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Subject: Setup Up Statistics rss

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Stephen Venters
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A while back I built the Star Wars: Rebellion Map Generator & Setup Helper. In doing so, I found there were exactly 2100 possible permutations. In the several months this has been online, it has generated over 540 games for people.

After posting it, I began doing some analysis on the different setups to determine if some setups favor one side of the other. Based on several factors (such as whether or not the initial Rebel systems had an Imperial neighbor), I assigned each of the 2100 setups a score from 0.0 (favoring the Rebels) to 10.0 (favoring the Imperials).

NOTE: After posting this thread, I've updated the algorithm so the text in this top post outlining how it calculates the scores is a bit out of date... see later posts for the updated algorithm.

It is a fairly simple calculation based on the net build output of units of both sides' initial systems (I assumed the Imperials would attack and subjugate all neighboring Rebel system thus shutting down the Rebel's ability to produce during the first build).

For example, if each of the 3 initial Rebel systems DON'T HAVE any Imperial neighbors, then the Rebels are very likely to get a strong initial build, especially if Mon Calamari was one of those systems. On the other side, if all 3 of the Rebels systems HAVE an Imperial neighbor, then it was assumed the Imperial player would subjugate all 3 in the first Round, ostensibly shutting down the Rebel side's initial production. (of course there are many factors that play into the first round, including new systems, dice rolling, etc... but I had to start somewhere)

Given the difference between the Rebel's build and the Imperials build, I assigned a score.


As you can see, with respect to initial build capacity, the setups more often favor the Imperials. This isn't surprising, but what is surprising is in almost 23% of the possible setups (score 7.5+), the Imperials can completely shut down the Rebel production on the first turn (the Rebel Base space will produce its 2 units no matter what). That makes for an insanely difficult start for the Rebels, especially when the Imperials produce 14 units!


Again, there is certainly more to winning this game than initial systems and initial builds, but I've played this game enough to know a weak start is hard to recover from, especially when playing a seasoned opponent.

If you're interested in seeing the 2100 permutations, check them out here.

Because of what I found, I added an option to my setup helper to remove setups that more heavily favor either the Rebels or Imperials when generating a game. It simply removes the lowest and highest scored setups to give you more "balanced". However, this option is only used about 7% of the time.

If you have any ideas for ways to "score" the initial setups, let me know. One thing I wish I could collect is which side wins. Otherwise, enjoy the analysis and I hope you find the setup helper useful.

Star Wars: Rebellion Map Generator & Setup Helper
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Saro Gumusyan

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I think a resource like this is very useful, especially for potential tournaments as I'd rather randomly pick a "neutral" setup as opposed to bidding for factions based on a favorable setup. That said, tournament records with starting systems would be useful date for your analysis, and I believe it's being recorded in the current Tabletop Simulator one.

You're correct in adding either side can recover from a big 1st turn build swing, since board coverage for the Empire can be just as important as Rebel adjacency. If the Empire gets the four corners (Rodia, Saleucami, Mygeeto and Sullust) they can start combing for the base sooner or put heat on the base. Of course the Rebels can already mess around with Imperial supply lines the first turn with an attack on a soft spot and a sabotage.


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Jacob Williams
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I really like your initial analysis. Would you share your formulas for scoring how good a set up is?

While I understand this is just a model, I do think youf base assumption of a 100% chance of Empire rolling every Rebel neighbor is flawed. I typically see a leader put on R&D every turn, and I observe a roughly 40% rate of Vader being sent out to capture someome. If Empire doesn't start with Corellia under full loyalty, they are likely going to try and work on that.

Again, I love this analysis! Just wondering if it can be more insightful by adjusting the variables and assumptions.
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David Umstattd
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While most imperial players will jump on adjacent rebel systems on turn one this shouldn't be assumed. Sometimes more important things are necessary, sometimes a savvy rebel player will attack a threatening imperial fleet and lock it down so it can't take a rebel system.

Anyway the way I always try to see it is the Rebels start with no systems. Any they do end up getting through imperial negligence is just Garvey. Utupah and rebel base production is a fine basis for any rebel fleet.
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Brad Miller
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Neat!

I'm building an application, (Windows only, sorry), to help run PBF/PREM games, but am not far enough along to run the stats. Nor the math skills anymore...
 
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Brad Miller
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Makes you wonder if FFG ran these analyses as well. They need to hire more mathematicians!

Or at least have a solid counter-strat for the rebels when faced with adjacent systems x3. Haven't played enough to know if they did.
 
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Scott Lewis
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Windopaene wrote:
Makes you wonder if FFG ran these analyses as well. They need to hire more mathematicians!

Or at least have a solid counter-strat for the rebels when faced with adjacent systems x3. Haven't played enough to know if they did.
While this analysis is interesting, I don't know if it really gives much information on how this starting score impacts the game. IE, without win/loss ratios to go along with various starting setups, it's more academic.

Ultimately, it boils down to whether either side has a chance to win. Strong (perhaps even lopsided) starts could impact it, but I'm not sure this analysis demonstrates to what degree that impact is. There are many other factors that go into it as well, such as what missions are attempted, where the Rebels locate their base (which includes some meta-strategy of knowing your opponent and trying to outwit them; sometimes putting the base in a less "ideal" location can end up safer as it seems so obvious to NOT be there).

Obviously we can't go back through all the games people have reported, but it would be an interesting thing to track: starting worlds, who won (and perhaps even in which round they won).
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ClimberStephen wrote:
A while back I built a web app that generates a random setup for Star Wars: Rebellion (Star Wars: Rebellion Setup Helper). In doing so, I found there were exactly 2100 possible permutations. In the several months this has been online, it has generated over 540 games for people.

I have used it about 20-30 times, i love it, thanks.

I look at your score when I do it, but in general as a rule of thumb the rebels are doing well if they have Mon Cal and the empire doesn't have selucami
the empire is doing well if they have a loyal corellia, loyal mustafar is also very useful.

there are many more factors(especially mission draw in round 1), and in our games we seem to 'beat' your odds quite often, if you added in the page that randomizes the planets a checkbox to say who one, i will fill it out at the end.
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Doug DeMoss
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My opinion is that missing either of the Mandalore-Mygeeto or Sullust-Mustafar pairs is a major problem to the Empire, missing Saleucami is almost as bad, and nothing else makes a significant difference as far as play balance.

The Empire being able to take out all three of the Rebel planets isn't as big a deal as you might think because they usually only find the time to make two moves anyway in my experience.
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Stephen Venters
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It's important to understand I am trying to take the "choices" out of the initial setup. How you play your first turn based on your experience, your starting missions, and how much blue milk you've had to drink will certainly be more relevant to the outcome of the game. I'm just trying to determine which setups lean one way or another based on a few simple assumptions.

demoss1 wrote:
My opinion is that missing either of the Mandalore-Mygeeto or Sullust-Mustafar pairs is a major problem to the Empire, missing Saleucami is almost as bad, and nothing else makes a significant difference as far as play balance.
I'll take a look at these and add some weight to them if it makes sense. I did add a bit more weight to a Rebel starting in Mon Calamari but the Imperials not starting in Saleucami which I felt was a minor boost to the Rebels first build.

On a related idea, I'm going to add a metric that counts the number of "available systems" for the Rebel Base. In that, I mean, how many systems are available that are not neighboring a starting Imperial system. I understand (and have done this myself) choosing the Rebel Base to be located immediately next to an Imperial system to perform a sneak attack is an awesome tactic, but in general, having more systems 2+ moves from the nearest Imperial fleet gives some flexibility (i.e. advantage) to the Rebel side.

Darth Coupon wrote:
That said, tournament records with starting systems would be useful date for your analysis, and I believe it's being recorded in the current Tabletop Simulator one.
That's a great idea! I'll see what I can harvest from posted tournament results.

David Umstattd wrote:
While most imperial players will jump on adjacent rebel systems on turn one this shouldn't be assumed.
ChromiumAgeCollector wrote:
...I do think your base assumption of a 100% chance of Empire rolling every Rebel neighbor is flawed
I agree it is a stretch to assume the Imperial player will attempt to shut down 3 of 3 neighbors. But getting at least 1, and probably 2, in the first turn is a safe assumption IMO. So maybe I'll scale that assumption back a bit.


jooice wrote:
I have used it about 20-30 times, i love it
Awesome! Thanks!


jooice wrote:
if you added in the page that randomizes the planets a checkbox to say who one, i will fill it out at the end.
Cool, I'll look into adding this as a feature.
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Stephen Venters
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Hi all,

So I spend some time updating the Balance Score generator and have seen some surprising results come out of it.

I reworked the assumptions based on the feedback here:
- The Rebel player will not want their initial Rebel Base location to be directly adjacent to an Imperial System
- During the first round and if possible, the Imperial player will attack and subjugate up to 2 of the Rebel's most powerful systems (in terms of build power). This means if all 3 initial Rebel systems are adjacent to Imperial systems, the Imperial player will attack the 2 the most powerful ones.
- In fact, it is preferable for the Rebels to not have any adjacent Imperial Neighbors at all
- It is good for the Rebels to start with Mon Calamari, especially if the Imperials don't start with Saleucami
- It is good for the Imperials to start with the pair Mandalore and Mygeeto or with the pair Sullust and Mustafar

I also applied more appropriate weights to the various values based on some statistical analysis I did on the permutations. It has produced a much more accurate view of the various setups. Here is the new balance distribution.


That said... I also found some tournament results and imported them and compared the winner to the balance score I assigned to each setup. Well, I'll let you see for yourself. It's at the very bottom of the page.

Star Wars: Rebellion Setup Permutations

Also, if you have any game results, PM them to me. I need the 8 starting planets and which side won. If you have the round it ended on, even better!
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Scott Lewis
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ClimberStephen wrote:
That said... I also found some tournament results and imported them and compared the winner to the balance score I assigned to each setup. Well, I'll let you see for yourself. It's at the very bottom of the page.
I'll admit, I'm not a statistician, but looking at them visually, it doesn't readily appear that there's a strong correlation between starting score and victory. In the game that the Rebels had the "advantage", the Empire won, and in the 4 games where the Empire did, each side won 2. The middle of the pack looks relatively spread out (if anything, it almost looks like the Rebels won more often with stronger Empire scores).

However, I may be misreading something about that table.
 
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Stephen Venters
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sigmazero13 wrote:
I'll admit, I'm not a statistician, but looking at them visually, it doesn't readily appear that there's a strong correlation between starting score and victory. In the game that the Rebels had the "advantage", the Empire won, and in the 4 games where the Empire did, each side won 2. The middle of the pack looks relatively spread out (if anything, it almost looks like the Rebels won more often with stronger Empire scores).

You're exactly right :/

That said, the reworking of the assumptions and statistics did flatten out the scores a lot.
 
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There are several pbf games on the pbf forum that will have all the info you need for them.
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Stephen Venters
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mrfan wrote:
There are several pbf games on the pbf forum that will have all the info you need for them.

What is the "pbf forum"?
 
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Witold G
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ClimberStephen wrote:
What is the "pbf forum"?
Play by Forum section:
https://boardgamegeek.com/forum/1796122/star-wars-rebellion/...
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Doug DeMoss
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ClimberStephen wrote:

- It is good for the Imperials to start with the pair Mandalore and Mygeeto or with the pair Sullust and Mustafar

That's not quite what I was getting at with my earlier comment - I said that it's bad for the Empire to be missing BOTH of either pair. Flipped around to an "it is good" statement, it should read "It is good for the Imperials to have at least one of the pair Mandalore and Mygeeto, and at least one of the pair Sullust and Mustafar."
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David Umstattd
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ClimberStephen wrote:

- It is good for the Imperials to start with the pair Mandalore and Mygeeto or with the pair Sullust and Mustafar

What's your reasoning for this? I would go and say "it's preferable for the rebels if the empire starts without the pair of Mandalore and Mygeeto or Sullust and mustafar" but I'm not all that sure about that.

Mandalore is kind a a meh planet.

Mygeeto, Corellia, and Sullust are good if they start out loyal not subjagated. though still good if just subjugated.

The thing is the systems that are most likely to start adjacent to rebel systems tend to have weaker production with the exception of Sullust which is only possibly adjacent to 1 rebel system.
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Stephen Venters
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I reworked the composite score calculation again, this time with the inclusion of 57 actual game results I was able to find online. The balance scores largely follow the results now.



The composite score weights break down like this:

Either side getting an "ideal" initial system configuration (which could cancel each side out) = 12%
Whether or not the initial Rebel Systems have enemy neighbor(s) = 24%
Initial build power (assuming Empire attacks 1 or 2 Rebel systems during the 1st round, if possible) = 41%
Number of Rebel Base location options (assuming they don't want it next to an Imperial system) = 23%

If there is a logged result for the given setup, I give the outcome of that game a 15% weight to the overall composite score (adjusting the above percents accordingly). That said, to be statistically significant, ideally I'd have 20-30 results for EACH setup. So if I only have a 1 or 2 game results for a given permutation, I only give the winning side "partial credit", so to say, in the composite score.

You'll notice that within the game results section, the games with the highest calculated composite scores (favoring the Empire), the Rebels only won 1 of the top 10 games! And 5 of the top 20.

What do you think?

Star Wars: Rebellion Setup Permutations

Game results can be seen at the bottom of the page.
 
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Doug DeMoss
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David Umstattd wrote:
ClimberStephen wrote:

- It is good for the Imperials to start with the pair Mandalore and Mygeeto or with the pair Sullust and Mustafar

What's your reasoning for this? I would go and say "it's preferable for the rebels if the empire starts without the pair of Mandalore and Mygeeto or Sullust and mustafar" but I'm not all that sure about that.

Mandalore is kind a a meh planet.

Mygeeto, Corellia, and Sullust are good if they start out loyal not subjagated. though still good if just subjugated.

The thing is the systems that are most likely to start adjacent to rebel systems tend to have weaker production with the exception of Sullust which is only possibly adjacent to 1 rebel system.

The reasoning is that it will take the Empire extra time to get to one of the corners of the board; without Sullust or Mustafar, Hoth and Endor are REALLY remote. Likewise for the corner near Mandalore and Mygeeto.

I'd argue that Mandalore, in particular, is NOT a "meh" planet. Sure, it doesn't produce a lot, but it's close to a TON of places.
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Stephen I thought you were going to add buttons to your randomizer saying:
Rebels won
Empire Won

will help you collect data.
 
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Stephen Venters
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Yep, I'm working on it
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Stephen Venters
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jooice wrote:
Stephen I thought you were going to add buttons to your randomizer saying:
Rebels won
Empire Won

will help you collect data.

I have updated the generator so you can log the result. After you generate a new game, you can log the result below the map:


If the browser closes, you can always reopen the generated game by viewing the latest games generated here: Star Wars: Rebellion Setup Helper
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ClimberStephen wrote:
jooice wrote:
Stephen I thought you were going to add buttons to your randomizer saying:
Rebels won
Empire Won

will help you collect data.

I have updated the generator so you can log the result. After you generate a new game, you can log the result below the map:


If the browser closes, you can always reopen the generated game by viewing the latest games generated here: Star Wars: Rebellion Setup Helper

Will be useful this weekend ! Thanks!
 
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David Medley
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The setup is nice, but the scores seem pretty out of whack. Right now the lowest score is 4.4 out of 10 and the highest is 8.5. If players use your recommended 2.5 to 7.5 scale, they'll only be eliminating good imperial setups. The factors that go into the rating seem very out of balance, as well.

I appreciate the effort. It might just be too complex to rate these setups, though.
 
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