The Newbie Matrix6 stats thread (complete)

[Toomai]

The following is a z-score graph. 0 means "is exactly average". 1 means "is 1 standard deviation above average"; -1 means "is 1 standard deviation below average". In other words, high bars mean "more replaces", while low mean "less replaces".

While this mostly says what you'd expect (PRs on either side are less likely to be replaced), it's fascinating to see that both of the town protective roles instead have average replacement rates.

[TierShift]

Can you perform significance calculations on this? It seems very interesting but I doubt anything but goon is significant due to sample sizes.

[tn5421]

Goon, Scum, VT, and Town are probably significant.

[Toomai]

My advanced statistics is a bit rusty, so I turned to this page that I found. According to it, with 374 town players replacing out of 980 slots, and 136 scum players replacing out of 280 slots, the z-score of comparing the two is -3.1292, with a p-value of 0.00174 - significant at p = 0.01. (For slots replaced instead of players replaced, Z = -2.4829 and p = 0.01314, which is almost also significant for p = 0.01.)

So as I understand it,

there is a 99% chance that replace-outs are significant between alignments

.

Here's a few more comparisons (all for "players replaced" as opposed to "slots replaced"):

• VTs vs all players: Z = 0.5059, p = 0.61006
  
• JKs vs all players: Z = -0.3093, p = 0.75656
  
• Cops vs all players:
  Z = -2.3338, p = 0.0198
  
  
• Docs vs all players: Z = -0.1237, p = 0.90448
  
• BPs vs all players:
  Z = -2.7577, p = 0.00578
  
  
• Trackers vs all players:
  Z = -3.6013, p = 0.00032
  
  
• Goons vs all players:
  Z = 3.0974, p = 0.00194
  
  
• RBs vs all players: Z = -1.0128, p = 0.3125

[chamber]

So as I understand it, there is a 99% chance that replace-outs are significant between alignments.

Which is surprising for absolutely no one who's been around for a while. Nice to have the stats I guess.

[Glass]

I find the tracker/cop stats very interesting, and it probably explains why I never replace into an investigative slot.

[Rob14]

Given the test you ran, there is a 99.9% chance that there is a statistically significant difference between the proportion of town that replace out and the proportion of scum that replace out. That is the correct conclusion from what I assume was a test where the null hypothesis is p1 = p2 and the alternative hypothesis is p1 =/= p2, where p1 is the proportion of town replacing out and p2 is the proportion of scum replacing out.

[Rob14]

Toomai, can you share your spreadsheet that you used to generate that last graph? I'd like to try something, but having your existing spreadsheet on replace-outs would be helpful.

[Toomai]

Follow the link near the bottom of the first post; all the data is there, and it updates every time I save the file.

[Rob14]

Wow, that's quite the spreadsheet and it's a bit hard to tell exactly how you've organized the data, due to frequent abbreviations.

If I wanted to compile a chart that shows replacement rates of just SEs by role, what's the best way to capture that data using what's already there? Is there a specific column in the Midpoints (replacements) sheet that could help with that?

[Toomai]

You probably want to use the CC-CT columns then. Here's some examples of what the values mean:

• For CC-CK, a "G0" means "a Goon slot that was never replaced", while a "G1" means "a Goon slot that was replaced at least once".
  
• For CL-CT, a "G0" means "a Goon slot that was replaced 0 times", while a "G2" means "a Goon slot that was replaced 2 times".

SEs are always in slots 7 and 8, but slot 6 can be a newbie or an SE depending how many SEs there were in the game; use BF-BQ of the main Data sheet to figure this out.

Then, you can do something similar to what the CV-DS columns do - CV-DC calculate how many of each role is in the game, while DD-DK counts the slots of that role replaced while DL-DS counts the players of that role replaced. So for example a 3 in a slot column means 3 separate slots were replaced, while a 3 in a player column means 3 players were replaced, which might be in different slots or the same slot.

[Rob14]

M'kay.

[Toomai]

Bumping this to note that in the case of a draw (which has happened recently), that game will be ignored for any win-loss stat, but still count for other stats.

[goodmorning]

In the "Replacement vs Winrate" spoiler in the OP, the first graph is by players replaced when I assume it should be by slots replaced. So something's gone weird there.

[Toomai]

Okay going to fix that.

[T S O]

it would be interesting, although borderline undoable, to see the percentage of scum wins when a partner dies d1 and they get no towncred from their death.

I managed to get to LyLo doing it, and only my laziness prevented me from winning, but it was so long and monotonous I'd wager <5% of people pull it off.

[Rob14]

and they get no towncred from their death.

That's not a mathematical thing, so it's literally impossible to objectively measure. You'd have to try to define a rigorous definition of what defines "getting towncred". Does looking town at start of Day 2 count, or do they have to never be questioned about their partner for it to be "getting towncred" for the lynch?

On the other hand, finding the percentage of scum wins when their partner days D1 would be doable.

[Toomai]

On the other hand, finding the percentage of scum wins when their partner days D1 would be doable.

And already done too.

• If scum is lynched D1, they go 5-33 (13.2%)

[Bicephalous Bob]

What percentage of games won by scum don't have any scum lynches?

[Toomai]

16.0% of town wins are semi-perfect (no town lynches).
7.4% of town wins are perfect (no town deaths).
62.8% of scum wins are perfect (no scum deaths).

I'll integrate this into the first post next time I do an undate.

[Bicephalous Bob]

Cool. I have no idea how hard it'd be to extract this, but could you compare the successful lynch rates of 7v2, 5v2, 3v2, 6v1, 4v1 and 2v1, as well as the actual rate:random lynching ratios? It'd be interesting to see if the random lynching assumption checks out at all, although the PRs prevent any real conclusions.

[Cheery Dog]

What about 7v1, 5v1, 3v1, 6v2, and 4v2? I'm sure all of those have happened at least once

[T S O]

has 7v1 ever had a scum win?

[goodmorning]

It has done twice in a row in Micros I've run.

But that's Micros.

[T S O]

That's still what I was going for.

Those are pretty impressive wins.