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Soshi_Sone

Ranked Binomials

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I've run binomials about one time a year for ranked seasons, with some refinements along the way.  Here are my latest calculations and assumptions.

The basic calculations determine the chance of ranking out given a certain number of games and a given win rate percentage.  The calculations are from 10.0 to Rank 1.  So this is what it takes once you reach Rank 10.  My new twist for these calculations is the assumption that a player can top out on 1/7 of games that are lost.  That is, one out of every seven losses, a star is not lost.  With those assumptions, here are your odds, based on win rate and games played:

              //   .5    //     .55     //     .6      //

100      //   0.0   //     0.5     //    6.2     //

200      //   2.8   //   31.0    //     82.6   //

300      //  11.3  //   70.0    //    98.9   //

400      //  25.8  //   91.2    // 100.0   //

500      //  37.7  //   97.3    // 100.0   //

  

 

 

 

 

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I am pretty good with numbers and I am haveing a hard time with his.

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Neat to see the numbers down. Just from looking at shipcomrade.com I noticed this trend as well. I mean, it should be fairly obvious, the higher your WR, the lower the # of battles needed to rank out.

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So according to this...I'll NEVER rank out...:Smile_teethhappy:

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1 hour ago, Soshi_Sone said:

I've run binomials about one time a year for ranked seasons, with some refinements along the way.  Here are my latest calculations and assumptions.

The basic calculations determine the chance of ranking out given a certain number of games and a given win rate percentage.  The calculations are from 10.0 to Rank 1.  So this is what it takes once you reach Rank 10.  My new twist for these calculations is the assumption that a player can top out on 1/7 of games that are lost.  That is, one out of every seven losses, a star is not lost.  With those assumptions, here are your odds, based on win rate and games played:

              //   .5    //     .55     //     .6      //

100      //   0.0   //     0.5     //    6.2     //

200      //   2.8   //   31.0    //     82.6   //

300      //  11.3  //   70.0    //    98.9   //

400      //  25.8  //   91.2    // 100.0   //

500      //  37.7  //   97.3    // 100.0   //

Did you account for R10 being irrevocable? That gives another bonus especially to weaker players. 

Also, a 55% WR player at 6-10 will not have a 55% WR at 2-5, but I can understand why you’d want to simplify the analysis.

Another stat I like to advertise is the variance of a negative binomial, which is large.

v = rp * (1-p)^-2

For a 50% player, that means you’ll have a standard deviation* of sqrt(0.5 / 0.25) = sqrt(2) = 1.44 That is 6-14 wins for every 10 losses, or a common win rate anywhere from 10/16 to 10/24 which is 42-62% WR just from “luck”. It’s not even luck because that is the range of just one standard deviation*.

* the negative binomial is not a normal distribution and any talk of standard deviation is just to make the range calculation more understandable.

Edited by n00bot

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Head spinning flashback to college stats class ensues .  :cap_fainting:

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29 minutes ago, n00bot said:

Did you account for R10 being irrevocable? That gives another bonus especially to weaker players. 

I did not account for irrevocable at R10.  So yes, this would skew the percentages somewhat; one would tend to have slightly better chances that otherwise shown.

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TLDR there’s a ton of luck and even good players need lots of games to overcome the swings. So even though 400 games might be enough for your level of skill on average, don’t be surprised if it takes 600 or more. 

Edited by n00bot

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This helps me understand why rank 7 is likely my best achievable rank and I have a very low chance to get to rank 1 and have never gotten lower than 7 and have fallen back to 9 twice so far

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What was your methodology?  A good process would be a sort of montecarlo where successive 'players' (observations) are obtained by running up through the ranks with the rules and a winrate, applied randomly to each step.  Or something like that, anyways, to obtain the luck effect of timing of wins and losses and star saving, where eg some good runs of losses right after irrevocable can be followed by strings of victories to the next irrevocable and so forth.  A large number of runs would give a very real picture of how it will work for real people, and a range, where eg "90% of players with a 55% winrate will rank out between 260 and 380 games".     Of course the real operational picture includes another statement eg "Due to luck with the number of good and bad teams, a player of a real 55% skill at ranked will have a winrate in a 200 game sample of between 53 and 57".  Which is where the luck in team quality comes in.  So two soundbites......  Sounds like a lot of work not volunteering but perhaps this is the process or similar?  

Just curious, zen like calm in ranked requires both steady nerves and a good understanding of luck,  a montecarlo provides a pretty real look at it although missing changing winrate as progression as another poster pointed out.  A ranked player needs to get luck in perspective, learn how to stop assigning losses to bad luck and wins to skill, which leads to a lot of rank ranked negativity.  All that bad luck I am having!  And so on.    I dunno seems pretty hard to derive a soundbite to show what lucks actual effect is.    Especially when a significant portion of players believe you can be carried to rank one, it is after all, mostly luck.....

 

 

 

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9 hours ago, drunkenduncan said:

What was your methodology? 

The binomial equation...that's really all you need..  There are online calculators so just plug and go.  Well, you need to know what to put in the equation, so I'll tell you how I arrived at those numbers.  

You must win 40 more games than you lose in order to Rank out from R10.

So, if you play 100 games, and you win at least 70 (i.e., 70-30 = 40)...then you'll rank out.  So, given 100 events at the WR probability, what are the odds of achieving 70 (or more) out of 100?  That's exactly what the binomial equation will give you.

If you play 200 games, you must win at least 120 games (i.e., 120 - 80 = 40).  

300 games, you win 170 (i.e., 170 - 130 = 40)

And so on.

Now, for the save a star, we can adjust the numbers slightly.  Multiply the loss by 1/7 and split the different between win loss.  For example, for the 100 take 30 and divide by 7.  We'll round to 4.  That's four loses you don't need to make up, so instead of 40 more wins than loses you only need 36 more wins than loses.  Instead of 70/30 it become 68/32.  Given 100 events at the WR probability provided, what are the odds of achieving 68 out of 100.  This automatically accounts for topping out on 4 of the loses. 

Edited by Soshi_Sone

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11 minutes ago, Soshi_Sone said:

The binomial equation...that's really all you need..  There are online calculators so just plug and go.  Well, you need to know what to put in the equation, so I'll tell you how I arrived at those numbers.  

You must win 40 more games than you lose in order to Rank out from R10.

So, if you play 100 games, and you win at least 70 (i.e., 70-30 = 40)...then you'll rank out.  So, given 100 events at the WR probability, what are the odds of achieving 70 (or more) out of 100?  That's exactly what the binomial equation will give you.

If you play 200 games, you must win at least 120 games (i.e., 120 - 80 = 40).  

300 games, you win 170 (i.e., 170 - 130 = 40)

And so on.

Now, for the save a star, we can adjust the numbers slightly.  Multiply the loss by 1/7 and split the different between win loss.  For example, for the 100 take 30 and divide by 7.  We'll round to 4.  That's four loses you don't need to make up, so instead of 40 more wins than loses you only need 36 more wins than loses.  Instead of 70/30 it become 68/32.  Given 100 events at the WR probability provided, what are the odds of achieving 68 out of 100.  This automatically accounts for topping out on 4 of the loses. 

K i see.  Do you see how my approach would account for timing of wins losses, where the irrevocables are, and team luck (number of good vs bad teams over the sample of say 200)?  Lotta work though not suggesting.  Thks for the work it does provide a good baseline.

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