# PK points system

### #1

Posted 26 June 2007 - 07:24 PM

Now, there are two possible ways to implement it, symmetric and assymetric.

Symmetric: You win a fight, you win a point. You lose a fight, you lose a point.

Pros:

Easy to implement and understand.

Would not cause players to target 'high prized' players.

Cons:

Slightly easier to cheat, by having a 'fallguy' who is willing to lose fights for you, in exchange for something.

New players will have a hard time gaining as many points as older players (because not only the older players are usually stronger, but they accumulated more points).

Asymmetric: You win a fight against someone with a higher PK score than you, you gain more points, and he loses more points. You win a fight against someone of a lower level than you, you gain less points, he loses less points.

Pros:

Harder to cheat the system, if someone is losing a lot of fights his score will become lower, and people winning more fights with that person will gain a very limited increase in their score.

Easier for newbies to catch up.

Cons:

Players with high score might be reluctant to fight, because any kill will just marginally increase their score, and any loss will drastically decrease their score.

Higher scored players will become a preferential target, since you can get more points off them if you kill them, and not lose as many points if they kill you.

Now that you know the pros and cons, please vote. If you ask questions that were already explained here, you will be suspended from the forums.

If you vote for the asymmetric system, it would be nice to provide a formula. There are the following variables: your number of fights, your loses, your wins, your score, and same for the enemy.

### #2

Posted 26 June 2007 - 07:59 PM

New Ranking = Old Ranking + (Rank of you/rank of other/two) * the result (with a win being 1 and a loss -1)

The two of course is used to not give extreme results.

Example Player1(50) vs player 2(1)

If player1 wins s/he will earn 25 points, and player2 will lose that amount. If player2 wins s/he will earn 0.01 points, and player1 will lose 0.01 points.

The problem with this is as stated, the person who is highly ranked will have a hard time earning points while people lower on the list can advance fast. Also, the score is developed by each fight and not by the number of points you have.

### #3

Posted 26 June 2007 - 08:23 PM

I also think there should be a cap on points gained, (could be 1 the lowest points you can gain (from no matter what win, and maybe 20, but the height cap could be many things)

for the actual formula, there would need to be a distribution of how much is gained compared to the differences in rank. Have a look at this link for an example on this:

http://chess.about.c...s/aa07b17_3.htm (I don't play chess, I got it linked from the ranking of a snooker game)

I agree with the format of sparhawks:

New Ranking = Old Ranking + result * ( )

but maybe a better way of working out whats in the brackets is needed...

I gotta take a trip to the pub, and have a think, when I'm done I'll post a full formula if no one has already posted a satisfactory one.

EDIT: regarding sparhawks example:

-if you increase player1s points by 1, the difference will be marginal, but if you increase player2s points by 1, the difference will be significant!!

-plus your example is favouring the higher ranked people, need to swap these two around 'Rank of you/rank of other'.

**Edited by Rockfall, 26 June 2007 - 08:29 PM.**

### #4

Posted 26 June 2007 - 08:43 PM

Cons:

Higher scored players will become a preferential target, since you can get more points off them if you kill them, and not lose as many points if they kill you.

I think that will work as a 'pro'. Also the reason I voted for this system.

### #5

Posted 26 June 2007 - 08:49 PM

agree

Cons:

Higher scored players will become a preferential target, since you can get more points off them if you kill them, and not lose as many points if they kill you.

I think that will work as a 'pro'. Also the reason I voted for this system.

### #6

Posted 26 June 2007 - 08:50 PM

New Points = Old Points + result * (the weight of ranking)

So if Player1 is ranked 20th and player2 is ranked 24th then if they face they each will earn/lose 15 points

20 = 15 + 1 * 5

10= 15 + -1 * 5

If player1 is ranked 1 and player2 is ranked 13 then

If player1 wins: Player1: 53 = 50 + 3 * 1, Player2: 12 = 15 + -1 * 4

If player2 wins: Player1: 42 = 50 + -1 * 8, Player2: 23 = 15 + 1 * 8

Where the range is:

With the format: rank range : higher person point gain/loss/ and lower person gain/loss

1-5 rank range:5/5 points

6-10: 4 points/6

11-15:3 points/8

16-20:2 points/10

21-25:1 points/12

26-30:1 points/14

31-35: 1 points/16

36-40:1 points/18

40+ : 1 points/20

Or any type of ranking, but note that these ratios are just here for hypothetical reasoning

**Edited by sparhawk, 26 June 2007 - 09:00 PM.**

### #7

Posted 26 June 2007 - 08:54 PM

I did some tests on a spreadsheet, and the results showed very distant values.

To avoid injust loss/gain of points, it would be nice if there is a cap.

For the start example, I'm working on a cap from 1 to 10: 5 taken from a/d difference and 5 from pk points difference.

I'm working on a formula here, when I finish I will edit here.

I also would propose some ideas to avoid cheating

- When a player reaches determined negative points (example: -50) he needs to go to a npc and pay a fee to make his points to zero and participate on the ranking again (otherwise neither he nor the other player who kill/die will receive points). This npc will "hold" all the negative numbers taken from players, then still will be possible to make the sum (all pk points of the players - points from npc) to reach the total 0.

This is just a suggestion, would make players to avoid cheat to avoid gc loss. Maybe will exist players who dont care about money and still will want to cheat

- Both players that cheat will have their score reseted, and plus both will be pkable for a week (for example). While pkable, they dont gain/loose pk points.

### #8

Posted 26 June 2007 - 08:58 PM

There comes a time in life for each and every one of us when we got to decide if one is the identity element of multiplication or not, some as you prefer to state this as the "one times ten is five" problem20 = 15 + 1 * 10

10= 15 + -1 * 10

### #9

Posted 26 June 2007 - 08:59 PM

The asymtopic system. As for the forumlae, there are any number depending on how you want it to behave. I'll start with the simplest, which I use quite a bit for rank vs rank tests:

Inverse Tangent, Raised

**Note: This curve represents the points transfered as a function of the difference in participants' scores.**

*Inverse Tangent*

The nice thing with this curve is that it converts any real number to a finite range, asymtopically approaching the limits. Raise and scale this curve so its limits are [0..2*b*]:

*dK* = *b* ( 1 + (2/pi) atan ( *a* [ *KB* - *KA* ] ) )

*KA* <-- *KA* + *dK**KB* <-- *KB* - *dK*

Where '*A*' and '*B*' are two participants, in which '*A*' is victorious. '*KA*' and '*KB*' are the original kill scores of '*A*' and '*B*' respectively, and '*dK*' is the quantity transfered from '*KB*' to '*KA*' as a result of the contest.

'*a*' is a scaling factor determining the gradient around *KA*=*KB*; that, how sensitive the formula is to differences in ranking. The larger '*a*', the more rapidly we approach the limits.

'*b*' scales the result. When participants have equal ranks, *KA*=*KB*, *b*-points will be transfered as a result of a contest. The maximum points transfered is 2b, when *KA*<<*KB.*

Advantages of this formula is that it is well defined and simple.

Disadvantages are that it needs to be tuned (*a* & *b* parameters), and it forces a symmetry which may not be idea.**Update 2007-06-27:Update 2007-06-28:**

~~Relationship between~~*a*and*b*which should work well (proof-by-handwaving):

*a* = 1 / *b*

~~giving a simplified form:~~

*dK* = *b* ( 1 + (2/pi) atan ( [ *KB* - *KA* ] / *b* ) )

**Reworking**: Its not quite that simple unfortunately. Lets decide that '*a*' will be the points difference, | *KA* - *KB* |, such that the reward is *b* ± ½ *b*. Then we need to define a scaling constant *s*, and rework the equation:

*s* = tan (pi / 4) ~= 0.0137

*dK* = *b* ( 1 + (2/pi) atan ( [ *KB* - *KA* ] *s* / *a* ) )

Now we can start to make some intelligent tuning to the formula, since we have meanings for the constants *b* and *a*:

*b*is the number of points awarded for a contest between equals.*a*is the score difference for which the award is changed by ½*b**(in the absense of a power term described below)*.

- The formula can be extended to include
*"combat rating"*,*C*, (*CA*,*CB*), which adds to*K*. A trivial value for*C*is*A*+*D*, as originally suggested; although with an adaptive systems this may not be necessary, as the*K*value should eventually represent a character's true combat rating.

- The equation is symmetric; this can be adjusted by taking the atan component, normalised to [0..1], and raising to a
~~fractional~~power:

*dK* = ( 2 ^ *n *) *b* ( 0.5 + ( 1 / pi ) atan ( [ *KB* - *KA* ] / *b* ) )^ ( 1 / *n *)*dK* = ( 2^*n *) *b* ( 0.5 + ( 1 / pi ) atan ( [ *KB* - *KA* ] *s* / *a* ) )^*n*

For example, with n = 2 this becomes:

*dK* = *4 b* sqrt ( 0.5 + ( 1 / pi ) atan ( [ *KB* - *KA* ] / *b* ) )*dK* = *4 b* ( 0.5 + ( 1 / pi ) atan ( [ *KB* - *KA* ] *s* / *a* ) )^2

For matches participants the points transferred is still *b*, but the range of *dK* is now [0..4*b*], meaning a weaker opponent can potentially win more from a contest.

If we are using n=2, we may want to redefine s, such that a is the difference in K such that the award will be either '½ *b'* or '2 *b*' (ie, the award is either halved or doubled relative to that of an equal contest). It is not possible to get a value of s to give these *exact *results, but we can determine a value which is as close as possible, minimising relative errors. This is:

*s* = 0.008 665 23

*(* Corrected power term in equation)(* Introduced 's' to give a definition to 'a')(* Determine a more suitable value for 's' for 'n=2')*

**Edited by trollson, 28 June 2007 - 12:22 PM.**

### #10

Posted 26 June 2007 - 09:03 PM

There comes a time in life for each and every one of us when we got to decide if one is the identity element of multiplication or not, some as you prefer to state this as the "one times ten is five" problem

20 = 15 + 1 * 10

10= 15 + -1 * 10

Ack, I had forgotten to change that number when I changed the value on my hypo sheet lower...

### #11

Posted 26 June 2007 - 09:19 PM

Say the limit is 10. Progressing from 9 to 10 would take, say, 1000 wins and no loses. Then you get all the way there, and someone kills you a few times, and you drop to 9. So a few failures would drastically affect your rank.

### #12

Posted 26 June 2007 - 09:26 PM

(if this is what was said, didnt really get all of it)

### #13

Posted 26 June 2007 - 09:42 PM

But i think it's a tough vote, it's fun and all that we want more pk points when we kill a higher ranked player, but what about those which are higher ranked? they indeed will get chased a lot and it will be more a bounty hunt then an improval of pk....

If it will be implemented as asymmetric, then just keep the points gained and points recieved low, so +1 when u kill anyone lower then +2-3 when u kill someone higher then u....

This will cause the fact that people not really WANT to chase higher ranked, cause of the chance u will get killed urself and it is not a major gap of pk points u will win when u do kill him/her...

But after all the real improval of pk in my opinion would be, making every PK area a non drop area )

just kidding...

But i do like the pk point way and i voted asymmetric

### #14

Posted 26 June 2007 - 10:03 PM

You are thinking of the curve as an experience table. It is not.trollson, I would rather not have a formula where in order to progress towards a certain limit, you need to put too much of an effort.

It does not suggest any limits on the PK scores of characters; rather the limits discussed are on the number of points transfered from loser to victor as the result of a single combat.

The curve describes the number of points transfered

*(vertical axis)*, given their difference in PK scores

*(horizontal axis)*.

- If you always fight other characters around the same score as yourself, then you get about the same number of points transfered (
*b*), regardless of absolute values. - If you fight people much lower than yourself, you risk losing more points
*(tending to 2b)*, and chance to win far fewer*(tending to 0)*. And visa versa.

- The assumption so far is that they are just a linear scale, and that there is no difference in difficulty between earning the 1st and 1000th point
*(cf. experience points)*. - If they exist in a space where gaining points becomes more difficult the more points you already have
*(cf. levels)*, then it requires a different model.

**Update 2007-06-27:**- Rankings matter, absolute PK point scores do not.

- Leagues based on "combat rating" ranges (eg, A+D) produce ranking lists for characters within their range. Ranges can overlap (eg, 0-50, 25-75, 50-100). PK score is independant of what league(s) the character is listed in, and retained when they move to the next league.

**Edited by trollson, 27 June 2007 - 09:51 AM.**

### #15

Posted 26 June 2007 - 10:05 PM

### #16

Posted 26 June 2007 - 10:06 PM

Doc

### #17

Posted 26 June 2007 - 11:52 PM

When you pm gossip about someone who is not on privacy mode, she gives a combat level. So I suggest using one's combat level as a point gain/loss.

When a player wins they get 50% of their oppnent's combat level, but if they lose they will lose 20% of their own combat level.

Example;

Player 1's Combat level 200

Player 2's Combat Level 100

Player 1 wins and gains 50 points

Player 2 loses 20 points.

A simple idea, it will also avoid people who are not so much famelier with math to figure out easily, instead of asking "If I fight and win against so and so how much points will I gain?"

### #18

Posted 27 June 2007 - 01:08 AM

If you voted for asymmetric, I am going to chose a formula that works, even if it is more complicated than a simple formula that doesn't work.

### #19

Posted 27 June 2007 - 01:38 AM

All-in-all it is a great idea with a lot of potential.

((maybe we could then have some PK-related quests based on PK score, for example))

### #20

Posted 27 June 2007 - 02:00 AM

If you look at the graph trollson has shown us, it is accurate to what we want to achieve, yet as entropy said we don't want to be using limits in points... So really we want to make things so fractional based on Trollsons graph that the highest/lowest ratings wouldn't be getting close to 5/-5 and more likely be maximised at around 3/-3!!!

EDIT: I realise I contradicted myself with the above, my formula is

*more*linear unlike trollsons...

Heres a simple formula (which represents what I mean):

New Ranking = Old Ranking + "result * mod(your level - enemy level) / k"

k = the cap of the highest difference available ( I would guess at 10)

mod = the modulus (or absoulute) value, basically giving a positive number

result => 1 = win, -1 = loss

the number worked out in between the "" would be rounded to an integer,

**but**with the lowest integer being 1, and the highest integer being 10....

An alternation of this could be; the value k is just the number 10, and there isn't a 'highest' cap on point transfer, although I think the cap is a very good thing and may potentially lessen the problem of:

Players with high score might be reluctant to fight, because any kill will just marginally increase their score, and any loss will drastically decrease their score.

This is just a fairly simple way about this, and although it works there could easily be 'improvements' to it

EDIT: some mistakes (maybe not all..)

**Edited by Rockfall, 27 June 2007 - 02:05 AM.**

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