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Subject: Vote on how to combine expansions rss

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Hi all. Inspired by this thread, I wanted to create a comprehensive diagram that illustrated which expansions worked well with which other expansions. After a certain number of votes, I'll create a visual diagram showing the relationships between expansions. Defunct, see below.

But first, I'll need votes from you!

Poll
1. Consider each expansion. What is the MAXIMUM number of OTHER expansions you would recommend adding to it? (This is not the number of expansions you would ordinarily recommend: this is the maximum you would recommend).
  0 (use this expansion alone) 1 more, at most 2 more, at most 3 more, at most 4 more, at most 5 more, at most Plays fine with all 6 expansions
Curse of the Dark Pharaoh
Dunwich Horror
King in Yellow
Kingsport Horror
Black Goat of the Woods
Innsmouth Horror
Lurker at the Threshold
2. Which of the following pairs of expansions play well or satisfactorily together?
Dunwich Horror + Kingsport Horror
Dunwich Horror + Innsmouth Horror
Dunwich Horror + Curse of the Dark Pharaoh
Dunwich Horror + King in Yellow
Dunwich Horror + Black Goat of the Woods
Dunwich Horror + Lurker at the Threshold
Kingsport Horror + Innsmouth Horror
Kingsport Horror + Curse of the Dark Pharaoh
Kingsport Horror + King in Yellow
Kingsport Horror + Black Goat of the Woods
Kingsport Horror + Lurker at the Threshold
Innsmouth Horror + Curse of the Dark Pharaoh
Innsmouth Horror + King in Yellow
Innsmouth Horror + Black Goat of the Woods
Innsmouth Horror + Lurker at the Threshold
Curse of the Dark Pharaoh + King in Yellow
Curse of the Dark Pharaoh + Black Goat of the Woods
Curse of the Dark Pharaoh + Lurker at the Threshold
King in Yellow + Black Goat of the Woods
King in Yellow + Lurker at the Threshold
Black Goat of the Woods + Lurker at the Threshold
      56 answers
Poll created by kungfro




And as promised, here's the diagram (I'll try to keep it up to date):

Update 9 Oct 2018:
I have always been a bit dissatisfied with the expansion-combo chart. The algorithm used to determine connectivity was spurious, I had to manually enter in every poll result, and I had to manually update the chart in Illustrator and re-upload it. All of these made me avoid updating the chart except rarely.

From now on, the analysis of the poll will be on the Expansions/Rumors page of the Arkham Horror Statistics report.

While I still have to manually paste the poll results into a spreadsheet, the steps to do so have been substantially simplified.

On the linked report page, the center column shows the analysis of the poll:

Top block: Expansion combinations / maximum other
Each pre-Miskatonic expansion is listed, as is the voter consensus for the maximum number of other expansions that should simultaneously be used with it.

As can be seen from the BGG poll results, the distribution of max expansions was bi-modal for every expansion. It seems that most players fell into two categories: players who were likely more concerned with maintaining theme and mechanics balance, who voted for a broad spread in max other expansions that centered around a low value (1 to 2); and players who likely enjoy the variety and unpredictability offered by the all-in style, who voted "it's okay to use them all" for every expansion.

As a result, as is true with bi-modal distributions, it was difficult to report a single best summary value for each expansion. Instead, for each expansion, I tallied the votes and compared the median number of other expansions to the median without considering the all-in votes. When these two values were the same, I reported that as the max. When they differed, I presented them both as the bounds of a range.

Bottom block: Expansion pairing / approval
(Aside from Miskatonic Horror) Each pair-wise combination of expansions is listed, alongside the "approval" percentage for the pair.

"Approval" is an estimate for the number of voters who own this pair of expansions and also believe the two expansions play well together.

These values are always higher than the "Vote Percent" values reported in the poll, because a non-vote on the poll could either represent a voter who does not approve of the combination, or a voter who does not own the combination (or has not played it, has no opinion, etc).

The final "approval" percentage was calculated as follows:

1. Since both polls are offered at the same time, it's assumed that participants in one poll correlate extremely highly with participants in the other.

2. The percentage of participants who own (or, have an opinion on) an expansion is estimated to be the number of votes for an expansion on the top poll divided by the number of voters in the top poll. If 40 voters had an opinion on the max number of expansions for Curse of the Dark Pharaoh, and 47 voters participated in that poll, then it's assumed that 40/47 ≈ 85% of voters own Curse of the Dark Pharaoh.

3. Out of necessity, it's assumed that voter ownership of one expansion does not correlate with ownership of any other expansion. That's probably not true, but there's no way to estimate that.

4. Thus it's estimated that the fraction of voters in either poll who own both expansions A and B is equal to the fraction who own A times the fraction who own B:

P(A&B) = P(A)*P(B)

5. This means that the "approval" percentage for expansion pair "A+B" is simply the Vote Percentage for that pair normalized by the fraction of voters who own that pair:

P(Approval) = P(Vote) / [P(A)*P(B)]

This approval percentage is given rather than just saying "may/mustn't use together," as was implied by the connecting lines on the old picture diagram. Obviously, higher approval percentage means that proportionally more voters who are familiar with that pairing would say that they work well together.
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