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Re: Official Stat Warriors Leader Board :: Mar 7, 2011 @ 11:45am

Cabin Boy txgangsta

Joined: Mar 12, 2007
Posts: 4001
Location: Texas

For 2v2, can it me that your weight is divided by your partner's skill?

Say your partner's skill rating (scale of 0 to 2, can be discussed later) is 1/2. This means that all your wins are divided by the .5 so for every 1 win, you really get 2. If your partner is amazing, his skill will be 2. This means every game you win with him, your only getting half a win. Your wins will half to be double with the good player.

Team switching will be no problem. "I'm not winning with him". Go ahead, move. Your wins will now count less.
Re: Official Stat Warriors Leader Board :: Mar 7, 2011 @ 12:03pm

Cabin Boy zmar01

Joined: Jun 6, 2009
Posts: 655

or you could do a total score.

Your initial score X the number of games you played - the total of every one of your partner's  initial scores
added onto your rank. maybe devide by some number to make it fit the stats.
like 1000 as i can imagine that number being high relative to the stats.

and i said i didnt want it to be that bigger factor. maybe 10% of an average overall rank score or less.


Or you could use their 2nd round score or final, rather than initial because too much is based on the initial score.
I havent even found a good formula for that anyway. may just be win% multiplied by some number.
post updated on Mar 7, 2011 @ 12:05pm
Re: Official Stat Warriors Leader Board :: Mar 7, 2011 @ 12:14pm

1 Stripe Admiral quantum

Joined: May 19, 2010
Posts: 454
Location: Every(No)where @ once.

Ouch zmar hurt my feelings :-/
Re: Official Stat Warriors Leader Board :: Mar 7, 2011 @ 12:54pm

Cabin Boy jazz

Joined: Feb 20, 2009
Posts: 534
Location: aka The_Musician

quick note:  I adjusted the Skill number so that it can never go BELOW 1.  So now, low numbers will not reduce your base Score value.  However, it can still go up. So the Skill number will now only ADD to your overall Score, rather then add or reduce it.  This should help offset the overly exaggerated bell curve effect a bit.

The new formula is being processed right now.  should show up in about 4 hours or so on the Leader Board.
post updated on Mar 7, 2011 @ 12:55pm
Re: Official Stat Warriors Leader Board :: Mar 7, 2011 @ 1:30pm

Cabin Boy ionizedfire

Joined: May 25, 2009
Posts: 177

Ouch zmar hurt my feelings :-/


You're #1 on my list quantum!
post updated on Mar 7, 2011 @ 1:30pm
Re: Official Stat Warriors Leader Board :: Mar 7, 2011 @ 3:08pm

Cabin Boy jazz

Joined: Feb 20, 2009
Posts: 534
Location: aka The_Musician

The new formula is up.  Looks better!
Re: Official Stat Warriors Leader Board :: Mar 7, 2011 @ 3:25pm

Cabin Boy esparano

Joined: Nov 5, 2009
Posts: 2566

Yeah zmar I see what you're saying.  I already said that I am going to play around with the numbers to make different flags worth different amounts.  This weekend I'll make those numbers better, I promise haha.  
Also, my equation doesn't ignore people who play a lot of games; it just takes number of games out of the equation.  Once players pass an initial "check," of number of games, it is assumed that their stats are accurate enough to show up on the leaderboards.

I do like your idea, but there are a few problems.  If players are given an initial "score" and other people's scores are calculated off of that score, eventually there will be MASSIVE score deflation or inflation, depending on the equation.  The only way to calculate someone's score based off of the skill of their opponent would be to include numbers such as win% and rank instead of an initial "score."  Since rank is based off of phil's system, I would have to play around with win% and a few other factors to make it independent from his system.  I'll work on the equation more and try to implement your idea more or less, because it's actually the same idea I had a while ago, but couldn't figure out how to do it.


Jazz, I like the ideas of "skill" and "mastery" and all that stuff, but in the end it just boils down to one single equation: 

score = Win Percent^3 * Rank^2 * Number of opponents^2. 

 This opponents^2 WILL mess the entire ranking system up.
 
http://toomanywheres.com/galcon/LeaderBoard.aspx?alias=sir_earl 
Exhibit A^

Number of opponents: 741
Average win %: 33%
Rank: 3rd in the entire leaderboard, GA


 I see only one real route.  The "field played" number is one of the numbers that is messing up the ranks a ridiculous amount.  I think that it is a good idea to include this in the ranks, but it shouldn't contribute to the overall score of a player.  Like, keep the column for it in the actual ranks, but take it out of the equation.  This will reduce the equation to:

score = Win Percent^3 * Rank^2 * Number of opponents

You still are going to need to cut out that remaining "number of opponents" though.   Especially since the number of total opponents doesn't really determine somebody's skill; it just reflects how many people the player happened to play against over a period of time.  It helps with accuracy, but not with skill.  

    So my main point is that all of this "skill" and "mastery" stuff disguises the flaws of the equation.  When you substitute and simplify to get a single equation, you see how big of an impact number of opponents makes.
post updated on Mar 7, 2011 @ 3:58pm
Re: Official Stat Warriors Leader Board :: Mar 7, 2011 @ 3:57pm

Cabin Boy jazz

Joined: Feb 20, 2009
Posts: 534
Location: aka The_Musician

I do see your point Esparano, but I do not think Win Percent^3 * Rank^2 is adequate enough to determine Skill.  The only way, is to set arbitrary thresholds which must be met before you are even included in the formula.  This to me totally disregards actual Skill of the players you are playing against.

Skill VS Skill is what I've after here, not Win % VS Win %.

Lets take sir_earl as the example Vs fifty6

http://toomanywheres.com/galcon/LeaderBoard.aspx?alias=sir_earl 

http://www.toomanywheres.com/galcon/LeaderBoard.aspx?alias=fifty6 

Can you honestly PROVE that fifty6's 47% Win percentage against 27 Single Stripes is waaaaaay better then sir_earls's 32% win percentage against 167 Single Stripes?
Re: Official Stat Warriors Leader Board :: Mar 7, 2011 @ 4:15pm

Cabin Boy ionizedfire

Joined: May 25, 2009
Posts: 177

Sorry just need to bring something up.

From 1v1 stats

Mastery = 100 * (Number of Opponents * Games Played) / Total Game Count At This Rank 

Against 3 stripes

Ion 
7 Different Foe's
197 Games Played 
Games Per Player: 28.1
Calculated Mastery: 29%
Win: 59%
Score: 578020

Matty 
11 Different Foe's
300 Games Played
Games Per Player: 27.3
Calculated Mastery:71%
Win: 50%
Score: 1366875


I thought mastery skill was a measure of games played per player?  Your current equation doesn't even come close to that, unless it measures something else?

Just pointing this out, but I have a higher average games per player, much higher win %, but matty's score is 2.4 times higher than mine.  

Major Flaw ^ ^ ^
Re: Official Stat Warriors Leader Board :: Mar 7, 2011 @ 4:24pm

Cabin Boy zmar01

Joined: Jun 6, 2009
Posts: 655

Back to my idea. 

High rank should be high win% vs players with high win%

how does that not work?
Re: Official Stat Warriors Leader Board :: Mar 7, 2011 @ 4:29pm

Cabin Boy jazz

Joined: Feb 20, 2009
Posts: 534
Location: aka The_Musician

Ion, its the Field rating.  You have played against 12% of the total 3 stripes, while Matty has played against 19%.  Those extra 4 players make a difference at the 3 stripe level!

Play 4 more 3 stripes AND maintain your higher win percentage, and you will be above Matty.
post updated on Mar 7, 2011 @ 4:30pm
Re: Official Stat Warriors Leader Board :: Mar 7, 2011 @ 4:30pm

Cabin Boy esparano

Joined: Nov 5, 2009
Posts: 2566

Ok I see what you're saying jazz.  I myself was unsure about the "arbitrary threshholds" thing, but that the was the only way I could think of to fix it.  I could scrap that completely if you like.  But I have a new idea.  Do you remember the trueskill ranking formula a while ago?

There were two factors when determining a player's rank.  Skill, and accuracy of that skill rating.  This is exactly what I'm trying to get at.  They call it:

# The average skill of the gamer.
# The degree of uncertainty in the gamer's skill.

The "skill" of the player is determined by the number of wins and losses, and by the skill of the other players in the game.  The change in skill is also connected to the quality of the match.  

Right now, I have win%  (which is the same as trueskill's wins and losses factor), and rank (which represents trueskill's skill factor).  Now, I suggested earlier that the player's skill could have a +- next to their score, indicating the accuracy of their skill score.  This is very similar to trueskill's "degree of uncertainty in the gamer's skill."  

Notice how trueskill SEPARATES skill and uncertainty.  They are two separate values and uncertainty is not factored into the skill rating.  To get a final score, they use this thing called a "conservative skill value."  It's calculated by 
conservative skill = skill -  3*uncertainty.  This is the lowest likely value for that person's actual skill value.  I would personally like to see a "skill" column in the ranks, with an "accuracy" column right next to it with a +-, then a "conservative score" column next to that.  

But notice how they don't include number of opponents or number of games anywhere in their final skill calculation.. And trueskill is one of the most advanced ranking systems ever, created by people who are a million times more intelligent than us, and who have degrees in statistics.
post updated on Mar 7, 2011 @ 4:32pm
Re: Official Stat Warriors Leader Board :: Mar 7, 2011 @ 4:31pm

Cabin Boy ionizedfire

Joined: May 25, 2009
Posts: 177

Ion, its the Field rating.  You have played against 12% of the total 3 stripes, while Matty has played against 19%.  Those extra 4 players make a difference at the 3 stripe level!

Play 4 more 3 stripes AND maintain your higher win percentage, and you will be above Matty.



Gotcha, thanks.
Re: Official Stat Warriors Leader Board :: Mar 7, 2011 @ 4:32pm

Cabin Boy jazz

Joined: Feb 20, 2009
Posts: 534
Location: aka The_Musician

Remember all...  this is a PROOF based system.  Meaning you must prove your Skill is higher through battle.
Re: Official Stat Warriors Leader Board :: Mar 7, 2011 @ 4:39pm

Cabin Boy esparano

Joined: Nov 5, 2009
Posts: 2566

Look, Jazz. You've done all this work creating programs, messing with stat dumps, collecting and sorting data, and creating a leaderboard with thousands of players.  The entire point of a good leaderboard, however, is to rank players by skill accurately.  As long as you use the current equation, the number of games and opponents messes everything up.  All of your work is for nothing if the leaderboard ranks people by number of games.  I'd love to keep helping to tweak the equation (which is the most important part), but we're stuck on the issue of number of games played.  I'm being as sincere as possible when I say that it is to your own benefit to scrap this "field played" etc. idea and use something else to ensure that the scores are accurate.
Re: Official Stat Warriors Leader Board :: Mar 7, 2011 @ 4:50pm

Cabin Boy jazz

Joined: Feb 20, 2009
Posts: 534
Location: aka The_Musician


But notice how they don't include number of opponents or number of games anywhere in their final skill calculation.. And trueskill is one of the most advanced ranking systems ever, created by people who are a million times more intelligent than us, and who have degrees in statistics.


The True Skill system does include numbers of opponents and games played, just not as raw numbers.  It's embedded into their algorithm as "The degree of uncertainty in the gamer's skill."  The more people/games played, the less uncertainty in their score.  Its wholly part of their equation.

For this Leader Board, the Mastery number reflect the degree of certainty in the skill, while the Field number reflects diversity of people that skill has been pitted against.  

Honestly, I think using those numbers makes MORE sense when the goal is to achieve a "who's best" type Leader Board, then simply determining the overall Skill of each player.
post updated on Mar 7, 2011 @ 4:51pm
Re: Official Stat Warriors Leader Board :: Mar 7, 2011 @ 5:01pm

Cabin Boy jazz

Joined: Feb 20, 2009
Posts: 534
Location: aka The_Musician

See...  I'm not after a system where 5 people can HAVE THE SAME SKILL ranking.  That is totally meaningless for a true Leader Board.  If 5 people have a Skill of say 90, then which of the 5 is best?  Skill alone simply can not give us what we are after here.  How do you determine which 1 of those 5 is best?  The answer is, you HAVE to prove it.  Through battle. 

Even in the True Skill system, you have to prove it.  A higher degree of certainty scores you a higher Skill number (or at least a more accurate one). 

So with all due respect Esparano...  I think you are wrong NOT to include that into your formulas.
post updated on Mar 7, 2011 @ 5:13pm
Re: Official Stat Warriors Leader Board :: Mar 7, 2011 @ 5:21pm

Cabin Boy jazz

Joined: Feb 20, 2009
Posts: 534
Location: aka The_Musician

.
post updated on Mar 7, 2011 @ 5:23pm
Re: Official Stat Warriors Leader Board :: Mar 7, 2011 @ 5:24pm

Cabin Boy esparano

Joined: Nov 5, 2009
Posts: 2566

Actually, trueskill doesn't include it in the skill calculation.  It includes it in the accuracy calculation. which is my point.  It would be pretty cool to have accuracy and skill calculated in two separate columns in the ranks.  Also, You could keep all of your mastery numbers as indicators of the accuracy of the skill calculation.  Just don't use them in the actual skill calculation.  Have mastery and field played contribute to the accuracy calculation only.
They're two separate numbers.  And I'm not telling you to make an exact trueskill leaderboard with whole number ranks, I'm just saying to use the same basic concepts that created such a successful system.  

By the way, I decided to scrap the old formula I had.  It was pretty good but still had flaws.  I'm gonna start from scratch and also make it independent of phil's ranks.  We're making a new leaderboard because phil's wasn't accurate enough.  It wouldn't make sense to base the new leaderboard off of the old leaderboard.
post updated on Mar 7, 2011 @ 5:26pm
Re: Official Stat Warriors Leader Board :: Mar 7, 2011 @ 5:29pm

Cabin Boy jazz

Joined: Feb 20, 2009
Posts: 534
Location: aka The_Musician

Also, You could keep all of your mastery numbers as indicators of the accuracy of the skill calculation.  Just don't use them in the actual skill calculation.  Have mastery and field played contribute to the accuracy calculation only.
They're two separate numbers.



I agree with you there.  We are on the same page up till this point.

But what happens next?  How do you end up with a SINGLE score value with which to rank people?

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