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Scores will get very high and very low [To-Address]

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Re: Scores will get very high and very low [To-Address]

Postby strmckr on Tue May 26, 2009 5:23 pm

http://research.microsoft.com/en-us/pro ... tails.aspx

heres the formual for true skill that you where going to research, :)

and a virtual calculor as well..

http://atom.research.microsoft.com/true ... lator.aspx
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Re: Scores will get very high and very low [To-Address]

Postby WidowMakers on Tue May 26, 2009 7:22 pm

The main problem with comparing Sudoku with: Chess, MTG, halo, or other multiplayer games, is that in all of those, each player plays defense and offense. Good players can sometimes lose to bad players. There are upsets and surprises. Match ups can determine the outcome and the most skilled does not always win. In sudoku, the faster you are, you will most always win.

Since it is basically a race (like the Olympic 100m) only the top 20 are ever going to make it to the big race. No matter how hard the rest of the people try, they are not good enough. Not matter the training or whatever, the y will still lose.

So while a new point system may help slow the pace of point inflation, the end outcome will be the top 10 players here will always be there (as long as they keep playing) and the majority of the rest will never have a chance.

If you play for fun then don't worry about score. That is basically what we need to accept.

WM
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Re: Scores will get very high and very low [To-Address]

Postby strmckr on Tue May 26, 2009 7:58 pm

even with competions for races there is upsets and defeats but that is more of a matter of conditioning.

bad heath or some other unexpexed evet will cause even the most conditioned athleat to still lose. these are the unknown factors in a race. sure an athelte peaks at some point in there ability thats there limit. they will lose to those with a beater peak in skill.

yes single games the have a trait that can swing a win in the lesser players favirt and upset are not so much the case in a race.

i know this from exprience ive topdecked many of matches and claimed vicorty in a board postion i should have lost.

but thats the nature of strategy games sometimes you get lucky, or ive fained a move and won from the misdirection tactic. same happens in chess.

the point in these is a gauge of relative skill a player holds over a long period of time.
luck is a factor but realative skill will still gain more wins over the long haul.

with this:

in both the top people on average will still be the top seats overal due to the nature of competion.

elo systems are used in
golf which is a direct compairison of skill.

sure heath and other factors may affect how you play its the same here.

those that play there best game "lowest score count" wins.

the problem with the current point systems is that there is no deffinte levelign to get a ranking order to whom is in the top 100

the point system in place over infalts everyone.

there is no clear leveling of the points to indicate whom is in the same levels of skill or not.
thats the idea behind the elo system.

to mark a average meadium to gage the level of skill a player has or doesnt have.
Last edited by strmckr on Tue May 26, 2009 8:10 pm, edited 2 times in total.
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Re: Scores will get very high and very low [To-Address]

Postby lancehoch on Tue May 26, 2009 8:03 pm

ckr, you make an interesting point about golf (and I believe the same system is used in golf and tennis). Would someone be able to configure a golf-esque scoring system? I know that the golf system has a recent history factor, so that would be something to discuss. But, it also gives points based on place finished and there is no "defense" for playing against someone who is better. The few questions that I have about the system that would make for good discussion points are: how long of a history should be deemed relevant, and how should the number of people involved in the game affect the points, and how should the difficulty affect the number of points?
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Re: Scores will get very high and very low [To-Address]

Postby strmckr on Tue May 26, 2009 8:12 pm

(and I believe the same system is used in golf and tennis).

true its used in a number of sports. and the equatiosn remain the same.

the history factor is calculated in the ranking points of the player..

i would suggest dling it and testing it out.

But, it also gives points based on place finished and there is no "defense" for playing against someone who is better.


the win % calculation is the determing factor in a match.

the equatiosn i have are from golf and mtg they are identical:

the only factors i have modified are the k values

which are from magic with the modification they increase by the number of people in the game up to the max for the class of puzzle.

if player b is the weaker player by a marger of huger porportions then their odds of wining is close ot 0%

i'll show an example.

layer a 2000 points
B : 500 points
player count = 2

puzzle is easy(1) K = (1*2) =2

player a finishs 1st win % [ 1/10^((500-2000)/400)+1) = .9998 ]
b finishes 2nd win % [1/10^((2000-500)/400)+1)=.0001789]

score A:= (2+1-1)/2 = 1
score B:= (2+1-2)/2 = .5

new score A:= 2000 + (2*(1-.9998)) = 2000
new score B:= 500 + (2*(.0001798-.5) = 501

so as you can see player a gains no points and player b still gains points.

this can also be done to show with more players in the game.
using the average poitns of the opponents.

player a 2000 points (3rd)
B : 500 points (1st)
C: 800 points (4th)
D: 1400 points (2nd)

player count = 4
total points = 4700

puzzle is hard(4) K = (4*4) = 16

player a win % [ 1/10^((470-2000)-2000)/400)+1) = 0.999]
b win % [1/10^((4700-500)-500)/400)+1)=0.009]
c win % [1/10^((4700-800)-800)/400)+1)=0.053]
d win % [1/10^((4700-1400)-1400)/400)+1)=0.849]

score A:= (4+1-3)/4 = .5
score B:= (4+1-1)/4 =1
score c:= (4+1-4)/4 =.25
score d:= (4+1-2)/4 = .75

new score A:= 2000 + (16*(.5-.0999)) = 1992
new score B:= 500 + (16*(1-.009)) = 516
new score C:= 800 + (16*(.25-.053)) = 803
new score D:= 1400 + (16*(.75-.849)) = 1398
Last edited by strmckr on Wed May 27, 2009 1:11 am, edited 7 times in total.
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Re: Scores will get very high and very low [To-Address]

Postby strmckr on Tue May 26, 2009 8:46 pm

and how should the number of people involved in the game affect the points, and how should the difficulty affect the number of points?


well if your increaseing the diffiuclty your increasing several factors:

time to solve will increase,

the number off applicale skills needed to solve increases as dose time to find them

thus alot more risk to solve quickly.

with increased risk the potential to lose is higher and only a hand full of peole can solve quickly but luck to find them is greater as well.

since its a risk either way upsets can happen more often but skill is heavily required since it takes more skill more points to make up for the luck factor is needed to keep the long term factors a minimal.

the number of players in a match can be a huge factor as well more risk for all those in it to lose poitns and gain poits
i went with a incremental system that factors based on the entries in the event.

to show what i mean lets take the above mutiplayer game and change the puzzle to easy difficulty.
this shows that the more skill required the wider range of point distribution between players is = to the diffrence in skill requirments calculated into the % win equations.


player a 2000 points (3rd)
B : 500 points (1st)
C: 800 points (4th)
D: 1400 points (2nd)

player count = 4
total points = 4700

puzzle is easy(1) K = (1*4) = 4

player a win % [ 1/10^((4700-2000)-2000)/400)+1) = 0.999]
b win % [1/10^((4700-500)-500)/400)+1)=0.009]
c win % [1/10^((4700-800)-800)/400)+1)=0.053]
d win % [1/10^((4700-1400)-1400)/400)+1)=0.849]

score A:= (4+1-3)/4 = .5
score B:= (4+1-1)/4 =1
score c:= (4+1-4)/4 =.25
score d:= (4+1-2)/4 = .75

new score A:= 2000 + (4*(.5-.0999)) = 1998
new score B:= 500 + (4*(1-.009)) = 504
new score C:= 800 + (4*(.25-.053)) = 801
new score D:= 1400 + (4*(.75-.849)) = 1400

Help!!: any way to fix the errors that happen wiht long posts i find i cant edit them effectivly they keep scrollign upwards.?
any one else have the same problem...
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Re: Scores will get very high and very low [To-Address]

Postby sudoking on Tue Jun 09, 2009 2:49 pm

What if instead of (loser's score / winner's score) we just used (loser's score / winner's score) ^ 2 i.e. squared to amplify the difference?
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Re: Scores will get very high and very low [To-Address]

Postby strmckr on Tue Jun 09, 2009 4:28 pm

that would still have the same effect, winniers points increases constatly.

with a points rating system its represents the skill of a player compared to each other so you can have a sence of equilbirum overal on their play styles.

if the levels never create a bell curve of points distribution there isnt any way to gauge the skill of each player.

it becoms a point race, as it currently is.

the problem here is that any half decent skill player can play players they know they can beat and always increse there score.

the leveling of the field forces players to play outside there skill class and improve to gain more points. if they cant you have a more accurate telling of there relative ability. they way i have it set up also allows a weaker player not to worry about loseing to a stronger player they gain experiance and very low amout of points from it.

the stronger player how ever risks losing points if they dont perform well.

thats why an elo system works.

the mathmatics for it its aroudn a grade 6 level.

the system is used where kids compete with out a problem.{pokemon,etc...basicalyl every game wizards of the coast has for competions has an age range of 6-90 playing in the turnamnets}

it is also acceptable that not everyone is mathmatically inclided and will be able to understand how it works.

thats why i show it in a simplistic break down.
thats the only way to show it.

a number of people can appreaciate how it works, others cant be bothered with knowing how it works.

i wouldnt worry about that part a whole lot.
Last edited by strmckr on Tue Jun 09, 2009 7:24 pm, edited 1 time in total.
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Re: Scores will get very high and very low [To-Address]

Postby strmckr on Tue Jun 09, 2009 4:41 pm

heres a recap.

starting points level usually is 1600 points.

Code: Select all
New point  = (old points + ( k * ( score – win %) ) )



Code: Select all
Win %

                                                           1
Win Probability = ------------------------------------------------------------------------
                           10^(( Opponent’s average rating – Player’s Rating)/400) + 1)



Code: Select all
Score:

N + 1 – Rank Finished
----------------------------
            N

where:
DNF  =  0



Code: Select all
K:

K = ( N * puzzle rating)


Puzzle rating:

Easy: = 1
Medium 2
Hard = 4
Very hard = 8

Where:
Dnf = quit
n = # of players
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Re: Scores will get very high and very low [To-Address]

Postby lancehoch on Wed Jun 10, 2009 6:30 am

sudoking wrote:What if instead of (loser's score / winner's score) we just used (loser's score / winner's score) ^ 2 i.e. squared to amplify the difference?

Are we still multiplying by 20? I think that this might work, if the multiplier is dropped to 10.
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Re: Scores will get very high and very low [To-Address]

Postby strmckr on Wed Jun 10, 2009 12:59 pm

that would still have the same effect, winniers points increases constatly

see 2 post.
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Re: Scores will get very high and very low [To-Address]

Postby lancehoch on Wed Jun 10, 2009 11:52 pm

strmckr wrote:
that would still have the same effect, winniers points increases constatly

see 2 post.

Yes, but if someone is the best on the site, to the point that they never lose, what would be the point of them playing if they cannot gain points? There will have to be a trade-off. The question is really not, how do we make it so that the top people never gain points, it is how do we make it so that the top people gain very very few (if any) points from low ranked people and only a few points from the high ranked people.
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Re: Scores will get very high and very low [To-Address]

Postby strmckr on Thu Jun 11, 2009 2:03 am

Yes, but if someone is the best on the site, to the point that they never lose, what would be the point of them playing if they cannot gain points? There will have to be a trade-off. The question is really not, how do we make it so that the top people never gain points, it is how do we make it so that the top people gain very very few (if any) points from low ranked people and only a few points from the high ranked people.

they can gain point , they have to find people within there points rank by a percentage so there odds of winning is less then 95%. othere wise they dont gain points. in which case they are playing to hold there positon or for fun.

the spread of points will peak at a point but the lower rank players control where it crests as they still gain points the more poitns they gain the higher that crest will be. its a distrubution curve of wining % that controls how points are won lost.

they essential gain no points from the lower ranked players, low ranked players still gain a small amount of points in stead of losing them like they do now.

they can only gain a small percentile amount of points based on there odds of winning even when facing all equally skill points of players or a range of closly related skilled players.

the great to 100% chance your odds of winning becomes you dont gain points instead you risk losing more.

if equal skilled playes are in teh same match they both exhib the same odds of winning thus one gains poitns the other losses.

download my excell sheet and test it out if you want.

http://strmckr.fileave.com/formula%20sheet.xls
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Re: Scores will get very high and very low [To-Address]

Postby euklid on Thu Jun 11, 2009 3:24 am

I have not read the whole thread in detail but I think the aspect I will mention is new:

In the ELO system a player that wins 75% of his games against an opponent ends up with 200 points more than his opponent. I.e., a 1200 player wins 75% against a 1000 player, a 1400 player wins 75% against a 1200 player, ..., a 2800 player wins 75% against a 2600 player

In the current ranking system of SpeedSudoku a player that wins 75% of his game against an opponent will end up with 1.7 times the points of his opponent. I.e. a 1700 player wins 75% against a 1000 player, a 2890 player wins 75% against a 1700 player, a 4913 player wins 75% against a 2890 player, a 8352 player wins 75% against a 4913 player,...

In chess there exist ELO numbers in a range of 1000-2800 ELO. Thus there are 9 'classes' (1000-1200, 1200-1400,..., 2600-2800) where the difference of one class means a win percentage of 75%. If we assume that there are also 9 classes of sudoku players (from absolute beginner to jaku111) then each class would have 1.7 times the points as the previous class. Therefore jaku111 would end up with 1.7^9=118 times the points of a beginner. At the moment we have reached a factor of approx. 16237/86=188 between top and worst rating, which assumes 10 'classes' of players.

Thus the ranking system with Grand Guru, Guru, Grand Master, ... is not significant. The difference between ranks cannot be an absolute value (4000/3000/2000/... points) but must be a factor, for instance 2 (16000/8000/4000/2000/1000/...). Otherwise, half of the players will be Grand Gurus. I assume that Grand Guru should start at 16000 points only. Unfortunately it takes a lot of games even for the best players to reach this limit. But as the scoring system is at the moment, several players will reach the 16000 points in the future...

euklid

P.S.: The other weakness of the ranking system has been adressed by others in this thread. I just want to confirm:
It is obvious that a 16000 player has an estimated win percentage of at least 99.9% against a 1000 player. Thus if he wins a race he should win only fractions of a point and if he looses a race he should loose tons of points. In the current ranking system he can still win 1,25 points and lose only 100 points (because the formula (loser's score / winner's score) * 20 is capped at 100 points). Therefore the points will go up.
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Re: Scores will get very high and very low [To-Address]

Postby strmckr on Thu Jun 11, 2009 7:06 am

euclid,

yes the point spread in elo systems is a bell curver where a ration of win pertencitls are a distrubited mean between them, thus a range of points spread represent as a percentile group are equal to a specific rank.

the points are still gained/losed by the % chance that a player can win verss a player of higher or equal points ranking.


P.S.: The other weakness of the ranking system has been adressed by others in this thread. I just want to confirm:
It is obvious that a 16000 player has an estimated win percentage of at least 99.9% against a 1000 player. Thus if he wins a race he should win only fractions of a point and if he looses a race he should loose tons of points. In the current ranking system he can still win 1,25 points and lose only 100 points (because the formula (loser's score / winner's score) * 20 is capped at 100 points). Therefore the points will go up.


yes the above is correct
the whole topic is:

the biggest problem here is that any player can advance their score beyond some thing that represents there actually ablity in the elo system you cannot inflate your score beyond a level with out improving your own ability.

in an elo system only equally skilled players in competion can increse there score when facing each other.

here you simply play millions of games and always increse.

un equally skilled players can increase there score if there win percentage is < then the opponents by a large % by a small percent. while the > % gains no points.

in here unequally skilled poitns is one sided. the better play gains more points and the weaker players fall even more.
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