Formulas for Most Efficient Point Collecting Strategies HELP

[Beckytheblondie]

Mathematician help sought.

Seeking to solve: Asymptotic point maximum for a given player given the constants of win percentage (on a map/settings), points won and lost, and average opposing player score.
Goal: To maximize point collection to reach asymptotic peak.

Example: Beckytheblondie

Starting Points (BP): 3014
Opponent Average Points (OP): 1750 (Speculation)
Points Won (PW): (OP/BP)*20 = 9.87
Points Lost (PL): (BP/OP)*20 = 5.16
Win Percentage on specific map or settings (W%): .85
Points Gained (PG): (PW)*W% - (PL)*(1-W%) = 9.87-5.16 = 4.7
New Becky Points Set: BP1 = BP+PG = 3018.7
New PW (PW1): 9.86
New PL (PL1): 5.17
.....
solve for {B1...Bn}
Asymptote = 4166

But how did I get to that value? I literally just copied and pasted the formula over 11,000 times to find when PW=PL

Can a formula like this be used to calculate what a players maximum point total could be given constraints of only W% and OP?

Can I gain more points by playing stronger players and decreasing my W% or by playing weaker players and increasing my W%?

Can I gain more points solely by finding a map that I can win a percentage more of the time? Is that all that is needed?

Thoughts? Additions?

[betiko]

Mathematician help sought.

Seeking to solve: Asymptotic point maximum for a given player given the constants of win percentage (on a map/settings), points won and lost, and average opposing player score.
Goal: To maximize point collection to reach asymptotic peak.

Example: Beckytheblondie

Starting Points (BP): 3014
Opponent Average Points (OP): 1750 (Speculation)
Points Won (PW): (OP/BP)*20 = 9.87 that would be weighting your W%
Points Lost (PL): (BP/OP)*20 = 5.16 that would be weighting your L%
Win Percentage on specific map or settings (W%): .85
Points Gained (PG): (PW)*W% - (PL)*(1-W%) = 9.87-5.16 = 4.7
New Becky Points Set: BP1 = BP+PG = 3018.7
New PW (PW1): 9.86
New PL (PL1): 5.17
.....
solve for {B1...Bn}
Asymptote = 4166

But how did I get to that value? I literally just copied and pasted the formula over 11,000 times to find when PW=PL

Can a formula like this be used to calculate what a players maximum point total could be given constraints of only W% and OP?

Can I gain more points by playing stronger players and decreasing my W% or by playing weaker players and increasing my W%?

Can I gain more points solely by finding a map that I can win a percentage more of the time? Is that all that is needed?

Thoughts? Additions?

the more you win rank the more you will need to fight stronger players to keep the same point gain assuming the win% remains the same.
But the higher the rank of the oponent, the most likely your your win% decreases. solution: boost your skills.
And win% can no way be considered as a constant..

[Beckytheblondie]

the more you win rank the more you will need to fight stronger players to keep the same point gain assuming the win% remains the same.
But the higher the rank of the oponent, the most likely your your win% decreases. solution: boost your skills.
And win% can no way be considered as a constant..

Good point, but betiko, you win 61% on Das Schloss (146 from 239) with a relative rank of (0.844). After 239 games that win percentage is pretty telling and predicting.

Or, I win 87% Feudal Epic 2 player freestyle adjacent, 85% FE2F chained, and 86% FE2F unlimited. So I'm pretty sure I can predict my win percentage on that map. There have been players like King_Herpes who have played thousands of games on a map with a winning percentage above 90%. Don't know if this record is beatable:

[player]King_Herpes[/player] City Mogul Field Marshal +7060 2358 from 2446(96%)

[Doc_Brown]

Mathematician help sought.

Seeking to solve: Asymptotic point maximum for a given player given the constants of win percentage (on a map/settings), points won and lost, and average opposing player score.
Goal: To maximize point collection to reach asymptotic peak.

Example: Beckytheblondie

Starting Points (BP): 3014
Opponent Average Points (OP): 1750 (Speculation)
Points Won (PW): (OP/BP)*20 = 9.87
Points Lost (PL): (BP/OP)*20 = 5.16
Win Percentage on specific map or settings (W%): .85
Points Gained (PG): (PW)*W% - (PL)*(1-W%) = 9.87-5.16 = 4.7
New Becky Points Set: BP1 = BP+PG = 3018.7
New PW (PW1): 9.86
New PL (PL1): 5.17
.....
solve for {B1...Bn}
Asymptote = 4166

But how did I get to that value? I literally just copied and pasted the formula over 11,000 times to find when PW=PL

Can a formula like this be used to calculate what a players maximum point total could be given constraints of only W% and OP?

Can I gain more points by playing stronger players and decreasing my W% or by playing weaker players and increasing my W%?

Can I gain more points solely by finding a map that I can win a percentage more of the time? Is that all that is needed?

Thoughts? Additions?

Sure. You can simplify this to a formula that's based solely on opponent's score and your win percentage.
Let a(n) be your current score, a(n+1) be your score after one game, b be your opponent's score (assumed to be constant), and w be your win percentage (expressed as a fraction).

Combining your equations above, we get
a(n+1) = a(n) + 20 w b / a(n) - 20 (1-w) a(n) / b
This can be re-written as:
a(n+1) = a(n) x [1 - 20(1-w)/b] + [20 w b]/a(n)

For simplicity, let's let
A = 1 - 20(1-w)/b
B = 20 w b
so
a(n+1) = A a(n) + B/a(n)

We can assume that your score asymptotically approaches some constant. So let's assume
a(n) = C - D m^(-n)
We really don't care about the values of D or m. In the limit where n goes to infinity, a(n) will approach C, so C will by your eventual score.

Plugging this into the equation above, we get:
C - D m^(-n-1) = A C - A D m^(-n) + B m^n / (C m^n - D)
Take the limit of this equation where n goes to infinity:
C = A C + B/C
Solve for C:
C = sqrt( B / (1-A) )

Plug in the values for A and B:
C = sqrt( w b^2 / (1-w) )

Your ultimate score will then be: b sqrt( w / (1-w) )

[Doc_Brown]

Your ultimate score will then be: b sqrt( w / (1-w) )

So now you can analyze this function to pick an optimal strategy. If you play opponents with higher points, your win percentage will drop. Let's model this using an error function (which is related to an integral of a Gaussian, so it should be a decent model).

w = 0.5 + 0.5 Erf( (3000-b)/1750 )

This basically means that if your average opponent has a score of 3000, you'll win 50% of the time. Your win percentage goes up to 84% when his score is 1750 and drops to 21% when his score is 4000. You can plug this equation for win percentage into the above formula for your eventual score, take the derivative with respect to b, set the result to zero, and solve numerically. This gives you the optimal score of your opponents. I get a value of 1210 for your opponents score, which gives you a win percentage of 92.6% and an eventual score of 4280.

[Beckytheblondie]

Great Scott!


Somebody give this guy a cookie. No. Becky points. Becky points galore.

[ManBungalow]

[player]King_Herpes[/player] City Mogul Field Marshal +7060 2358 from 2446(96%)

Wow.

[AndyDufresne]

Your ultimate score will then be: b sqrt( w / (1-w) )

So now you can analyze this function to pick an optimal strategy. If you play opponents with higher points, your win percentage will drop. Let's model this using an error function (which is related to an integral of a Gaussian, so it should be a decent model).

w = 0.5 + 0.5 Erf( (3000-b)/1750 )

This basically means that if your average opponent has a score of 3000, you'll win 50% of the time. Your win percentage goes up to 84% when his score is 1750 and drops to 21% when his score is 4000. You can plug this equation for win percentage into the above formula for your eventual score, take the derivative with respect to b, set the result to zero, and solve numerically. This gives you the optimal score of your opponents. I get a value of 1210 for your opponents score, which gives you a win percentage of 92.6% and an eventual score of 4280.

So much math, but not too difficult. Thumbs up.


--Andy

[Gillipig]

If you really want to rise the ranks here's some advice. I've only managed to follow them for a short time myself. It is VERY boring!

1) Create your own games. Never join others.
2) Decide who you're going to play against. Short term it can be done by inviting others to join your games. Long term by foeing everyone that beats you.
3) Take ALL of your turns!
4) Don't create more games when you're playing badly or are frustrated. When you're on a roll though, keep the games coming.
5) Analyze your games. Why did you win/lose? Is it likely that you'll continue to increase in points while playing the games you're playing? Use maprank to see whether or not you should change the type of games you're playing.
6) Look at what type of games the players highest on the scoreboard play. And try to model your own play after them.
7) Forget about fun altogether. You should play as if your life depended on it!

[Gen.LeeGettinhed]

Hey lil-pig, those estrogen treatments are really kicking in. My amendments to prior submission:

If you really want to rise the ranks here's some advice. I've only managed to follow them for a short time myself. It is VERY boring!
1) Create your own games. Never join others. CREATING IS FASTER, BUT "NEVER" JOIN OTHERS? DEPENDS ON MAP AND SETTINGS. NEVER SAY NEVER.
2) Decide who you're going to play against. Short term it can be done by inviting others to join your games. Long term by foeing everyone that beats you. #1 IS A HUGE POINT. PLAY PEOPLE YOU CAN BEAT; NO NEED TO FOE PEOPLE UNLESS YOU SET UP PUBLIC GAMES AND DON'T WANT TO GET BEATEN BY MUCH BETTER PLAYERS
3) Take ALL of your turns! TRUE. ALMOST NEVER MISS A TURN.
4) Don't create more games when you're playing badly or are frustrated. When you're on a roll though, keep the games coming. VERY TRUE.
5) Analyze your games. Why did you win/lose? Is it likely that you'll continue to increase in points while playing the games you're playing? Use maprank to see whether or not you should change the type of games you're playing. VERY TRUE. DO WHATEVER YOU CAN TO MINIMIZE LOSSES.
6) Look at what type of games the players highest on the scoreboard play. And try to model your own play after them. BUT BE CAREFUL OF MODELING AFTER GLG, HE'S GOT A BAD REP
7) Forget about fun altogether. You should play as if your life depended on it! DISAGREE WITH BOTH.

8 ) DON'T LOSE.
9) PLAY TEAM GAMES WITH GOOD TEAMMATES -- BUT DON'T PLAY GAMES YOU HAVE A HIGH PROBABILITY OF LOSING AT
10) DEVELOP THICK SKIN FOR HAVING THE INTELLIGENCE AND PATIENCE TO DEVELOP A GOOD SYSTEM -- EVEN IF IT'S ALL WITHIN THE RULES. PEOPLE WILL DETRACT FROM YOU.

[lord voldemort]

Learn the ins and outs of how to farm against low ranks. Search for any and all technicalities.

[Beckytheblondie]

Learn the ins and outs of how to farm against low ranks. Search for any and all technicalities.

Ok, sure, but there can't be a mathematical constant for that, can there be?

[Robinette]

This is a universally accepted formula...

[AslanTheKing]

i am not following my own advise, so here it is

don't play 1 vs 1 games
don't play escalating games,
if u have 0 - 1200 points, play only terminator with 8 guys until u get to 1900- then stop playing terminator
don't attack higher ranked guys in the first 3 rounds

[ljex]

Mathematician help sought.

Seeking to solve: Asymptotic point maximum for a given player given the constants of win percentage (on a map/settings), points won and lost, and average opposing player score.
Goal: To maximize point collection to reach asymptotic peak.

Example: Beckytheblondie

Starting Points (BP): 3014
Opponent Average Points (OP): 1750 (Speculation)
Points Won (PW): (OP/BP)*20 = 9.87
Points Lost (PL): (BP/OP)*20 = 5.16
Win Percentage on specific map or settings (W%): .85
Points Gained (PG): (PW)*W% - (PL)*(1-W%) = 9.87-5.16 = 4.7
New Becky Points Set: BP1 = BP+PG = 3018.7
New PW (PW1): 9.86
New PL (PL1): 5.17
.....
solve for {B1...Bn}
Asymptote = 4166

But how did I get to that value? I literally just copied and pasted the formula over 11,000 times to find when PW=PL

Can a formula like this be used to calculate what a players maximum point total could be given constraints of only W% and OP?

Can I gain more points by playing stronger players and decreasing my W% or by playing weaker players and increasing my W%?

Can I gain more points solely by finding a map that I can win a percentage more of the time? Is that all that is needed?

Thoughts? Additions?

a while ago i made an excel spreadsheet that calculated a players maxium score given the parameters of win percent and average opponent. It could also factor in team games if that was the game type someone was best at. The problem with such a system is that as you get a higher score, more and more better players will join your games with the increased points they stand to win.