I was curious about how likely it would be, in general, to get to legend after a reasonable number of games after hitting level 5, assuming different base win rates. I also had some other goals like getting a qualitative sense of how streaky truly random games would be. (I don't go into that in this post, though.)
I ran across this Reddit thread, which had some good information (before the rank 5 floor was implemented) and there are links in there to more people who did the same thing. However, certain questions weren't really answered well. ("If I play 500 games after I get to rank 5, how often will I fail?")
So I ran my own simulation. For a number of likelihoods to win, it conducts 100,000 "seasons" starting at rank 5, 1 star, with a floor at rank 5, 0 stars, and calculates a random series of 500 game results assuming that likelihood to win. Assuming a fast deck which averages 6-minute games, 500 games would be about 50 hours of play after hitting rank 5.
If the player achieves a win while at rank 1, 5 stars, the season is marked as having "achieved Legend." At each likelihood to win, it outputs the number of those 100,000 test seasons in which its random sequences of games resulted in reaching Legend, along with the average number of games played. (The simulation assumes that one stops at 500 games if one does not reach Legend.)
Percentages vary from run to run by about a tenth of a percent. These are results from a single run.
Likelihood to Win
Made Legend within 500 games
Avg. Games Played
45%
3.73%
493
46%
7.21%
486
47%
13.01%
475
48%
21.31%
458
49%
33.26%
433
50%
47.28%
401
51%
61.94%
362
52%
75.09%
322
53%
85.89%
281
54%
92.90%
243
55%
97.01%
211
56%
98.88%
184
57%
99.65%
162
58%
99.92%
145
59%
99.99%
131
60%
100.00%
119
A couple interesting things jumped out at me about these results:
Having a likelihood to win slightly below 50% may yet get one to Legend a decent percentage of the time.
Having an excellent likelihood of winning of 54-55% (comparable to the best decks in ranks 5-L) still leaves a 5-10% chance of NOT making Legend in 500 games.
Percentage chances of reaching legend varied by 1-2% from run to run.
So it still takes about 11 hours at a 60% winrate ... never realized how far away I was actually away from reaching legend when I hit rank 3 last season. Felt so close, since it was my first time being rank 3. I guess I sink about 30-40h per month into this game. This includes all ranks, questing and creating decks. So i should dedicate an entire vacation to reach legend ... probably not gonna do that ... :/
thx for enlightenment. I'll be happy with rank 5 in future seasons.
By the way mentioned 54-55% wr is not 'excellent', imho it's pretty mediocre or below average. Excellent WR is 65+, good one is 60.
In order to not have 1-2% variance in results consider increasing test runs count to 1-10kk.
What is your problem?
The point, as he very clearly stated, was to see how many games you must play to reach Legend with a given win rate. If you're not interested, why did you click?
I'm pretty sure no one cares that your definition of "excellent" is different from his. I sure don't. But I will say that 55% is definitely not "below average." Mathematically speaking, that's about the most ignorant statement you can make.
Rollback Post to RevisionRollBack
"Why, you never expected justice from a company, did you? They have neither a soul to lose nor a body to kick." -- Lady Saba Holland
By the way mentioned 54-55% wr is not 'excellent', imho it's pretty mediocre or below average. Excellent WR is 65+, good one is 60.
In order to not have 1-2% variance in results consider increasing test runs count to 1-10kk.
What is your problem?
The point, as he very clearly stated, was to see how many games you must play to reach Legend with a given win rate. If you're not interested, why did you click?
I'm pretty sure no one cares that your definition of "excellent" is different from his. I sure don't. But I will say that 55% is definitely not "below average." Mathematically speaking, that's about the most ignorant statement you can make.
1. No problem, just curious. For me such simulations seem like waste of time, so may be I don't understand something.
2. Sometimes I click some random links. Sorry.
3a. But it's simply math! With wr 55% it's borderline possible to reach Legend with reasonable amount of games. Consider Rank 5 as half way to Legend, and OP talks about 211 games from R5, it is 400+ games per month. You should be play HS professionally to spend so much time on it.
3b. If you want to know 'average' winrate on R1-R5 around Legend players, just make poll. I'm pretty sure 55% is lower border, not average.
intresting,but how can you hit legend with a negative winrate?
Lose 10,000 games at Rank 20, then go on a win streak to Legend.
Obviously that's a ridiculous scenario though. It's impossible to get from Rank 5 to Legend with a negative win rate. Anyone who couldn't get a positive win rate before Rank 5 is very unlikely to suddenly improve after Rank 5.
intresting,but how can you hit legend with a negative winrate?
Lose 10,000 games at Rank 20, then go on a win streak to Legend.
Obviously that's a ridiculous scenario though. It's impossible to get from Rank 5 to Legend with a negative win rate. Anyone who couldn't get a positive win rate before Rank 5 is very unlikely to suddenly improve after Rank 5.
Well say you lose 30 games in a row at r5 and then win 26 games et voila you are @ legend with wr<50%.
P.S. negative winrate is nonsense.
Rollback Post to RevisionRollBack
This disclaimer Will cleanse any sense of innuendo or sarcasm From the comments that might actually make you think And will also insult your intelligence at the same time. So, if it sounds sarcastic, don't take it seriously. If it sounds dangerous, Do not try this at home or at all. And if it offends you, just don't read it.
By the way mentioned 54-55% wr is not 'excellent', imho it's pretty mediocre or below average. Excellent WR is 65+, good one is 60.
In order to not have 1-2% variance in results consider increasing test runs count to 1-10kk.
Regarding what is a "good" win rate: Take a look at the statistics by level on hsreplay.net (which requires a premium account). Win rates in the 60+ range for specific deck lists are reasonably common below level 10, but between level 5 and legend, average win rates per deck list (across all players playing that deck) of around 54-55% are mostly as high as they get, with some outliers getting up to 59%, and these deck lists have only one or a couple people playing them in their data set (as indicated by the fact that they record low numbers of games, like 1000.)
Vicious Syndicate average win rates per deck archetype are generally under 52%, although these are aggregate numbers that may include people playing relatively poorly.
I agree with you that a handful of players sustain win rates that are much higher. These often probably result from normal variation -- in a population of thousands, some people will have high win rates. In these types of simulations, some game series result in those kinds of win rates even for players/decks who would revert to a less effective mean. The percentages listed in my post, on the other hand, are the inherent win rate for the player/deck, the mean to which the result reverts over an infinite number of games.
I also agree in principle that some decks with a higher skill cap might allow a player to sustain much higher inherent win rates essentially forever. Hearthstone's ladder system offers no way to tell the difference between this and someone who's just gotten lucky.
Why do the simulation? It provides a window into how much statistical variation affects one's season result. Actually achieving legend within 500 games requires a measured win rate of almost 53%. One in 1000 people who get their game to the point that they have an actual win rate of 59% would fail at this in a season by random chance. Meanwhile, 1/3 of those who have a 49% likelihood of winning each game get lucky enough to achieve it in 500 games.
I personally undertook this for a slightly different reason: I wanted to generate random streaks of game results at certain percentages to see how streaky they looked to me. I'd had the sense that my own game results were much more streaky than a random result would predict, and rather than jump to the conclusion that the matchmaking system were rigged (which a lot of people do) I figured looking at known-random results would be an interesting exercise.
The short answer is that random results with a somewhat better than 50% win rate are very streaky and it's quite common to make round trips to rank 5, zero stars, on the way to legend. So, maybe the best response to a losing streak is to just shut up and keep playing, unless one's play has glaring weaknesses that can be fixed.
intresting,but how can you hit legend with a negative winrate?
Your actual win rate must be better than 50%, but that's not the same as the likelihood of winning each game. Essentially, you do so by being sufficiently lucky over a long enough period of time that your wins exceed your losses by 25 games, not counting losses that occur at the lowest rank.
3b. If you want to know 'average' winrate on R1-R5 around Legend players, just make poll. I'm pretty sure 55% is lower border, not average.
It is simply math. Some matters are really difficult to determine analytically, though, which is where simulations like this can be helpful. One of those areas of difficulty is determining analytically the likelihood of winning streaks. There are some academic papers out there on trying to predict analytically the likelihood of long streaks of coin flips, and it turns out to be a somewhat tricky problem. Simulating is really easy.
I'm not really interested in what Legend players have to say about their own win rates from rank 5 to rank 1. Their actual win rate is strictly determined by how many games it took them to get there, but unless someone has repeated consistent performance season after season, it's impossible to distinguish getting lucky from skill. It's especially difficult with pros who can bang out a thousand games to get to legend within a week, no problem. (Also, I'm quite certain that in an anonymous online poll, people have a tendency to self-report higher win rates than they actually experience.)
Again, looking at the hsreplay.net data is really illuminating. There are plenty of deck lists played by only a few people, with game counts in the range of 1000 over a few days. You would expect to see some true outliers if it were possible to sustain 60%+ win rates over a very long period at rank 5 and up, but the very best deck lists are slightly below that, and the more games are recorded for a given deck list, the closer to 50% the averages get. Also, many of these "outlier" deck lists are highly inconsistent from day to day in their win rate, which adds to the likelihood that they got there as a matter of luck rather than being inherently really strong or being played by really strong players.
Regarding what is a "good" win rate: Take a look at the statistics by level on hsreplay.com (which requires a premium account). Win rates in the 60+ range for specific deck lists are reasonably common below level 10, but between level 5 and legend, average win rates per deck list (across all players playing that deck) of around 54-55% are mostly as high as they get, with some outliers getting up to 59%, and these deck lists have only one or a couple people playing them in their data set (as indicated by the fact that they record low numbers of games, like 1000.)
Vicious Syndicate average win rates per deck archetype are generally under 52%, although these are aggregate numbers that may include people playing relatively poorly.
I agree with you that a handful of players sustain win rates that are much higher. These often probably result from normal variation -- in a population of thousands, some people will have high win rates. In these types of simulations, some game series result in those kinds of win rates even for players/decks who would revert to a less effective mean. The percentages listed in my post, on the other hand, are the inherent win rate for the player/deck, the mean to which the result reverts over an infinite number of games.
I also agree in principle that some decks with a higher skill cap might allow a player to sustain much higher inherent win rates essentially forever. Hearthstone's ladder system offers no way to tell the difference between this and someone who's just gotten lucky.
Why do the simulation? It provides a window into how much statistical variation affects one's season result. Actually achieving legend within 500 games requires a measured win rate of almost 53%. One in 1000 people who get their game to the point that they have an actual win rate of 59% would fail at this in a season by random chance. Meanwhile, 1/3 of those who have a 49% likelihood of winning each game get lucky enough to achieve it in 500 games.
I personally undertook this for a slightly different reason: I wanted to generate random streaks of game results at certain percentages to see how streaky they looked to me. I'd had the sense that my own game results were much more streaky than a random result would predict, and rather than jump to the conclusion that the matchmaking system were rigged (which a lot of people do) I figured looking at known-random results would be an interesting exercise.
The short answer is that random results with a somewhat better than 50% win rate are very streaky and it's quite common to make round trips to rank 5, zero stars, on the way to legend. So, maybe the best response to a losing streak is to just shut up and keep playing, unless one's play has glaring weaknesses that can be fixed.
Statistics is a lie. We are talking about players who actually reachedLegend, not who play between R1 and R5. (Btw if you be really able to find this winrate distribution (of players who did it to Legend), it would be super interesting, and we'll see what is 'good/bad/excellent winrate' in reality)
Deck aggregate winrate means nothing in terms of players winrate, because with same deck some players go up and some go down, it's only a measure of deck quality in current meta.
Because how many people do really play 1000 games in the season? (I remind you that R1-R5 is a only half way to Legend)
So in reality by my own experience 55% is a lowest practically achievable win rate to reach Legend, it will took 300-400 games in the season, and it's a lot imo.
Even if you find your own result heavily different with your simulation prediction - it still means nothing, because in simulation you're ignoring psychological factor, tilting and so on.
It is simply math. Some matters are really difficult to determine analytically, though, which is where simulations like this can be helpful. One of those areas of difficulty is determining analytically the likelihood of winning streaks. There are some academic papers out there on trying to predict analytically the likelihood of long streaks of coin flips, and it turns out to be a somewhat tricky problem. Simulating is really easy.
I'm not really interested in what Legend players have to say about their own win rates from rank 5 to rank 1. Their actual win rate is strictly determined by how many games it took them to get there, but unless someone has repeated consistent performance season after season, it's impossible to distinguish getting lucky from skill. It's especially difficult with pros who can bang out a thousand games to get to legend within a week, no problem. (Also, I'm quite certain that in an anonymous online poll, people have a tendency to self-report higher win rates than they actually experience.)
Again, looking at the hsreplay.com data is really illuminating. There are plenty of deck lists played by only a few people, with game counts in the range of 1000 over a few days. You would expect to see some true outliers if it were possible to sustain 60%+ win rates over a very long period at rank 5 and up, but the very best deck lists are slightly below that, and the more games are recorded for a given deck list, the closer to 50% the averages get. Also, many of these "outlier" deck lists are highly inconsistent from day to day in their win rate, which adds to the likelihood that they got there as a matter of luck rather than being inherently really strong or being played by really strong players.
Answered above.
+
The more popular deck is then closer its statistical wr to 50%. Because it's how the meta works.
So in reality by my own experience 55% is a lowest practically achievable win rate to reach Legend, it will took 300-400 games in the season, and it's a lot imo.
Even if you find your own result heavily different with your simulation prediction - it still means nothing, because in simulation you're ignoring psychological factor, tilting and so on.
At a 55% likelihood to win (not win rate, but likelihood to win) the average person will achieve Legend in 200-250 games from rank 5.
And yes, I am ignoring all the psychological factors. My reason for doing this was not to suggest that it's a realistic model for how people's runs go, but to see what the results look like if one has a strict likelihood to win and a purely random result within that likelihood. Essentially, I wanted to see what the picture looked like setting all those nonrandom human factors aside. Turns out that the results and trip through the ladder looks a lot like what real people report -- lots of streaky moves up and down, strings of losses that go from rank 3 to rank 5 and back again, etc.
That said, there's not a lot of evidence that very many real players in practice sustain a very high win rate (over 55%) over thousands of games. I'm not saying it's not possible, but it seems to be pretty rare.
"The more popular deck is then closer its statistical wr to 50%. Because it's how the meta works."
Sure, absolutely. What I'm saying is that I'd expect to see outlying, very uncommon decks with crazy high win rates if it were possible to sustain such win rates. Instead, even the outlying decks don't have exceptional results above rank 5.
That said, there's not a lot of evidence that very many real players in practice sustain a very high win rate (over 55%) over thousands of games. I'm not saying it's not possible, but it seems to be pretty rare.
And there is not a lot of counterevidence as well.
I opened my own stats for all time I play ranked, only selection from R1-R5, ~1400 games. And not in all of these seasons I really climbed to Legend. But it's 57% and I consider myself as pretty average player with plenty of misplays and so on. With Shaman and Warrior it's even 59%. With Warlock it's 55% and it was really tough to get to Legend with that deck. That's why I consider 55% as mediocre/bad wr in Legend run. It's doable, but it's not really a lot of fun. So when you say that very high win rate is 55+%... I don't think so. A lot of pro players have consistent 70+% win rate between Rank 1 and 5, so for me it's 'very high'. 65+ is high. 60+ is good. 57 is average. 55 is mediocre/ lower border. It's definitely possible to do it with 53 or even less, but I think it's seldom happens.
I'd be interested to know your numbers for the last week or so. Win rates have notably tightened up since the start of this season. I'm looking only at statistics for the last week for ranks 1-5 in my statements above.
I'd be interested to know your numbers for the last week or so. Win rates have notably tightened up since the start of this season. I'm looking only at statistics for the last week for ranks 1-5 in my statements above.
I think these data don't change over years, they are meta-independent.
If you want statistics for last week... I don't have it because playing pretty casually atm at low ranks. And even if I have it, statistics matters only with selection of thousands of games.
Sure, I was just expressing curiosity about how you'd been doing in the last week assuming you were playing a bunch, not suggesting it was particularly statistically significant.
I think these data don't change over years, they are meta-independent.
I assume you mean for you personally, since it's well-documented that aggregate win rate differences among deck archetypes have tightened up a lot with this expansion.
I assume you mean for you personally, since it's well-documented that aggregate win rate differences among deck archetypes have tightened up a lot with this expansion.
Players win rates =/= decks win rates.
Especially when you talk about whole HS population deck win rates mean nothing. It make sense only with selection of Top 500-1000 Legend games.
Because one player could have 65% win rate at Legend rank.
And another player could have 35% with same deck at rank 20. And another 1000 players with same deck on same rank 20 with same result. And you'll see the deck has 45% win rate by statistics.
I was curious about how likely it would be, in general, to get to legend after a reasonable number of games after hitting level 5, assuming different base win rates. I also had some other goals like getting a qualitative sense of how streaky truly random games would be. (I don't go into that in this post, though.)
I ran across this Reddit thread, which had some good information (before the rank 5 floor was implemented) and there are links in there to more people who did the same thing. However, certain questions weren't really answered well. ("If I play 500 games after I get to rank 5, how often will I fail?")
So I ran my own simulation. For a number of likelihoods to win, it conducts 100,000 "seasons" starting at rank 5, 1 star, with a floor at rank 5, 0 stars, and calculates a random series of 500 game results assuming that likelihood to win. Assuming a fast deck which averages 6-minute games, 500 games would be about 50 hours of play after hitting rank 5.
If the player achieves a win while at rank 1, 5 stars, the season is marked as having "achieved Legend." At each likelihood to win, it outputs the number of those 100,000 test seasons in which its random sequences of games resulted in reaching Legend, along with the average number of games played. (The simulation assumes that one stops at 500 games if one does not reach Legend.)
Percentages vary from run to run by about a tenth of a percent. These are results from a single run.
A couple interesting things jumped out at me about these results:
Here's the Python code for the simulation, for anyone who cares. Please don't bother commenting on naming or style, this was quick-and-dirty.
thanks for an awesome guide!
So it still takes about 11 hours at a 60% winrate ... never realized how far away I was actually away from reaching legend when I hit rank 3 last season. Felt so close, since it was my first time being rank 3. I guess I sink about 30-40h per month into this game. This includes all ranks, questing and creating decks. So i should dedicate an entire vacation to reach legend ... probably not gonna do that ... :/
thx for enlightenment. I'll be happy with rank 5 in future seasons.
What's the point of this simulation?
By the way mentioned 54-55% wr is not 'excellent', imho it's pretty mediocre or below average. Excellent WR is 65+, good one is 60.
In order to not have 1-2% variance in results consider increasing test runs count to 1-10kk.
Hall of Fame (ignore list): aleathas, Baylith, cendol, DiamondDM13, Dominieq, doomr, glitterprincess, hamtarofr, Heck, Jwigg33, Kaladin, Krewger, Legend_Entomber, libertyprime, Maukiepaukie, PandarenHero, randjob, s2mikey, SchruteBucks, The_Giratina, TheWamts, ticandtac, tictactucroc, tsudecimo, WaffleMonstr
"Why, you never expected justice from a company, did you? They have neither a soul to lose nor a body to kick." -- Lady Saba Holland
Hall of Fame (ignore list): aleathas, Baylith, cendol, DiamondDM13, Dominieq, doomr, glitterprincess, hamtarofr, Heck, Jwigg33, Kaladin, Krewger, Legend_Entomber, libertyprime, Maukiepaukie, PandarenHero, randjob, s2mikey, SchruteBucks, The_Giratina, TheWamts, ticandtac, tictactucroc, tsudecimo, WaffleMonstr
This disclaimer
Will cleanse any sense of innuendo or sarcasm
From the comments that might actually make you think
And will also insult your intelligence at the same time.
So, if it sounds sarcastic, don't take it seriously.
If it sounds dangerous,
Do not try this at home or at all.
And if it offends you, just don't read it.
It is simply math. Some matters are really difficult to determine analytically, though, which is where simulations like this can be helpful. One of those areas of difficulty is determining analytically the likelihood of winning streaks. There are some academic papers out there on trying to predict analytically the likelihood of long streaks of coin flips, and it turns out to be a somewhat tricky problem. Simulating is really easy.
I'm not really interested in what Legend players have to say about their own win rates from rank 5 to rank 1. Their actual win rate is strictly determined by how many games it took them to get there, but unless someone has repeated consistent performance season after season, it's impossible to distinguish getting lucky from skill. It's especially difficult with pros who can bang out a thousand games to get to legend within a week, no problem. (Also, I'm quite certain that in an anonymous online poll, people have a tendency to self-report higher win rates than they actually experience.)
Again, looking at the hsreplay.net data is really illuminating. There are plenty of deck lists played by only a few people, with game counts in the range of 1000 over a few days. You would expect to see some true outliers if it were possible to sustain 60%+ win rates over a very long period at rank 5 and up, but the very best deck lists are slightly below that, and the more games are recorded for a given deck list, the closer to 50% the averages get. Also, many of these "outlier" deck lists are highly inconsistent from day to day in their win rate, which adds to the likelihood that they got there as a matter of luck rather than being inherently really strong or being played by really strong players.
Hall of Fame (ignore list): aleathas, Baylith, cendol, DiamondDM13, Dominieq, doomr, glitterprincess, hamtarofr, Heck, Jwigg33, Kaladin, Krewger, Legend_Entomber, libertyprime, Maukiepaukie, PandarenHero, randjob, s2mikey, SchruteBucks, The_Giratina, TheWamts, ticandtac, tictactucroc, tsudecimo, WaffleMonstr
Hall of Fame (ignore list): aleathas, Baylith, cendol, DiamondDM13, Dominieq, doomr, glitterprincess, hamtarofr, Heck, Jwigg33, Kaladin, Krewger, Legend_Entomber, libertyprime, Maukiepaukie, PandarenHero, randjob, s2mikey, SchruteBucks, The_Giratina, TheWamts, ticandtac, tictactucroc, tsudecimo, WaffleMonstr
"The more popular deck is then closer its statistical wr to 50%. Because it's how the meta works."
Sure, absolutely. What I'm saying is that I'd expect to see outlying, very uncommon decks with crazy high win rates if it were possible to sustain such win rates. Instead, even the outlying decks don't have exceptional results above rank 5.
Hall of Fame (ignore list): aleathas, Baylith, cendol, DiamondDM13, Dominieq, doomr, glitterprincess, hamtarofr, Heck, Jwigg33, Kaladin, Krewger, Legend_Entomber, libertyprime, Maukiepaukie, PandarenHero, randjob, s2mikey, SchruteBucks, The_Giratina, TheWamts, ticandtac, tictactucroc, tsudecimo, WaffleMonstr
I'd be interested to know your numbers for the last week or so. Win rates have notably tightened up since the start of this season. I'm looking only at statistics for the last week for ranks 1-5 in my statements above.
Hall of Fame (ignore list): aleathas, Baylith, cendol, DiamondDM13, Dominieq, doomr, glitterprincess, hamtarofr, Heck, Jwigg33, Kaladin, Krewger, Legend_Entomber, libertyprime, Maukiepaukie, PandarenHero, randjob, s2mikey, SchruteBucks, The_Giratina, TheWamts, ticandtac, tictactucroc, tsudecimo, WaffleMonstr
Sure, I was just expressing curiosity about how you'd been doing in the last week assuming you were playing a bunch, not suggesting it was particularly statistically significant.
I assume you mean for you personally, since it's well-documented that aggregate win rate differences among deck archetypes have tightened up a lot with this expansion.
Hall of Fame (ignore list): aleathas, Baylith, cendol, DiamondDM13, Dominieq, doomr, glitterprincess, hamtarofr, Heck, Jwigg33, Kaladin, Krewger, Legend_Entomber, libertyprime, Maukiepaukie, PandarenHero, randjob, s2mikey, SchruteBucks, The_Giratina, TheWamts, ticandtac, tictactucroc, tsudecimo, WaffleMonstr