S19 Current Player Odds

[FML|red7z7]

Hey guys. I took it upon myself as a sort of fun exercise out of curiosity to calculate the odds for each of the remaining 12 players to win the season. As a byproduct of that calculation I was also able to calculate the chances of each player getting top 3 and top 7 after Round 6, which is relevant to who goes to the semifinal and who gets a gauranteed spot in the final. Hope you all find this interesting or useful and maybe I'll do more of these analyses in the future :). Cheers!

How did I do these calculations? I wrote a python script which simulated the season playing out match-by-match for one-million times, with random players winning each match each time. That means this calculation assumes each player in any given match has an equal chance of winning that match.

Some notes:

• I accounted for M25 being played already, that outcome was fixed
• I accounted for renaud and ostones double score cards being used in R6. Thus if either of them chooses not to use it for some crazy reason, everything here is totally wrong
• I accounted for TB points, even subtracting renaud and ostones DS ones
• I accounted for matchups for R6 changing based on outcomes of R5
• I did not account for possible future gains of TB points. This may be slightly significant as I gave Renaud a TB point for R5 while two other players will yet gain a TB point for R5, but I did not calculate for that
• I did not account for any future match swaps
• I did not account for people getting future top-score +1 bonus
• I did not account for players missing/being subbed

**Disclaimer: It is likely that there could be errors in the calculations or the graphs because I'm human, there are a lot of variables to account for, and I'm not being paid to do this**

(1)
First up, heres the chances of each of the players getting into the top 7 (in other words, the chance of not being eliminated after round 6). Most notable is Renaud, sk2flash, and noexxx are 100% gauranteed to not be eliminated!
*The x-axis shows how many games out of 1 million resulted in that player not being eliminated after round 6. Thus, divide by 1000000 to get the % likelihood.

For those interested, I've provided what the cutoff scores are for the top 7 as well. The following chart shows the likelihood of each of the score-values on the x-axis being the cutoff value. For example, see that there is nearly 60% chance of 100 being the minimum score to make top 7. There is a small chance the cutoff will be as low as 90. Missing values, such as 96, are impossible.

(2)
Next up, we have the chances of each player making top 3 after R6, guaranteeing them a spot in the s19 finals. Notably, Renaud has over 98% chance of getting in, while Yaws has a 0% chance of it at this point!

Again I've provided the chances of each of the possible minimum values, this time for making top 3 after R6. It is most likely (with a 30% chance) going to be 115 points, but there could be a freak-accident making it as low as 105 or as high as 131!

(3)
And finally, here are the chances of each player winning the entire S19. It's looking good for Renaud right now at nearly 25% chance! **Edit: corrected this value. I simulated 1 million outcomes for up to R6, but after that for final it's easy to calculate odds -- 4 possible winners of the semi, and 4 possible winners of the final for each outcome of the semi, thus 4x4 = 16 more outcomes for each of the 1000000 outcomes of R6. Thus, divide by 16 million for the final rather than 1 million to get percentage! For reference, ostone has a 14% chance, and yaodintakoi has a 7% chance, and yaws has a 1.5% chance. Every player still has a chance though! **Edit: to clarify, this distribution is not the chance of a player winning the final match in isolation. Instead, it accounts for each of the matches played between R5, R6, and semis as well, and then the chances of winning the final after all that.

**Note: if anyone feels like checking my work or running the code themselves, feel free message me. I also might upload it to github or something and post the link later.**

[Pinballmap]

Nice work. but i can not see the pictures. Dont know why.

[FML|WorpeX]

This is amazing!!! Awesome work Red, I love it!! Pictures don't work but the text says it all. :D

[rsm!]

Assuming this does not take player skill into account, shouldn't it be impossible for a player to have greater than a 25% chance to win s19?

[Pinballmap]

I think thats correct . 25% is the maximum when you are playing the finals. waiting for the graphics though.

[FML|Mage]

Maybe it takes in previous results so far this season and somehow factors that in for skill/chances to win.?

[Pinballmap]

He mentioned :

That means this calculation assumes each player in any given match has an equal chance of winning that match.

[FML|Mage]

Oh... then yeah I'm confused by the 40% chance.  Red wake up!

[Pinballmap]

i think 40% that Renaud will get place 3 or higher makes more sense then.

[FML|WorpeX]

I think it also takes into account the amount of times a player makes it into the finals as well. Since his calculations simulate the whole season a million times, its to be assumed that Renaud makes it into the finals more times on average then the rest of his peers, which is why he has a higher chance of winning the season. So, yes, he has a 25% chance to win the finals but since Renaud makes it into the finals more times then everyone else in his calculations, his odds of winning are higher.

[FML|Mage]

I think it also takes into account the amount of times a player makes it into the finals as well. Since his calculations simulate the whole season a million times, its to be assumed that Renaud makes it into the finals more times on average then the rest of his peers, which is why he has a higher chance of winning the season. So, yes, he has a 25% chance to win the finals but since Renaud makes it into the finals more times then everyone else in his calculations, his odds of winning are higher.

Yeah!  This is what I meant to say

Really!

Why do I get the feeling none of you believe me

[FML|red7z7]

Oops, I had linked the images directly from my google drive and forgot to change the share settings. Should be fixed so you can see the images now!

Assuming this does not take player skill into account, shouldn't it be impossible for a player to have greater than a 25% chance to win s19?

Not quite -- the equal 25% chance applies only to individual matches. When you factor in current point standings, and multiple matches being played, you get a distribution that reveals different chances for each player after each round.

I think it also takes into account the amount of times a player makes it into the finals as well. Since his calculations simulate the whole season a million times, its to be assumed that Renaud makes it into the finals more times on average then the rest of his peers, which is why he has a higher chance of winning the season. So, yes, he has a 25% chance to win the finals but since Renaud makes it into the finals more times then everyone else in his calculations, his odds of winning are higher.

That's exactly right. That should also be more clear now that you can see the graphs and the numbers on the axes. Just divide by 1000000 to get percentages.

[FML|Mage]

Images work for me now, this is incredibly awesome!  I hope to see some more stuff like this in the future though I'm sure it's a lot of work.

Very nice job though

[Pinballmap]

Yeah i like stuff like that, really great work red!

[zTsoso]

Fantastic job, Red. I really appreciated the graphs figures and everything. It seems plausable. Although something within me is making me think: "never tell me the odds"  .