players, 57.1 of them will greet assuming the pattern of the data is constant. (Clearly a faulty assumption, but not one that is inherently bad for broad strokes analysis). The only reason it matches the observed probability that a newbscum player will greet is that the sample size I adjusted it to was already 100.

I'm analyzing the probability independently of the probability of rolling scum in any given game, because I don't care about the odds that you rand scum in the game. I only care about the odds that a greeting is from scum.

Taking our new sample sizes of 100, we can simply cross compare. 57.1 out of 100 will greet as scum. 26 out of 100 will greet as town. Because the sample sizes are equal, you don't have a weight to each, so the sample size of greetings becomes 83.1 greetings, 57.1 of which will be from scum. And now you have a roughly 69% chance that any given greeting will come from scum, with a few clearly faulty assumptions taken into consideration. I'm assuming, for the sake of expedience that the accuracy of those assumptions is fairly high, although we could discuss a random sample collection method that would increase the accuracy further.

The whole point is changing your data so that the sample size of T and S are equal, and then comparing T[g] and S[g].

[Jingle]

Changing is probably the wrong word. I'm just finding an equivalent ratio.

[Jingle]

If it helps, you can change the ratio to any common number. So you could say 4/7 scum players greet and 1.82/7 town players greet.

Then you get P(g=S) of 4/5.82 and P(g=T) of 1.82/5.82.

[mhsmith0]

The whole point is changing your data so that the sample size of T and S are equal, and then comparing T[g] and S[g].

I sort of think I follow you, but I think this particular point is off

In any standard situation, T and S aren't in fact equal.

Over the long run, T = 3.5 * S (2 scum per 7 townies), which is why (if you're interested in "what are the odds that a given greeting comes from scum or town") the underlying distribution of town and scum matters a lot



To put it another way (I'm sure I'm mangling the example), an IQ 150+ person (or whatever trait you associate with financial success) is much likelier to be a garbageman (or whatever blue-collar profession you wish) than a billionaire

Odds of being IQ 150+ in general population is X
Let's say the odds of a particular billionaire being IQ 150+ is Y ( and Y > X, maybe even Y >>> X if you like)
and let's say the odds of a particular garbageman being IQ 150+ is Z (and Z < X, maybe even Z <<< X if you like)
but there are many many many more garbagemen than billionaires

[Jingle]

In any standard situation, T and S aren't in fact equal.

Exactly? I don't think you're quite understanding the point.

I'm divorcing the chance of rolling town vs rolling scum as a separate event, because if you don't the number of players of each alignment in the game matters, which means the math changes as a game progresses and alignments are revealed. If all other considerations are equal and otherwise the odds of T=S, a player will be scum with the tell a little over twice as often.

If you want to get the number for a specific setup you set up a different ratio. D1 in a 2v7 with 0 confirmed you want the numbers to be #/2 and #/7 (or an equivalency).

In this case it would be 1.14/2 and 1.82/7.

P(S&S:g) would then be 1.14/(1.14+1.82) or 39% compared to the original 2/9 being 22%

You could also get that number, however, by applying the setup odds to the general odds I gave earlier (Hence the and function).

If you keep the original numbers (69%) as the strength of the tell, however, you can also apply it to a situation where say, you have 4v1 with 1 conftown. Or 3v2. Or literally any situation where a newbie enters the thread by greeting.


As far as accounting for the shift via actual scum rolls vs expected scum rolls, that's also unnecessary when applying to a situation, because the % chance of rolling scum is presumably known.

[u r a person 2]

all i know, is that if you look at newbie slots with 1st post thread-wide greetings and one of those slots look scummy independent of this tell, they are probably scum

and if you look at those slots and all of them look townie outside of that, your scum is probably in the SEs

and if no one greets the thread, your scum is probably in the SEs

[Jingle]

What if you are scum? Please advise.

[John Pierce Gantt]

This is my first post in my first (well, somewhat) game.

Greetings. If my name is too long for you to type, you may call me JP Gantt or just JP.
Just don't call me JPG because I am a real life human being, not some pixelated piece of art.

With that said.

@Inferno390

, why are you bothered about the miller claim now instead of few hours before, when you placed a vote?

I was town though.

[u r a person 2]

What if you are scum? Please advise.

scum read greeting and never look back ;P

[u r a person 2]

This is my first post in my first (well, somewhat) game.

Greetings. If my name is too long for you to type, you may call me JP Gantt or just JP.
Just don't call me JPG because I am a real life human being, not some pixelated piece of art.

With that said.

@Inferno390

, why are you bothered about the miller claim now instead of few hours before, when you placed a vote?

I was town though.

this is the kind of post where I would immediately call it a likely false positive because line 2 and the question don't jive with my expectation for uncomfortable scum entrances where greetings are produced

[Ramcius]

PS a "true" bayesian analysis would involve both a prior and a posterior distribution getting some kind of semi-arbitrary mutual weighting. Presumably the prior would be 2/9 = 22.2% (odds of a player randing wolf, also essentially the null hypothesis of the tell being meaningless), and then the weighting is based on w/e you think is appropriate, and I'm much, much, MUCH too lazy to even attempt to lay out the logic involved in that decision making process
(but tldr the "true" answer is "something less than 43.5%, and it's somewhat arbitrary exactly how much closer you get to 22.% vs 43.5%")

Percentage being much higher than 22% makes sense, if you consider psychological aspect - scum players are under much more pressure and first impression is important. Therefore coming in with a greeting is less hostile and more likely to earn some sympathy. On other hand town want jump in and hunt scum, so they often skip greeting

[yessiree]

If it's significantly different from town %, yes.

Sure, it's simple math, 57% of greetings came from town players

Bayesian:

P(X is scum | X did a greet) = P(X did a greet | X is scum) * P(X is scum) / P(X did a greet)

= (20 / 35) * (2 / 9) / (46 / 135)

~= 37%, compared to a baseline 2/9 of ~22%. (I'm not sure where TTTT's 71%/28% is coming from?)

Most scumtells are going to come more often from town players than scum players, due to a combination of their not-100% reliability and the fact that most players are simply town; it can still be a valid scumtell.

you should not use the true probability that X is scum (2/9) since the the Naive Bayes model should only be used on a dataset when you have no other assumptions or knowledge about the underlying data.

so in this case, P(X is scum) as seen from our observation should be 35/135
Then P(X is scum | X did a greet) ~= 43.5%, and
P(X is town | X did a greet) ~= 56.5%,
which adds up to 1.

[Bicephalous Bob]

You'd be foolish to scumread a player based on this alone

The average D1 scum lynch rate is probably worse than 37%, so I'd say it would make sense to lynch new players based on this alone. In any case, this is the strongest correlation between a linguistic cue and alignment I've ever seen. I'll reference this thread in the next version of my paper. Drop me a message if you want to be cited by another name than Loopdan. I'll also try to replicate this for Normal games sometime in the future.

[Prof Hamm T Smiggles III]

@Bicephalous Bob - I would like to be cited in your next academic paper as "Prof Hamm T Smiggles III". Thank you.

[Loopdan]

^Confirm. That's me.