Proposed ranking formula (basic version only)

[Fionn]

This is basically the cut and pasted text of an email I sent regarding a scoring system I came up with for a ladder which we'll create at CMHQ:

" I was thinking of using a couple of equations basically... They can be made

into one large equation obviously but since I have three prime factors

involved in the equations and each is calculated separately I think it makes

sense to explain it as three equation PLUS I can't write squared etc etc

using simple text and it'd be confusing otherwise.

The first two are from chess...

Rn = Ro + K(W-WEM)

Rn is the new rating.

Ro is the old (pre-event) rating.

K is a constant (32 for 0-2099, 24 for 2100-2399, 16 for 2400 and above).

W is the score in the event ( from 0 to 100... To fit the CM scores into the

formula the score will have to fit into the range 0 to 1 (in other words a

score of 50 in-game will = 0.5 W ). We won't simply have it being 0 or 1 but any value in between will be valid also.

WEM = Win Expectancy Modified

WEM = ( 1-We) x ( ( attackers point value squared over 1000) divided by (defenders point value squared over 1000) ) ) divided by points factor constant determined by role in game

e.g. if meeting engagement then points factor constant = 1.. If we are calculating points from the attacker's perspective then points factor constant = 2.5... If defender than points factor constat

= 0.4 (reverse of 2.5)

We is the expected score (Win Expectancy) from the following formula:

We = 1/ (10 (dr/400) + 1)

Where Dr = difference in ratings.

This system would take into account the degree of the win, the ratio of

forces committed and the inherent increase in difficulty due to being the

attacker (and thus the fact that the attacker needs more points).. Without

the WEM factor the attacker would ALWAYS be penalised for having more forces

since the formula would assume that an attacker attacking with 2000 points

has an equal chance of winning the game as the defender if the defender has

2000 points.. My testing has shown me that the attacker would need roughly

3200 points to have an equal chance of winning with an equal level of skill.

It is a modification of the chess system to reflect the following:

1. Not ALL sides are equal.

2. Not all ROLES are equal.

3. Not all VICTORIES are equal.

Comments?

Particularly I'd like to hear comments about my points factor modifier.

I find that an attacker with 3200 points vs a defender with 2000 points yields a very even game. SOME standard factor must be taken into account to equalise non-mirrored games. What do you think a suitable factor would be (I'm using 1.6 squared obviously)

[Goanna]

I am a bit confused. Do the points for an attacker or defender refer to their previous scores, or does it have to do with how many points worth of forces they are using in the game being scored?

[Fionn]

Points in this message refers to the "points" available to the player for buying his force or the cost of his pre-selected force.

Rank points are referred to as "rating"

[MrPeng]

INRE subtitle of thread: "basic version only" Hell! if those are basic formulae then i am just as big a retard as everyone thinks!

Peng in too deep

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Peng sez "die a lot now."

[CoolColJ]

ewwww makes my head spin

I need some asprin

ccj

[Fionn]

Well, there's a few added "wrinkles" to the formula for special cases (although I amn't going to put them into Version 1 since they won't be necessary).

This is just the basic starting formula which can be upgraded to become more all-encompassing if certain game types prove popular (operation PBEMs etc).

[Bil Hardenberger]

What are the old and new ratings if you have new players?

Can you give us an example, perhaps using one of our completed games as an example?

Here are the stats:

Axis (Fionn): 2296 points, Attacker, Score:45

Allies (Me) : 2969 points, Defender, Score 55

Perhaps that will help us all understand it better...

[Guest Bobb]

Gee whiz guys it is just a little bit of counting up and down -- in specified ways - -<G>

So we want to get us a new rating after playing:

So we start with an old rating.

Then we figure in a comparison of the relative strengths of the opposing forces.

And we figure in the relative strengths of privious play for the oponents.

And then we consider the score obtained by playing.

And we balance out things for the role required of the players, (defense, attack, head on ecounter, etc.)

Finally to make things come out in a convient way for the ending number to fit between expected beginnings and endings, we put in some convient cheater figures

(not as in unfair or lying)

The trouble comes when we start seeing that damned slang the guys who understand that counting stuff use as others such as military buffs who talk in AFVs, AWOL etc.

People who think like that have obviously strained their common sense organ and it makes em talk funny and in circles and generally leave out a bunch of stuff they take for granted and expect everyone else to have in mind. (That was a runon sentence just now, but easier to deal with than math talk which often comes off as runoff talk.)

Actually Fionn make a fair amount of sense here considering. It ain't easy to put such a balancing act together. Sort of like the Walenda tribe of tight wire performers who do that pyrimid thing way enough up in the air to put a premium on not screwing up. It is a thing of beauty to behold and it holds an additional special beauty that only the performers can get into.

Actually it is not a very high flying form of math that we have here, but is does take a quite a lot into consideration. Even this system is likely to be an over simplifacation that could be tweeked up.

For instance, figure in whether any foreign substances have been introduced into the players and their relative succeptability and responsiveness to said substances. Or whether the players are handicapped by spousal or parental pressures. Now that should be enough to start quite a list of additional factors to include.

I know a blind lady who is president of the local computer club. If she plays CM using the assistance of JAWS, a program which turns her computer screen output into English, will there be a factor to figure in a handicap for her?

This could go on and on, and I have seen a lot on this board, have much more talent for the sort of thing than I do. Any way, this is a hell of a way to respond to a serious effort to make evaluations of relative play strength of players. I apologise.

By the way Fionn, how is startup handled, when there is no Old Rating? Are the results a bit volitile in the early figuring?

And how do you come up with some of the apparantly arbitrary factors to apply to engagement types?

And how do you make the unwashed accept squaring figures and then dividing them by 1000? You don't! Gee, ---- Well that is understandable, Fionn, I accept it on faith in the way your fingers really seem fly when you count. Squares and things take wing.

By the way, that reminds of one of those damned emails most folks collect too much of.

It explained that certain groups of people can be rendered harmless in bed and other convient and otherwise sites. They place a strong item of fireworks (Cherry bomb in the US)into a can and having lit its fuse, proceed to count to 10 while holding it to one ear. The desired effect occurs when the subject puts the can between his legs upon having to change hands to count beyond 5.

And that reminds me of something else, but I won't inflict that on anyone now.

[Fionn]

Well, startup results would be a little volatile. I was figuring on just liberally borrowing from chess and simply adding a WEM percentage of 100 points to each person's account for each win they get.. e.g. if you win by 70% to 30% you'd get 70 points (roughly.. that isn't quite accurate but its close and doesn't confuse anyone )

Then, as soon as someone gets to 1500 or 1600 points I'd institute the full rating system since 500 or so points is enough variation IMO to allow the introduction of such a system.

<BLOCKQUOTE>quote:</font><HR> And how do you come up with some of the apparantly arbitrary factors to apply to engagement types? <HR></BLOCKQUOTE>

Actually the ONLY differentiation is between attack and defence and that is based purely on my playing of the game. Based on the evidence before me I'd have to say I've player more CM than ANYONE else on the planet and so, while I won't say my guesstimate is perfect it is as good as we can do until someone plays more than I and comes up with a more accurate figure (which'll be a long time ).

Oops, I think I just noticed an error . It's late so I'll check it again tomorrow and fix it then if it really is wrong (too tired to trust my brain right now).

[bazooka10165]

Fionn - Math isn't my thing, so maybe you can set me straight, but: If two players are evenly rated, their DR will be zero. (unless "difference in ratings" means something other than what I think - in which case disregard the rest of this post) Under your formula, this will result in a WE of 1 for both players [1/((10*(0/400))+1)]. A WE of 1 will result in a WEM of 0. [(1-1)*(force balance multiplier)]. This will be true regardless of how mismatched the force composition is. Unless I'm missing something, in a game between two equally rated players, a player who routes an SS armored division with a company of green bazooka squads, is rewarded no better than if he had won with a division of Pershings. The losing player in such game would receive a positive modification in his ranking even if he had greatly superior forces since K(W-WEM) will always result in a positive number if the WEM is 0.

Perhaps the WE formula should have a +2 not a +1 at the end, giving evenly match players a WE of .5 instead of 1. Shouldn't two evenly matched players, playing an evenly matched meeting engagement, each have a WE and a WEM of .5? Its too late at night for me to see if this works.

I hope this entire issue is not a figment of my mathmatically challenged mind.

[Tom Servo]

too many words and numbers...

[Fionn]

Zooks, yup that's the error ..

[guachi]

A few comments from the statistically inclined.

Some of your equations are over-complicated.

<BLOCKQUOTE>quote:</font><HR>WEM = Win Expectancy Modified

WEM = ( 1-We) x ( ( attackers point value squared over 1000) divided by (defenders point value squared over 1000) ) ) divided by points factor constant determined by role in game<HR></BLOCKQUOTE>

'"attackers point value squared over 1000" can be re-written as AP^2/1000 and "defenders point value squared over 1000" can be re-written as DP^2/1000.

The "divided by" between the two is the same as multiplying by the inverse. This gives you AP^2/1000*1000/DP^2. The 1000s cancel out giving you AP^2/DP^2. Simplyfying a little results in (AP/DP)^2.

<BLOCKQUOTE>quote:</font><HR>We is the expected score (Win Expectancy) from the following formula:

We = 1/ (10 (dr/400) + 1)<HR></BLOCKQUOTE>

The We calculation is also a little too complex. "10 (dr/400)" can just be rewritten as dr/40.

Not only does the WEM formula not take force composition into account when the players are equal (as bazooka noted) the We formula seems to give strange results.

Example: I have a rating 400 points higher than you and we are playing a meeting engagement with identical points allocated to our forces.

We equals 1/((dr/40)+1). dr/40 is 10. Add 1 for 11 and the We is 1/11.

Since the forces are equal the second half of the WEM equation is 1. The WEM at this point is (1-1/11)*1. The WEM is thus 10/11.

Plug this into the first formula given and you'll see that someone with a rating 400 points higher than his opponent should win the game by a score of 91-9 jsut to keep his score from changing. That doesn't seem correct.

If, in the above example, the players were of equal rank the WEM would be 0. With a WEM of 0 no matter WHAT score you get, your rating will increase.

Jason

[Hunter]

Fionn,</p>

While noting the errors and criticisms above, there are some nice features in your rating system. Notably:</p>

1. You take into account ratings to determine new ratings (like the chess ratings)</p>

2. You take into account the difficulty of the scenario, which is required. </p>

3. You take into account the range of results that can be achieved. This is very necessary in a game with such a wide range of results. </p>

All this is pretty good </p>

I have the following comments about the system, and how it may be improved:</p>

Regarding (1) above - It was a while since I got my first rating in chess, but I thought they started me off at 1000 and then just applied the system to everybody I played? This sounds better than some arbitrary system below 1500?</p>

Regarding (2) above - What about the terrain, the weather and ground condition? Without taking these into account (and I understand the difficulty) it will always be possible to construct situations where the 1.6 factor you mention for the Attacker is the wrong number. Some of the ex-CC2,3 players (NOT mentioning names!) would have a field day with this.

Would it be possible where a scenario is published to also post a 'handicap rating' or similar? The scenario designer could note for example that the normal rating modifier of 2.5 for the attacker should be replaced with 2.8 in this instance (as the defensive position is quite strong, the ground is muddy or whatever)

Writing this has made me thing again (ow!). Why hasn't the scenario designer used 'Axis Bonus Points' to even out the scenario? If he has, then we don't need to know how many forces are involved do we?</p>

Regarding (3) above - Isn't it going to be very hard to progress at higher levels? Because there is a range of results (unlike chess 1,0,1/2) it seems that it will be quite difficult to improve your rating by playing very good players, as you may achieve a victory, clearly, but only a narrow one (say 60:40). This gives you a very marginal change, compared to the 100:0 result you may achieve in Chess. Can you imagine being beaten 80:20? It seems unlikely in most scenarios. I think the 'damper' effect introduced with the varying constants may need to be thought about some more </p>

Keep working on it, I'm sure we will agree on it eventually </p>

Bruce</p>

[guachi]

I re-read Fionn's initial post. He wanted comments in particular about the points factor modifier.

The idea is a good one. Basically a square of scenario force ratio to some kind of 'standard' force ratio. I particularly like the idea of squaring as it amplifies the effect of force differences.

Tangentially related to ratings is tournaments. There has been talk previously about tournament types. I don't think there is any 'correct' type so if CMHQ (or anyone else) sets any up I would like to see a variety of tournament types.

Jason

[argie]

I agree with Hunter.

Terrain, Visibility and Weather (the last two in close relation) have a huge impact in the possibilities to win a scenario. Maybe could be added some modifier to your "point factor modifier".

You know, an attacker attacking through fog have an advantage. A defender defending in mountain terrain, have an advantage too.

I think there are the only modifers objective enough to be considered that your system lacks. But I could think a lot more complicated if you wish

Ariel

[This message has been edited by argie (edited 03-19-2000).]

[Guest gyrene251]

Just Comments...as for unrated players starting their run on the ladder, why not a separate list until "x" amount of points or games are played and then the player is moved to the main ladder. It's extra bookkeeping but may work nonetheless...just my 2 cents worth.

[SS_PanzerLeader]

Fionn I was working on doing a ladder myself but with my courseload it proved to be impossible to find time for. I had gotten started on it and I think if I recollect I had gotten a pretty good formula (Haven't run tuns of data through no time)

You are welcome to it if you like

It accounts for the actual command abilities of player taking into account the resources that were lost in accomplishing their goal (visa/versa)

It also acknowledges that amount of play activity by a player ( within reason)

The rating system may be started from zero with players being unranked until >5 games played

If you are interested I will send it or post it..... it looks like it would work well - You are welcome to analyze it an take part or all if you wish to use - and of course none if ya don't like it

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SS_PanzerLeader.......out

[Fionn]

Jason,

Yes, you're right. I intentionally wrote the formula out in "longhand" so as to minimise the chances of confusinf readers.

Also, your assesment that a player rated 400 points higher would need to win 91/9 to keep his rating is wrong. It'd have to be more along the lines of 55/45 .

I copied the wrong version of the formula into the email I sent ;(. I didn't notice it before posting it here ;(.

With a WEM = 0 (meaning the players had equal ratings) the players would have to get a 50/50 split to keep their ratings equal.

That's the way it works in the formula which I finalised on... This formula was my first "rough draft" which brought the various concepts together (in a flawed way). I then corrected the errors in the final version but when I went into Word I just copied the first formula (the draft) and not the second, final, formula *DOH!*.

The squaring is based on a little combat formula which Nelson used when figuring out how to divide his fleet up at Trafalgar and has a long history ( over 600 years) of naval use. Basically it holds that a force which outnumbers you 2:1 actually should be able to wipe you out at the cost of 25% casualties and not the 50% you'd expect in a meeting engagement by virtue of the fact that its greater numbers give it greater firepower and other tactical advantages.

<BLOCKQUOTE>quote:</font><HR> What about the terrain, the weather and ground condition? <HR></BLOCKQUOTE>

And ANY attempt I make to model these factors is simply going to introduce error into the model. Sometimes snow aids the defender, sometimes it aids the attacker. The ONLY way to create a fair modifier for snow etc would be for me to inspect each and every PBEM map with respect to the forces being bought and assigning a unique modifier to it.

1. I don't have the time or inclination to examine each individual PBEM map.

2. There is NO way other than inspection of each map which can account for the highly variable effects of terrain, weather etc.

3. If we said forested terrain = a 1.2 defensive modifier that would be flawed the vast majority of the time.

Same goes for individual ratings for scenarios. These ratings are highly likely to be flawed.

While I ACCEPT flaws I'd much rather accept consistent flaws than inconsistent and variable flaws. Consistent flaws generally average out over time.

As for the progression thing. MOST battles I've been involved in result in the winner having 75+ points. Just yesterday I won a game 99 to 1 . Like I said, my experience with the system is involved in the creation of the formula and I'm confident progression will be eminently possible.

Argie,

Personally I think the DEFENDER has a massive advantage in foggy weather in general. I also find that mountain terrain can, if used properly greatly benefit the attacker.

My basic point is that while EVERYONE can agree that being the attacker requires a "modifier" most people are going to disagree with the effects of fog on the attacker/defender relationship if we make a general rule. IF we choose to make rules on a case by case basis then I'd simply say that I surely don't have the time to do such an examination and that if any of you are willing to spend hours a day examining maps objectively then I'll consider it hehe.

SS-Panzerleaderm

Sure, send it my way.. I'll have a look at it (might cover something I missed).

[SS_PanzerLeader]

there is no current email listed - and I had to reuinstall ICQ need addy plz

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SS_PanzerLeader.......out

[guachi]

I figured that the formula you posted was the wrong version, as you stated.

I'm not quite sure how to change it. The We for two equal players on an equal battlefield should be .5, correct? Doesn't chess ranking have ... (thought stopped due to Yahoo search)

Found the problem. The formula I found looks like this: 1/(10^(D/400) + 1).

Sorry for the confusion, Fionn. It's amazing what the absence of a symbol will do to a math equation.

Using my example again:

A ranking difference of 400 means D/400 is 1.

10^1 is 10

10 + 1 = 11

Giving a We of 1/11

This means a person with a ranking 400 points higher than his opponent should win the game 91-9

A ranking difference of 0 would yield:

10^0 = 1

1 + 1 = 2

We = 1/2

this means players of equal rank should have a 50-50 game. (duh)

A difference of 40 points would yield:

10^(40/400)

10^.1 = 1.25

1.25 + 1 = 2.25

We = 1/2.25

1/2.25 = 4/9

This means a player with a ranking 40 points higher than his opponent should win 56-44.

As to force differences, the point I was really trying to make was that the 1000 used in your calculations is unnecessary. You could use 1 billion and it wouldn't change the formula any.

You can actually simplifiy the equation even further:

(AP/(DP*SR))^2 (The formula actually looks better on a piece of paper)

AP is attacker point value

DP is defender point value

SR is standard ratio for the type of engagement

The squaring results in a larger effect for having an above (or below) average force.

Example:

Equal players with attacker having 5% more points than standard.

We = .5 as calculated above

As far as the formula is concerned, actual points is unnecessary for this example as the formula will reduce to 1.05^2. The .05 is the 5% extra points that the attacker has.

1.05^2 = 1.1025 or a 10% adjustment to expected win percentage.

Modified Win Expectancy is thus .5*1.1

.5*1.1 = .55

This can yield some strange results.

If my Expected win % is, say, .7 and the modification for points is 1.5 the results say I should win the game with a score of 105-0.

Basically, no matter how well you play, your ranking will drop. IOW, don't play really unbalanced scnarios (in your favor) against people far worse than you.

Net result is, the ranking system is simple (honest, it is! ). Now that I've looked at it, I like it.

The only thing that may need tweaking is the point ratio used for a given type of scenario. Fionn, I trust your judgement on this. A thorough record of game outcomes should provide an indication if the ratios need to be adjusted. No doubt there will be a massive number of data points available soon after the game is out so any adjustment should be quick.

I can understand why Fionn used long hand. Math formulas look goofy otherwise unless you are used to them (like I am)

Jason

[Fionn]

Ah, bloody typos .. (referring to the Dr/400 typo.

As for

<BLOCKQUOTE>quote:</font><HR> This can yield some strange results.

If my Expected win % is, say, .7 and the modification for points is 1.5 the results say I should win the game with a score of 105-0. <HR></BLOCKQUOTE>

Not really (although this version might say that).. My intention is that the 1.5 is applied to 1- expected win % = 0.3

0.3 /1.5 = 0.2

Thus a player with all these advantages would have to win by 0.7+ 0.2 = 0.9 or, in other words, a score of 90/10

This means that no-one has to get scores of over 100 points at any stage due to the formula.

The whole basis is that by relativising variables we can express everything in %s and thus avoid the weird results you mentioned which could occur if we didn't relativise things.

One nice side-effect of this system is that it penalises players who pick on newbies since they are going to have to win by a HUGE margin if they want to have any chance of gaining points. A good player facing a newbie might well have to win 95 /5 if he wanted to actually gain points. ( This eliminates one MAJOR annoyance in ranking systems since a win by 1 point vs a newbie is no longer as good as a win by one point vs another good player.)

Honestly players should probably only fight others who are within 200 points or so of them (rough guess ) or face the need to win by some truly spectacular margins .

Also, even IF an experienced player beats a newbie by 99/1 since he might have HAD to win by 95/5 in order to gain any points he will gain VERY few points by winning . Again, discriminates against those who seek out and kill newbies and greatly encourages players to play those only slightly below or above their rank.

[Guest hunt52]

Would people be interested in having a ranking system compute "rank" as well as score and place? Something like the top player is a 5 Star the next couple are lower star generals then [enormous gap in my knowledge of military organization] have something like 2^5 Captains and 2^6 Lieutenants and 2^7 Seargants? I think this would add some flavor to the ranking system. It also might be cool to give out medals to people who beat someone who has a much, much better rank than they do.

Just my thoughts.

Perl is much less evil than first appears.

- Bill

[CoolColJ]

I've never been in any rankings system ever, and never will. It just kills the fun of the game, and puts too much pressure on you. Things always get too serious.

Thanks but no thanks

ccj

[Guest hunt52]

actually, I won't participate either, just think that should one exist it would be cool to have more than just a number rank.

- bill