Xavori, on 02 November 2017 - 03:42 PM, said:
Wait. I got it. The example anyone could understand.
Let's say you have a random number generator that creates the numbers 1-10 11 times and adds them together. The program then writes in a 12th number that is always 10.
You want the highest number possible. You've even cheated and made one of the numbers the best it can be. Is this going to produce top-notch results the majority of the time?
No.
You'll get everything between 21 and 120. Your mean is going to be ~60. That's barely above average. And that's even though you cheated and made sure one of your numbers was the absolute best it could be.
So even with that absolute best possible number 8.3% of the time, random numbers are still random.
Your example is the correct one to use, your conclusion from it is erroneous though. You've stated right here that your mean is going to be above average. That means you are having a statistically significant effect on the result through your actions. The system is no longer completely random and is biased towards the one that generates the 10.
Your mistake I think is that you are interested in getting the highest number possible, you aren't. What you are trying to get is a number that is higher than another randomly generated team that doesn't have your perfect 10. You don't need top notch results every time, you just need results that are slightly better than your opponents. They will also have their share of problems so as long as you can edge them out you will trend positively.
Let me actually do this to show you how it works.
Here is an example:
https://docs.google....#gid=1406785854
It generates 400 matches with 23 of the players being completely random between 1-100. The 24th player is always on team 1. The first sheet has random but static values for the other players. If you change the "skill" of the player you get the following KDRs
01 = 0.56
10 = 0.60
20 = 0.65
30 = 0.76
40 = 0.88
50 = 0.97
60 = 1.16
70 = 1.29
80 = 1.42
90 = 1.60
100 = 1.86
Unsurprisingly the above average players have WLRs that are higher than 1 and the worse players have ones that are less than 1.
There's also a second sheet that regenerates all the numbers every time a cell value is edited (I'd recommend downloading it since it's faster to update that way). If you select and empty cell use use the delete key you can see various WLRs for the same skill player over different sets of 400 matches. Unsurprisingly you'll see some variation in the number. What you will notice is that the higher skill players usually have higher WLRs and the worse players have lower (sub 1) ones.
The more matches you add the tighter these groupings get. While it's possible for a skill 1 player to end up with a higher WLR than a skill 100 it is extremely unlikely.
In practice the distribution will be different which means a really good player like Proton can have an even greater effect on a match (say skill of 150) because there would be extremely few other players at that level while the vast majority would be grouped around 50.
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Ya know. If the matchmaker and PSR were accurate, everyone would eventually have 50/50 W/L records in solo drops.
Close to it. The problem is that T1 is bloated and has a massive skill gap between the top and the bottom.
This post gives a good graph of it. If skill was more evenly distributed and matched things would trend to 50/50.