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TerraNova Player-Rank: 2 TerraNova is a male
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Galaxy Progress Rating: ending the game Reply to this Post Post Reply with Quote Edit/Delete Posts Report Post to a Moderator       Go to the top of this page

[ This is a bit long, almost like a technical paper. Erwin, I hope at least you read it all the way through. Smile Skip to the graphs if you’re bored.]

I'm all for ending galaxies diplomatically, but there needs to be an additional mechanism that stops a runaway leader from carrying the game on and on until he owns all the planets. At that point the game is no longer fun, but simply a tedious exercise in maximizing points, with pretty much only the leader actually doing anything, and nobody else having any hope. If the leader doesn’t want to end the game, well, currently it’s not clear what would happen.

So I propose "Game Progress Rating", or GPR, based primarily on the distribution of scores, and a few other factors. If the GPR is greater than 1 for 100 consecutive turns, the game ends. This is the endgame: the players have 100 turns to seek an edge over their neighbours on the rank chart, maybe even push the GPR lower than 1 to buy more time.

I have a formula for the GPR which I like, but first I'll go over what I considered important to represent in the formula. The GPR has to take several things into account:

- current score of all players
- distribution of those scores
- number of players
- how close the fight is for first place

The GPR has to rise as the imbalances in power increase, but there should be an especially strong compensating factor if the gap between the top two players is close, or extremely large.

So after much analyzing of past galaxy scores, as well as looking at the progress of the GPR for current games, I arrived at the following formula:



An explanation of the terms:



The first term is the base of the rating; it’s what I started with. As the distribution of scores becomes more uneven, the rating goes up. The squaring emphasizes the effect, and makes the scores of the top empires more important.



This term compensates for the closeness of the top two empires’ scores. If the top two have identical scores, this term equals -2. This reduces the GPR if the top two empires are very close, to give more time for them to compete for first place. Once the top empire has more than double the score of the second place player, this becomes a positive, helping the game come to a quicker end if there’s a runaway winner.

The extra +1 in the numerator is to make it come out to 0 when all empires have equal scores, i.e. the beginning of the game.



This would be the endgame trigger value, if you simply added up the numerator terms and compare them to the denominator term. Basically, the value gets bigger as the number of players, i.e. galaxy size, gets bigger, to allow the number of competitive empires to be whittled down a little more. I chose to divide the two totals to get a nice clean condition of “1” for all galaxies, regardless of size.

Note that fame can be used instead of score in the formula; there would only be a very tiny difference due to rounding off.

So what does this look like when applied to the various games? Here’s a chart that lists all the galaxies and their GPR, along with the number of players, turns, and the scores of the top 5 players in the end for comparison (as well as the ratio of the top two). You’ll notice several galaxies went on well past being resolved, as runaway empires consumed all. The ones that seemed to end at a reasonable conclusion are the ones I looked at to calibrate the formula.

(click to enlarge)


Speed Galaxies are short, and tend to end prematurely, at least compared to the regular galaxies. However, the GPR isn’t really intended for them, since they’re shorter and have a time limit anyways.

I also graphed the GPR over time for recent galaxies. I included a line at 1.2 since I was considering a sudden end condition at that value; not sure that’s a good idea though.

(click to enlarge)


EDIT: A more complete set of GPR history graphs. Light blue line shows where GPR crosses 1, green line shows when GPR > 1 for 100 turns. Red line is actual game end.

(click to enlarge)


One of the practical effects of using the GPR is you can't simply just attack small empires and then have a showdown at the end. You have to be aggressive and go for your more equal competitors too. Otherwise, the elimination of too many small empires will drive the GPR up, ending the galaxy before a 1-on-1 showdown is possible. This keeps the galaxy as interesting as possible for more people, while discouraging excessive small-empire ganking.

In the endgame, when the GPR has gone above 1, if any contenders want a real chance at buying time and resetting the end counter they need to attack the leader. Attacking smaller empires will simply drive up the GPR even faster; this is an option too, though, a mad scramble in the last 100 turns for more points, but it’s soon over, letting everyone get started on the next galaxy.

Like I said above, an optional sudden end condition could occur at GPR = 1.2, but that’s maybe a bit harsh and unpredictable.

Keep in mind I still support a diplomatic end option (some kind of voting scheme?), which would let you end the galaxy before the GPR condition forces the issue.

Thoughts? On tweaking, on the formula, on the basic idea? If nothing else, look at the pretty graphs.

EDIT Feb 2, 2009: updated invalid image links

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This post has been edited 4 time(s), it was last edited by TerraNova: 04.02.2009 04:31.

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RE: Galaxy Progress Rating: ending the game Reply to this Post Post Reply with Quote Edit/Delete Posts Report Post to a Moderator       Go to the top of this page

quote:
Originally posted by TerraNova
I also graphed the GPR over time for recent galaxies.


How did you get a hold of that data?

This is insane amount of work. One of the best posts I've seen anyone make. Usually people will just throw out random numbers/equations/percentages and try to prove they are right, but man this shows exactly what you propose and how it would do in previous galaxies. People should take notes. Wink

LOL at G40...6.1 GPR! Kasim milked the fame off that one!

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03.11.2007 07:05 quickstrike is offline Send an Email to quickstrike Search for Posts by quickstrike Add quickstrike to your Buddy List
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Thread Starter Thread Started by TerraNova
RE: Galaxy Progress Rating: ending the game Reply to this Post Post Reply with Quote Edit/Delete Posts Report Post to a Moderator       Go to the top of this page

Thanks man, glad you read it. Smile

quote:
Originally posted by quickstrike
How did you get a hold of that data?


The hard way, by checking and copy/pasting the the current scores from the Galaxy Overview page every day.

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03.11.2007 07:19 TerraNova is offline Send an Email to TerraNova Search for Posts by TerraNova Add TerraNova to your Buddy List
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Excellent post, TerraNova! Really great work indeed!! I can't believe you manually copied the results of all galaxies into your Excel sheet every day... You could have asked for a sql dump of that information, or in fact if you want I can still provide one.

Back on topic, very nice work there too and I like your proposal! I also agree that a automated end condition is certainly required - a diplomatic version (voting system) would only be a secondary requirement, and could be implemented at a later stage.

What I am missing though is taking Alliances into account. If the first and second ranked player are allied this needs to have an impact on the end game condition. We discussed this a while ago in the end game condition thread. It would be great if you could weld the suggestions of this thread into your solution.

If we then find a method that covers alliances as well, I would like to make this the next big topic on my agenda.
03.11.2007 10:00 Erwin [CS] is offline Search for Posts by Erwin [CS] Add Erwin [CS] to your Buddy List
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wow.

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great work. perhaps this will serve as an example of the appropriate way to propose major gameplay changes. i mean don't expect me to work this hard but maybe someone will. Tongue

i do have a couple of things to say about alliances though

if alliances are used in the calculations(which i am in favor of) how would it work if player #1 is allied with player #3 and player #2 is allied with player #3 but player #1 and #2 are at war? what i am trying to get at is overlapping wars and alliances could create some problems in almost any scenario.

another game of this type that i used to play online treated alliances as seperate entities with a limit on the number of players in any given alliance. i don't know if that would be a good fit for spaceciv since that game was, by design, completely centered around alliances. i believe that the general sentiment is that this game should remain essentially a one player game with alliances being somewhat transitory. sorry quickstrike, i have no concrete evidence of that its just the impression i have gotten whenever discussions about alliances have occurred.

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Thread Starter Thread Started by TerraNova
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Thanks all. Really glad you like the idea Erwin; I mean, I enjoyed making the graphs, but this way I can keep moving forward with the idea. Smile

quote:
Originally posted by Erwin [SC]
I can't believe you manually copied the results of all galaxies into your Excel sheet every day... You could have asked for a sql dump of that information, or in fact if you want I can still provide one.


It's not so bad, it's one copy/paste per results page, since it pastes nice and neatly into Excel as a table. The SQL dump might be useful, though. I have a MySQL DB set up on my web account, and often when doing this kind of thing I've thought of setting up some kind of PHP html-scraper and automating the whole process, maybe even getting a Flash plotting thing going... but then I end up thinking "nah, I'll just do it in Excel; less debugging". Still, I do keep thinking about it...

It would be really handy if you had data on turn-by-turn score history in some nice dump-type form, though. Smile


Regarding alliances, I did indeed read that thread, before I even started on this idea. Obviously one disadvantage is I didn't have access to past alliance info on all these games, so I couldn't look at any hard data on the matter.

However, I did look at the scores for all the Galaxies, and tried to check whether if several of the big empires below the top empire were theoretically allied against the leader, how much of a realistic chance they would have. The top two score ratio plays largely into that, but the squaring function also accounts for it nicely. So actually I believe the way the numbers work out already takes into account the worst case alliance scenario for the leader.

If the top two are allied, then really there's no problem. They will devastate the galaxy with their superior forces, eliminating smaller empires. This, due to the squaring effect, will bring the game to a quicker end anyways. I know I was in such an alliance in Galaxy 46, which ended up with a GPR of 1.4. We had thoroughly defeated our main competitor, and at that point were unstoppable. The Galaxy was really just the two of us at that point, even if there were a few survivors; even though our scores were close, according to the GPR formula and actual reality this was indeed a done game. Theoretically there could have been a one-on-one showdown, but really, it's more interesting to end the game and move on at that point.

Another example I looked at frequently was Galaxy 19. There the top 5 scores in the end were 259, 238, 122, 28, and 21, with a GPR of 1.3. So, basically, only three empires. Let's suppose the third empire of 122 isn't actually just the remaining research and battle score of a devastated empire, and he (or she) could ally with Mr. 238 against Mr. 259. Could be epic, maybe. But look at the rest of the Galaxy; completely devastated, utterly outmatched by the top three. That's why the GPR is 1.3, despite the top 2 being so close. If No. 2 and 3 wanted to stop No. 1, they should have done so much earlier, instead of preying on weaker empires, and kept the fight interesting, i.e. started doing more interesting stuff earlier in the game. But really, that galaxy probably had a top 2 alliance too...

Or was the concern that you wanted to end Galaxies even earlier based on alliances? Because that plays into where I believe alliances should affect ending the game: the diplomatic/voting option. If we automated it, who's to say any of the current alliance aren't temporary alliances of convenience, waiting for the backstab that brings true glory? (OK, obviously I'm a Diplomacy player.) It should be a defined vote, and then true alliances can have their influence heard.

And this leads to the biggest problem with including alliances in any hard-coded inevitable end condition: it's too easy to abuse, and very susceptible to gamey behaviour. This was similar to the problem with the recently slowed reputation exploit, but in this case you don't need to keep gaming the system, you really only need to do so at key moments. I think that kind of stuff should be left to the diplomatic option; the GPR > 1 should be the failsafe, robust, looking only at hard numbers and not easily manipulated.

However, I will keep thinking about the alliance question. I've played around with many different schemes, too many to describe, including looking at top X% of players, Standard Deviation, and so on. Actually, I guess I'll start thinking about the diplomatic option too, following on that thread; the diplomatic and automatic systems maybe have to be considered together to fill in the blanks properly. Even so, an automatic method should probably be implemented sooner rather than later I think. Good ending conditions are crucial to making a satisfying game. Smile

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03.11.2007 17:31 TerraNova is offline Send an Email to TerraNova Search for Posts by TerraNova Add TerraNova to your Buddy List
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Well I guess it is worth trying your formula as is, without taking alliances into account (unless you, or anyone else comes up with a better solution?) We can still modify the calculation method at a later point if required, as long as we have the basic system in place.

Btw, I emailed you the scores-dump. Thanks so much again Smile
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Awesome, thanks. And my pleasure. Heh, big file, might be time to write a MATLAB program for the charts.

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i have nothing further to say(about this subject and only for right now LOL ). i bow to your seamlessly constructed proposal.

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Here's the GPR graphs for all the Galaxies there was data for. The red line indicates when the game actually ended. The light blue line shows where the GPR reached one, and the green line shows where GPR > 1 for 100 straight turns (when according to my proposal the game should end).

Black title means all ranks, blue is unranked, red is Rank 1.

(Click on really skinny thumbnail below)
EDIT: Updated to show multiple GPR > 1 triggers correctly.




I also made score history graphs (separate thread). Player labels are shown for any player that, at any point, had a score at least 15% of the top player's current/winning score.

I put them all together like that to make it easier to browse. And don't worry, I didn't make them all manually, I wrote a script, and use the data thankfully provided by the Space Civ team Smile .

The GPR end condition seems to fit pretty well. Ironically, the one game that gives me pause is one I was in, Galaxy 46. Using the GPR=1 for 100 turns condition, that game would have ended just as me and Eldor were really starting to consume marko (see the score graph), instead of later when I could better reap the rewards of victory. Actually, the GPR *almost* dipped below 1 before 100 turns past the trigger.

But with the GPR condition in play, we would have acted earlier, instead of reinforcing by conquering helpless empires, which we were all doing for a while.

EDIT Feb 2, 2009: updated invalid image links

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I just noticed this post.....and Holysh#t balls......i cant believe i read the whole thing, extremely well thought out.

that formula is pretty crazy and i couldnt understand it, but your explanation of it was good.

i just dont know what to say to that....as with uncounted, i bow Shocked

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I updated the GPR history graphs (here) to properly show when the GPR goes over 1 several times, before staying above 1 for 100 turns.

EDIT Feb 2, 2009: updated invalid image links

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I noticed that in some of the galaxies the GPR never goes > 1 and the game was ended. How would the GPR system have ended those galaxies? I'm not sure what happened in those galaxies, but what would happen if the players remained at a consistent, nearly equal score, but continued to wear each other down? Is that were the vote thing would come into play?
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Basically, it means those game ended "prematurely". But yes, the GPR should be complemented by a voting system as well, in order to deal with stagnant galaxies, or galaxies where everyone agrees to end it before the GPR would end it.

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