A Simple Stat Analysis (From an Engineer who studies statistics)

Azeranth··3 votes·510 views

So recently there has been this idea floating aroun the community that "The Ranked System is Broken. Bleh bleh bleh bleh bleh" and it forces you into to lose situations. Well, here is some simple math to make it clear to you.

Because of how ranking works, and LP gains/losses being roughly equalized there is almost the same number of player on their way up the ladder as there are going down it. League ranking is a zero sum game. It would stand to reason that players who are where they belong generally hover around where they belong, gradually improving or falling behind the curve. Things tend to even out, such is the rule of averages. HOWEVER. There is a bottom, right now there are a number of people sitting at B5 0 LP where they justifiably belong and because of that the following is a serious plague of low elos.

There is a drastically higher chance that you will be required to carry any particular game the closer you are to a one of the fringes of a rank

Now, follow me here everyone, lets assume that while you are playing exceptionally well on anyone particular day, there are at least 5 other people who are not playing just as well and 4 who probably are playing just as good. Which means that when you are on the way up, you are pushing others down. The natural cause and effect of games. BUT when you win, moving up, you are kicking up the settled middle ground of things, meaning that pure random statistics dictate that as you get closer to the top, your games have a higher probability of you playing with someone from the bottom. There is presently a enormous gap in my game knowledge and mechanical skill now on my way to silver from my current spot in B3 than when I first ranked as B5 and promptly fell to that 0 LP position I mentioned before. So as you rise, the chances of getting someone bad on your team. In order sustain a win streak, it is required that you consistently head up your team. Meaning, that if you can not maintain that you suffer an increasingly high PURELY RANDOM CHANCE of encountering a feeder on your team.

Now think, if you progress slowly up, maintain a solid positive Winrate of around 60%, this trend will still persist but it will not seem to happen as severely or inconveniently because it is harder to notice whos fault the game is when the game wasn't in contrast to multiple other games with the other team not properly capitalizing on small mistakes which gradually snowball out of control. SO that means there is also a rather severe placebo effect in place on "Forced Losses"

Then to top it all off, think about this. In our games, we often perform poorly and manage to be extremely heavy every once in a while. I would say just by browsing various statistics and accounting for Mains, Playstyles, Counterpicks, and Elo every is the reason they lost one in every 11 games. That's a trend I observed, without hours of meticulous data, but it would seem to be about true. Which means that if you are performing well, and destroying enemies in other games, the law of averages dictates that after a game of the heavy person being on the other team and you crushing them there is a clean 50% chance they are then on your team, simply because you removed the possibility of you being the feeder because you're on a hot streak. 2 games and the chances suddenly sky rocket up to 57% at three games its 83% by game four is only a 8% chance that pure random statistics will gift you with not having the feeder and a 9% chance that no one feeds at all on either team. Which means by the time you reach the fourth game, if you aren't having someone making your game nearly impossible, it would be more suspicious.

The opposite is true as well, if a game is hard carried, the next match tends to be easier, casual even especially if this occurs back to back. The same reasoning applies with after one hard carry game, there is only a 37% that the feeder will be on your team this game and after 2 hard carries only a 28% chance. Plus this is all operating on the assumption that you aren't doing poorly and you are playing flawlessly.

But, even if you don't want to take my word for it that simple statistics dictate the more games you win without hard carrying, the more likely your next game will be impossible then just think about it. If you don't deserve to be in an ELO, then you should be able to carry it. Statistics which define the "average" shouldn't apply to you because you are above the average of your player base. requiring a person to carry one out of every 4 wins they have and attempting to assure that each team has a solid mix people both on the way up and the way down is a healthy ranking mechanic. Being forced to carry is good for player skills and keeps the ranking more accurate and decisive. It ensures hardstuck because hardstuck means that people don't float out of their ELO. it is the realty check that assures that when one summoner ends up flying up the ladder, some lucky person can't ride the wave every now and again while maintaining a barely positive win rate.

Matchmaking isn't perfect but statistics and common sense suggest that its healthy that every win streak should come to a climax where the player either clutches it out or chokes and tilts super hard.

3 Comments

Incognonymous1 votes

Because of how ranking works, and LP gains/losses being roughly equalized there is almost the same number of player on their way up the ladder as there are going down it. League ranking is a zero sum game. It would stand to reason that players who are where they belong generally hover around where they belong, gradually improving or falling behind the curve. Things tend to even out, such is the rule of averages.

Explain. "It may stand to reason...", but only after potentially hundreds of games. Riot cites the large of large numbers to explain such disparities between placement and actual level, but it's obvious that number is somewhat ambiguous, and possibly changing with every variable added to the game-- a seemingly increasing figure as the game adds mechanics.

Not that I disagree with the general premise, OP. I'm only questioning some fundamental assumptions.

Azeranth1 votes

The idea being that if you beling in gold, once you reach gold you will probably on hover up or down 1 teir

Incognonymous1 votes

{quoted}

The idea being that if you beling in gold, once you reach gold you will probably on hover up or down 1 teir

MMmm. Isn't that margin also an assumption? Not just that, but it's an assumption with continual play, since decay was expanded.

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