as seen on Reddit Link with a 55% winrate it takes you 227 games from Rank 5 to Legend rank. I would like to know how to do that calculation, but for example starting from a higher rank/different amount of stars. I know above R5 you have winstreaks so I'll leave that calculation out, but for the higher ranks (since there are no winstreaks) it's easier to calculate. Anyone who is good at explaining the calculations in easy to understand language (since my native language is not English.) Thanks in advance for this (stupid) question.
No such thing as a stupid question. Hope this shows why it takes a while at 55% win rate:
You need to go through 5 ranks, 5 stars each, so let's say you need to acquire a total of 25 stars;
If you win one then lose one you played 2 games but achieved absolutely nothing;
At 55% win rate you will earn just ONE star at 5 wins to 4 losses (a total of 9 games);
That is ONE star per 9 games played and you need 25 of those, so 9 games x 25 = 225.
Note: the difference between 225 and 227 is because I used exact 55% win rate, whereas the actual figure is 55.55(5)% which makes up for that extra 2 wins required. Just used simple numbers for an easier demonstration.
But what about if you use a different %, how do I "insert" the different % in that figure ? :)
So, I actually decided to welcome the challenge and work it out. I am ashamed to admit that I have almost completely forgotten everything math-related that I learned in school, but then again that has been quite a while ago. Either way, after flexing some of those left-over brains I came down to this formula:
Games = -25 / (1 - 2 * Win Percentage)
Yes, that is a -25 (negative 25) at the start there.
So if you insert any given Win Percentage you should get a total number of games (wins and losses together) you'll need to make it to Legend from Rank 5. Keep in mind that for obvious reasons your Win Percentage has to be above 50% (otherwise there is simply no point, as there won't be any progress/climbing).
If you want to know how I got down to that formula - let me know and I'll post an explanation to the best of my ability.
Note: I'm sure some one can come up with a better/cleaner formula, but I have to go to sleep now and that's the best I could do for now! Just couldn't go to bed without solving the riddle, it really got to me :p
It's a bit of an approximation because your total number of games is lowered a bit if your last rank is done with a win streak. But it still does a pretty good job of showing the total game number.
It's probably more applicable to "grindy" fast decks (that are draw dependent and more likely to win-lose-win-lose) whereas longer control decks rely on your piloting skill (and some draw luck) to boost your win-rate, so even though the games are longer, you can hit legend at a comparative (if not faster) pace.
You also need to count ''extra'' stars from achieving a higher rank and dropping the next game. Your calculation is therefore, wrong.
Is that really an extra star? You have the same number of stars, but instead of "rank 4 and 5 stars" it counts "rank 3 and 0 stars". If you lose another game, you go down to rank 4-and-4, so no bonus...
The only bonus you get is if you enter rank 5 on a winstrak from rank 6.
You also need to count ''extra'' stars from achieving a higher rank and dropping the next game. Your calculation is therefore, wrong.
Is that really an extra star? You have the same number of stars, but instead of "rank 4 and 5 stars" it counts "rank 3 and 0 stars". If you lose another game, you go down to rank 4-and-4, so no bonus...
The only bonus you get is if you enter rank 5 on a winstrak from rank 6.
Nope its not , although rank 2 5 stars feels worse then rank 1 zero stars xD but It's the same,star-wise
I was thinking about it, and the reason this is confusing is that the rank-up is in fact delayed, like as if you needed to turn 21 to enter your 20s.
Rank 4- 5 stars should in have been the first step of rank 3. But again, it does create a little buffer not to lose the rank, and in lower ranks it does make sense.
You also need to count ''extra'' stars from achieving a higher rank and dropping the next game. Your calculation is therefore, wrong.
That doesn't make it wrong? The equation works off an assumption that a starting point to a climb is at Rank 5 - 1 star (since as you hop over to R5 you have that star available to you).
Also, keep in mind that the formula is just a model of reality that is there to indicate a volume of games and it works of math where we can't really integrate game mechanics and have to work with just numbers while using a generic and simple scenario.
However, if we do want to integrate more complex, real-life scenarios like the one you mentioned - then all we need to do is to just incorporate them into the formula!
The scenario that you describe only means that your own assumption needs to be incorporated, adjusting the formula accordingly (changing -25 to -26, and then it caters for your scenario).
Similarly, we can arrange the formula for a scenario where you you get to Rank 5 from Rank 6 - 5 stars while being on a Win Streak. That way you do actually start R5 with 2 stars. That scenario will mean that we need to change -25 to -24, as there's one less win required.
Edit: However, if there's someone with a cleaner/better/more accurate formula - please share! I told you at the start that to my great shame I forgot almost everything I used to know someday so there might be a better formula for this.
So if you need 25 stars and have a 55% win rate then it is:
X = 25/(0.55-0.45) = 250 games
The reason why the guy from reddit got 227 is probably this:
Most people's win rate will probably drop somewhat at higher ranks, so reality will probably be closer to using numbers from two different lines in the chart instead of the same line the entire time.
My formula assumes the win rate is your medium win rate from 5 to legend. Also the formula does not work properly on ranks lower than 5 because you can get extra stars from win streaks.
You also need to count ''extra'' stars from achieving a higher rank and dropping the next game. Your calculation is therefore, wrong.
Those are no "extra" stars. If you are rank 5 with 5 stars and win again, you will be rank 4 with 1 star, no extra star. If you have a 100% win rate from 5 to legend, you need to play 25 games.
Also if you are rank 4 with 0 stars and lose again, you lose the star from your previous rank and you are rank 5 with 4 stars, you don't save a star. So someone with rank 5 and 5 stars is in the same position as someone with rank 4 and 0 stars, it just means that one person climbed to that position and the other fell down to it.
Ah, that's so much nicer than the abomination I came up with! I knew there had to be a cleaner/better way to get around this.
If you don't mind sharing, could you illustrate how you got that formula down? I just really enjoyed solving the puzzle and would really like to see a different approach. If it's too long or too much effort and you can't be bothered - I perfectly understand.
Ah, that's so much nicer than the abomination I came up with! I knew there had to be a cleaner/better way to get around this.
If you don't mind sharing, could you illustrate how you got that formula down? I just really enjoyed solving the puzzle and would really like to see a different approach. If it's too long or too much effort and you can't be bothered - I perfectly understand.
No problem.
The logic is: you need 25 more wins than losses from rank 5 to legend. So these 25 more wins represent the difference between games won and lost. Lets assume a 55% win rate. That effectively means how of the 55% of wins, 45% will cancel out with the 45% of losses, and the rest 10% of your won games are those "pure" 25 extra wins and 25 is 10% of 250.
Note how "(all_games_you_win)/(games_played)" is just your win percentage and "(all_games_you_losse)/(games_played)" is just your loss percentage. So now we have:
Also i would like to point out that the guy from reddit did something wrong in his simulations because if his virtual player with 55% wins really played 227 games that means he won 126 games and lost 101. This is NOT a 55% win rate but rather a 55,5066% win rate. This shows how much just 0.5% more wins can make a big difference.
I assume he did not take into account how if you loose your first game or two you get down to rank 6 and now you need 26 or 27 stars. Otherwise his "below 50% win rate" players could never reach legend. Either that or his random generator is somehow faulty.
I assume he did not take into account how if you loose your first game or two you get down to rank 6 and now you need 26 or 27 stars. Otherwise his "below 50% win rate" players could never reach legend. Either that or his random generator is somehow faulty.
It doesn't matter if you first lose or not: all that matters is the win rate after X games in total.
Which is probably also why his 'below 50% win rate' player actually meant 'below 50% chance of winning'. Such a player can stil get lucky and get over 50% win rate. But you need by definition >50% win rate to level up.
Yes, some players will get lucky, but not 10 000 simulated players for every rank as mentioned in the reddit post.
However, if you set your star counter variable in a range from 0 to 25 for the simulations, then yes, the below 50% players will get legend eventually, all of them. And i assume he did exactly this because it also explains why every set of players actually reach legend in less games than expected. It would also be easier to program.
But if the number of necessary stars can go above 25, then if those players with under 50% start loosing they will just fall deeper and deeper and the number of games for some of them would be infinite. Also, this would drag the average down for those players way worse than the numbers indicate (I expect). For real players this does not really happen because your win rate rises when your rank falls, but he specifically mentions how the win rate in his model stays the same as players change rank.
Actually, never mind, he did explain how he addressed the issue, i'm sorry, i was wrong. :)
Note that the first count stops increasing as soon as they hit rank 5 for the first time. If they lose some following games and drop back to rank 6 or lower, those are still counted towards the second set.
I didn't carefully read the italic stuff. :(
edit: The difference in expected numbers could then very well be win streaks from when simulated players occasionally fall to lower ranks.
Hello,
as seen on Reddit Link with a 55% winrate it takes you 227 games from Rank 5 to Legend rank. I would like to know how to do that calculation, but for example starting from a higher rank/different amount of stars. I know above R5 you have winstreaks so I'll leave that calculation out, but for the higher ranks (since there are no winstreaks) it's easier to calculate.
Anyone who is good at explaining the calculations in easy to understand language (since my native language is not English.)
Thanks in advance for this (stupid) question.
Mhyr
No such thing as a stupid question. Hope this shows why it takes a while at 55% win rate:
Note: the difference between 225 and 227 is because I used exact 55% win rate, whereas the actual figure is 55.55(5)% which makes up for that extra 2 wins required. Just used simple numbers for an easier demonstration.
Hope that helps.
But what about if you use a different %, how do I "insert" the different % in that figure ? :)
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It's a bit of an approximation because your total number of games is lowered a bit if your last rank is done with a win streak. But it still does a pretty good job of showing the total game number.
It's probably more applicable to "grindy" fast decks (that are draw dependent and more likely to win-lose-win-lose) whereas longer control decks rely on your piloting skill (and some draw luck) to boost your win-rate, so even though the games are longer, you can hit legend at a comparative (if not faster) pace.
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Thanks for the formula ! So happy that the community is so helpful ^^.
You also need to count ''extra'' stars from achieving a higher rank and dropping the next game. Your calculation is therefore, wrong.
Used to be a proud Handlock player.
Legend 17 times.
Still flirting with the ladder from times to times with Renolock.
Is that really an extra star? You have the same number of stars, but instead of "rank 4 and 5 stars" it counts "rank 3 and 0 stars". If you lose another game, you go down to rank 4-and-4, so no bonus...
The only bonus you get is if you enter rank 5 on a winstrak from rank 6.
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number_of_games_needed = (number_of_stars_needed) / (win_rate - loss_rate)
So if you need 25 stars and have a 55% win rate then it is:
X = 25/(0.55-0.45) = 250 games
The reason why the guy from reddit got 227 is probably this:
My formula assumes the win rate is your medium win rate from 5 to legend. Also the formula does not work properly on ranks lower than 5 because you can get extra stars from win streaks.
edit:
Winrate-50=amount of stars you get per 50 games.
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I hope you get what i mean, sorry but English is my 3rd language. :)
Also i would like to point out that the guy from reddit did something wrong in his simulations because if his virtual player with 55% wins really played 227 games that means he won 126 games and lost 101. This is NOT a 55% win rate but rather a 55,5066% win rate. This shows how much just 0.5% more wins can make a big difference.
I assume he did not take into account how if you loose your first game or two you get down to rank 6 and now you need 26 or 27 stars. Otherwise his "below 50% win rate" players could never reach legend. Either that or his random generator is somehow faulty.
Yep, that's perfect! Thank you very much, that was quite interesting to follow the logic and thought process. And you did a good job explaining it.
But on another note, never thought I'd be having fun solving puzzles on a bloody Hearthstone forum haha.
Yes, some players will get lucky, but not 10 000 simulated players for every rank as mentioned in the reddit post.However, if you set your star counter variable in a range from 0 to 25 for the simulations, then yes, the below 50% players will get legend eventually, all of them. And i assume he did exactly this because it also explains why every set of players actually reach legend in less games than expected. It would also be easier to program.But if the number of necessary stars can go above 25, then if those players with under 50% start loosing they will just fall deeper and deeper and the number of games for some of them would be infinite. Also, this would drag the average down for those players way worse than the numbers indicate (I expect). For real players this does not really happen because your win rate rises when your rank falls, but he specifically mentions how the win rate in his model stays the same as players change rank.