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Luck+Climbing ELO+Math

Uzbekiann·1/21/2020, 7:48:32 PM·7 votes·1,914 views

I oftentimes see people on the forums saying... "just play enough games... eventually the feeders will end up on the other team... or the afks will end up on the other team... that's just how statistics work..."

Well I'm here to tell you that that is NOT how statistics work. I will gladly explain it, but even better. Go take a quarter and flip it 100 times... then flip it 100 more times... then flip it 100 more times... Record each set. Sure, there is a 50% chance to flip heads and a 50% chance to flip tails... but I will go ahead and tell you there is roughly an 8% chance that you will flip 50 heads and 50 tails... Does that sound like a really really small chance, that's because it is... more likely the statistic will be skewed in one direction or the other. Mainly because this is something called an independent statistic... Meaning that flipping a tails has no influence on the result of the next flip.

It is a very small chance, but I promise if you do enough sets of 100 flips... You will EVENTUALLY end up with 100 tails/heads and 0 of the other. With that in mind... is it so hard to believe that players in league might be having a similar experience?? There are hundreds of thousands of players on league... the chances that a few of those players are getting the shit end of the stick EVERY GAME is actually quite likely... And vice versa... There are probably players in high plat/diamond who have no right being there, but have had the opposite end of that independent statistic, getting teams that carry them nearly every game. These results are skewed even further because of mmr... A string of bad luck can make any future good luck less impactful, and a string of good luck can save you from suffering the full consequence of a future string of bad luck.

One other common rebuttal for this is the "bronze to challenger series"... and yes... I realize that a player of THAT caliber will most likely climb the lower ranks very quickly regardless of the teammates that they get. That really doesn't prove anything. This is like a 260lb pro runningback going into a middle school football game... at that point, your teammates dont even matter.

Then there is the psychological effect of bad luck. Though this is a lot harder to measure, and therefore I'm just kind of adding this in as a touch of flavor for the conversation... but not as proof of anything. Often times in real life people who go through a series of bad luck, can tend to perform tasks worse afterwards... Tilt exists in the real world too. Let's say you are an investor, and the market takes a crash. Some investors might stick to what they know and not be swayed. But there will definitely be many investors who then take chances they wouldn't normally take to save the losses that they have accrued through poor luck. This concept also applies to gambling... many people will take a string of bad luck, and then make poor decisions to try to dig themselves out from that bad luck.

All in all there's not really a way to "fix" any of this. That's definitely not what I'm gunning for here... This is more just food for thought and topic for discussion. My best advice for you and for myself sometimes is to just take a break and remember that it is just a game. There are plenty of single player games out there that you can master and be proud of. But there will always be a touch of luck in multiplayer games. Just accept it and try to enjoy yourself... If you aren't having fun... don't play.

Edit: Re-reading this, I just want to clarify that I am in no way trying to take anything away from people who have worked very hard to climb to where they are. Around 30-40% of players will most likely have between 40%-60% luck... meaning feeders/afk's on both their team and opposite team relatively equally. Allowing player skill to be the deciding factor to a larger degree.

Edit 2: If your post clearly shows that you have less IQ than my teammates for the past week then I am not even going to try to converse with you. This post is not saying its impossible to climb. Learn to read or just don't comment... I'm not saying the game is ENTIRELY based on luck. But denying that randomized teammates adds a factor of luck is ignorant. Maybe you never got paired with a group of worthless classmates back in high school for a project... ya know... the people that would literally do the bare minimum and expect you to do all the work... and then remember when your grade was indicative of the final result? At least then you could complain about your classmates being worthless and possibly save your grade. I don't know how else to say this... If you can't comprehend it... don't reply. Also... my math was a little off so I corrected it, thanks to the person who pointed that out (an actual useful post)

29 Comments

DamSonWhUFndThis1/21/2020, 8:13:10 PM4 votes

I oftentimes see people on the forums saying... "just play enough games... eventually the feeders will end up on the other team... or the afks will end up on the other team... that's just how statistics work..."

I think we both agreed (I didn't read it after this) that this quote is BUNCH OF BULLSHIT, IT'S LIKE SAYING ONE DAY YOU WILL WIN THE LOTTERY IF YOU KEEP BUYING TICKET EVERYDAY

Kai Guy1/21/2020, 9:57:01 PM3 votes

This is more just food for thought and topic for discussion. My best advice for you and for myself sometimes is to just take a break and remember that it is just a game. There are plenty of single player games out there that you can master and be proud of. But there will always be a touch of luck in multiplayer games. Just accept it and try to enjoy yourself... If you aren't having fun... don't play.

This is solid advice. If the games feel like folks should not play it.

That said im confused how you got 2.5% for 50. We want to find the probability right? So 2^100 is the number of possible result combinations yes? So 1,267,650,600,228,229,401,496,703,205,376. combinations. The probabilitys will be off that.

So I used Binominal distribution for to find my probability With N=100 K=50 the P and Q are 0.5 each. The result was 0.07958923738717872. Converted into a whole percentage its 8%. So I am seeing over 300% higher odds then you. (using % here just to show how it can be a misleading, not many folks think the gap between 2.5 and 8 is all that high)

What formula did you use for the 2.5%? I don't understand where your getting that number.

Also the assumption of 50% is that your accurately placed. The argument players make is they are incorrectly placed but the system cant handle the human RNG impact.

Lets say your good enough to push the odds into your favor vs to the players around you up. Call it 60% advantage. Running that for 100 games? The odds to see 50% will actually drop. Your at about 1% odds to see that 50/50 split. Because your more likely to score higher then 50. The probability of you having 50 "heads" or higher would be 0.9832383134968385. So... 98% to see Results >= 50 with P 0.6 and Q 0.4

So far as the FEEDERS argument. You have to remove the player from the equation for team distribution as they are a consistent variable. So if a game has a game losingly bad feeder in it the odds break down to be 4/9 and 5/9 for what team they distribute into. So 0.44 and 0.56 when rounded. That's better odds then Many Vegas games and is a clear house advantage for a non feeder player.

The thing that confused the hell out of me is the obsessions with "streaks" starting at 3. Like WWLWW and WWWWL basically look the same with the assumption of equivalent variables. Have to make that assumption as in Elo ΔR is impacted by K and We variable not just (W) . Elo adjustment commonly expressed as the simplified Rn=Ro+K(W-We)

Rn is Rating after adjustment is ran. Ro is rating prior to adjustment. ΔR (Delta R) is Change in rating, positive or negative. Number of points between RN and RO. We is system expectations. Its built from Players Ratings and the expectations of scoring probability. K is best expressed as uncertainty, and serves to impact the Max # of points gained or lost.

FeedKaylePlease1/21/2020, 8:46:24 PM3 votes

Most sensible post I've seen in a while on these boards.

Eedat1/21/2020, 9:40:00 PM2 votes

You forgot that there are 4 randoms on your team and 5 on the other so it isn't 50/50.

So uh, RIP your entire thread

Skia Asteri1/21/2020, 8:56:11 PM1 votes

{quoted}

Go take a quarter and flip it 100 times... then flip it 100 more times... then flip it 100 more times... Record each set. Sure, there is a 50% chance to flip heads and a 50% chance to flip tails... but I will go ahead and tell you there is roughly a 2.5% chance that you will flip 50 heads and 50 tails... Does that sound like a really really small chance, that's because it is... more likely the statistic will be skewed in one direction or the other. Mainly because this is something called an independent statistic... Meaning that flipping a tails has no influence on the result of the next flip.

That is how it applies when the MMR system has an accurate measurement of your ability to win games. Even then, if LP/Rank has not caught up to your MMR you still go up by going about even. When MMR is close to LP/Rank, then climbing is about being good enough at winning that the "coin" representing your teams odds of winning being unfair by a statistically significant margin due to match making rating you too low. Which, after you reach the point where games are close to a fair coin flip in terms of your odds of winning, means you need to get better.

And yes, getting better does make a huge difference even without reaching Challenger levels of skill. Check the stats on my 3 most played champions in Season 8, where I started much below the MMR I should have been at due to barely playing ranked in Season 6 and not playing ranked at all in Season 7. That is 2 and a part soft MMR resets, and I had been actively playing lots of normal matches during that time. The stats reflect a climb from Bronze 3/4 MMR for flex and soloq at the start of placement to ending Silver 1 soloq and Gold 4 flex with Gold 4/5 MMR for both.

Kuthillick1/21/2020, 8:43:17 PM1 votes

So your point is... statistics exist? I'm honestly at a loss at what this post is supposed to do beyond that. Yes, you can have a string of bad luck. Yes you can have a string of good luck. I'd argue that the string of good luck is slightly more common for the same reasons that you are more like to have AFKs, ragers, inters, etc. on the enemy team than you are on your own.

Statistics are going to exist anywhere. You are talking about strings of good and back luck that fall beyond the third standard deviation of a traditional bellcurve. We can use the standard bell curve for win rate since by necessity anytime a team of 5 players win, a team of 5 players loses which means the mean win rate would be 50% or 0.5. This doesn't take into account "Loss Forgivens" but those are exceptionally rare and would not move the statistics any measurable distance either direction compared to the amount of games played. Anything beyond the 3rd standard deviation of a bell curve means that 0.13% of players experience it and while i haven't done the exact math of your examples, I am guessing that your examples of 100 coin flips would be even more rare than that. If we would combine the two sections (the exceedingly lucky and unlucky, which counterbalance each other), we still come up with only 0.26% of players that would experience this result in a row. Again, this is a higher number, perhaps exponentially higher, than what you are suggesting.

At the end of the day this post just seems to point out that thanks to statistics, no matter how likely or unlikely, there remains a minute chance that these situations MIGHT happen. You eschew the more possible chances of benefiting from luck and instead direct the readers attention to the minute possibilities of extreme situations to lend credit to those who have more than likely fallen victim to an unconscious negativity or confirmation bias for their own results, which are usually predicated upon limited sample size.

Subdue1/23/2020, 1:57:26 AM1 votes

All of the "logic" in the original post is based on the incorrect assumption that the matchmaking system has completely random probability. It doesn't. It matches players with other players who have a statistically similar level of ability to win. Losing a game means you'll be playing the next game with players who are statistically slightly less able to win, and winning a game means you'll be playing the next game with players who are statistically slightly better able to win. In other words, the more you lose, the easier the next game should be, and the more you win, the harder the next game should be.

Applied to your coin flip analogy, the coin would have to be a bit more and more likely to land on heads each time it lands on tails, and more and more likely to land on tails each time it lands on heads.