It's really funny how well aligned your regression is aligned with the dataset - do you have the equation / standard dev (you can get these from Excel - or send me the datapoints and I'll look at it).
I think one parameter that'd be interesting to look at is the standard deviation on MMRs as well (very relevant at your level). E.g. if your team has the same MMR than theirs (let's say 5000 average) but yours has 5 5000 players and theirs has 2 4ks, 1 6k, etc then you'd expect an adjustment in winrate expectancy even if the team MMRs are the same.
Very good piece of analysis nonetheless.
[x] 5,6k rank brag
[ ] actual math
cba to check but did u even use basic stuff like =correl for actual proper math?
Wow I have seen this on first page but didn't care about it. But if it's made by you pretty sure it's something good. Gonna read now.
basically i got a graph which tells you your chances of winning if your real mmr is different from your current (e.g. smurf, boosting etc)
according to this i should be winning at least 70-75% of my matches despite having someone stealing my bottle, intentionally putting branches in my inventory to take my aegis, 1x9 lineups etc etc now all of this would be true if we're talking about the time before ti4 compendiums appeared, now you can't compare swiftending's smurf to today's 5k+ bracket. it's illogically as fuck because of the high amount of 3k mmr players sitting on high mmr accounts, especially in EU or US east
newest to oldest, i dont think i've encountered bottle stealers or item stealers recently (mirana from my latest match kept sending the courier back to put my items in stash since minute 1)
http://www.dotabuff.com/matches/832254730
http://www.dotabuff.com/matches/832225390
http://www.dotabuff.com/matches/832203759
http://www.dotabuff.com/matches/832168237
http://www.dotabuff.com/matches/832140689
http://www.dotabuff.com/matches/830585786
http://www.dotabuff.com/matches/830559349
http://www.dotabuff.com/matches/830497366
http://www.dotabuff.com/matches/830448561
http://www.dotabuff.com/matches/830403401
i'd enable dotabuff on that smurf but i abandon a lot and kda is probably pretty low due to my hero being sent out to die 100 times :) nothing too much spectacular to see
BUT YEAH im not denying your point, just saiyan with the ti4 compendiums, it's invalid ~_~
"basically i got a graph which tells you your chances of winning if your real mmr is different from your current (e.g. smurf, boosting etc)"
u cant do such things since it isnt a solo in game.
9other ppl have variables too.
they could all be smurfing, they could have a bad day and make you lose, they could ruin the game on purpose, you could fail cuz ur cat walk on fuckin keyboard ETC.
anyway there is thousands of variables, im bad at math but i could count at least ten billions other variables without even trying.
cqfd all u did is complete bullshit imo.
Learn basic maths, before spreading bullshit on the work of other, thx.
I still don't get how people cann't even understand/use the most basic probability... and then spread bullshit, and pee on some serious work of analyzing.
btw there are quite a few account buying retards in NA and i'm sure there are more in EU like wave said (just take a look at epicnpc, vast majority of people offering to do boosting/selling are from EU due to the plurality of the world's dota players playing on EU West/Russki servers, the greater minority from NA) so i'd be interested if someone did the same thing for different servers and see if there's any statistical anomaly due to these people ruining and skewing games due to being almost auto-loss factors
i do think ur work is quite accurate since i won like 75% of my games from 4300-4700 about 3 weeks ago and i had something like 60% on the climb to 5000 (which is my "true" rating since it's on my main)
*once u get to values close to 50%, it's not very accurate anymore. what's the difference between winning 55% and 60% of your games? If you play 100 games that's 10 net wins worth of difference (250 MMR) yet the amount of effort needed to play 100 games and then track the differences in outcome is pretty huge. someone with 5300 mmr could easily win 55 or 60 out of 100 games at 5000 MMR, so obviously taking into account this variance is important (Swiftending's own data confirms that)
i think SEA is quite fortunate in that pinoys can't afford to buy accounts :DDD (jokes aside, i haven't run into any account buyers in the 50 or so games i've played there across both accounts in solo ranked)
This is minor but I believe the numbers can be skewed depending on your starting and ending points (using my own experience):
So let's say I have 4300-4700 = 75% win rate (4500 average MMR), which is 175 team average difference. 175 x 5 (assuming I'm the only one with deflated rating on an account, which is probably not true a lot of the time) = 875 higher MMR
875 + 4500 = 5375 "actual rating" (I don't think I'm this high lol)
Then I have 4700-5000 (4850 average) = 60% win rate (4850), which is 70 team average difference. By the way, I'd also like to add that I was "stuck" at 50% for 1-2 days @ 4800, might just be shit luck or me picking suboptimal heroes but this shows how a huge sample size is critical
350 + 4850 = 5200 (this is more accurate than the last figure i'd say since i had trouble maintaining 5300 on that smurf but i stayed at 5200 for like 15-20 games, I'd have to play more games to find out if I drop to 50% at 5200 now that i'm 5000 on my main, but I'm not touching ranked solo for a while)
Now if I were to recalculate this using data from 4200 (lowest point I've ever reached) - 5000 (highest point I've ever reached without smurfing), which would provide the greatest sample size, I would likely end up somewhere around 5100 just because my win rate is much lower, but for a model this is quite accurate. I'm just saying how the person chooses ending and starting points can definitely affect the "true" MMR calculations and probably manage to delude himself in the process into thinking he's higher than he should be.
One last critical point: I'm sure if there's anything you've learned from me (besides the fact that I'm a huge asshole in pubs), it's that one should never underestimate the power of tilt in affecting your "true" MMR. So for someone like me you'd have to introduce a SHIT ton of variance because I could be playing like a 4.5k mmr retard after losing 2-3 games in a row.
@Zenoth:
Nice job!
@Once u cyka u never go blyat:
I'm assuming you're questioning the homoscedasticity/heteroscedasticity of the data?
@Zenoth:
"while I get two symmetrical lines around 25 as expected, I get fluctuations around the line."
There was a dev post in the past about how the total team MMR is adjusted based on team stacks.
For example, (5k+5k)+(4k+4k)+(4.5k) vs. (4.5k+4.5k)+(4.5k+4.5k)+(4.5k)
Both teams average 4.5k, but one team is considered to have a higher chance of winning.
That might explain the deviations from the norm.
Edit: The Reddit guys beat me to it:
http://de.dota2.com/2013/12/matchmaking-2/
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http://www.reddit.com/r/DotA2/comments/2dfjge/reverseengineering_the_effects_of_average_team/
sorry im tired and dont want to re-format the whole thing