Statistical Look at TI4 Qualifier Predictions - Americas
This weekend I put some time aside to have a deep look at how the Qualifiers were going to go in each of the regions. I intended to rewrite much of the work I did last year (http://www.datdota.com/blog/?p=423 and http://www.datdota.com/blog/?p=458) to allow for more verbose and clear analytics of results, and maybe patch up any unnoticed bugs.
As data is time-sensitive (teams have up and down weeks which cause some fluctuations in the statistics), and there’s some time until the other Qualifiers, I’m going to publish the prediction for each qualifier a day or so before the Qualifiers begin, just so that the most accurate statistics are given.
The Americas qualifiers is going to have 11 teams after the fiasco with Revenge eSports. This doesn’t fundamentally change anything in predictions of who is going to win them, although there are some small variances with the inclusion or exclusion of teams.
Before we continue, let me explain the format of the tournament. Each team will play each other team once (best of one matches). After that, the four teams with the most games will advance to a double-elimination bracket, with the top 2 seeds starting in the winners bracket, and the bottom 2 seeds starting in the losers bracket. All matches are best-of-three, except the finals. Although not stated, I believe the finals will have a 1 game advantage to the winners bracket team.
Ok, let’s dig into some stats. This is all off a 10^6 run Monte Carlo simulation, using a head to head formula of their last six-month game history (with an emphasis on games in the last month), interpolated by the teams current and monthly Elo scores (http://twopee.noxville.co.za/team/list). Monte Carlo simulations are where you repeatedly simulate hypothetical scenarios, using random numbers to decide what to do at certain situations. In this case, if we have that Team A has a 30% chance to win against Team B, we can randomly generate a number between 0 and 1. If it's below 0.3, then team A wins, if it's above 0.3, then Team B wins. If you repeat the same Monte Carlo individual simulation enough times, and observe the outputs, the average outputs tend towards the true chance of that event occurring. For more information about Monte Carlo, check out http://en.wikipedia.org/wiki/Monte_Carlo_method
First up was the “Group Game Win Average”, or, the average number of games each team won in the group stage part of the simulation. Because these are averages, and decimals of numbers are allowed, these don’t seem to have any meaning as cardinal “what we expect” numbers, but rather as ordinal rankings of how we expect to see the team positions end. The inter-group results of these teams are available here: http://twopee.noxville.co.za/international/qualifiers and any head-to-head result can be checked out here: http://twopee.noxville.co.za/team/head-to-head
Group Game Win Average
- North American Rejects ~ 7.3756
- TeamLiquid ~ 7.127
- Sneaky Nyx Assassins ~ 6.8879
- TOP5 ~ 5.1542
- CNB ~ 4.9061
- BANearth ~ 4.7468
- Revenge ~ 4.5529
- SP ~ 4.0341
- uG ~ 4.0308
- EHUG ~ 3.1424
- ISG ~ 3.0422
Next up is the “Chance to qualify for playoffs”. This refers to the double elimination bracket to see which one of the top 4 teams will win overall. We see once again North American Rejects, TeamLiquid and Sneaky Nyx Assassins at the top, but by a much larger margin. This implies that although TOP5 looked not altogether that far behind Sneaky Nyx Assassins in the Group Game Win Average table, there exist a lot of situations in which CNB and BANEarth pip them at the post (or tie with them on points and then lose subsequent tiebreakers).
Chance to qualify for playoffs
- Sneaky Nyx Assassins ~ 87.17
- North American Rejects ~ 84.97
- TeamLiquid ~ 83.78
- CNB ~ 29.88
- BANearth ~ 29.42
- TOP5 ~ 26.87
- uG ~ 18.88
- SP ~ 15.48
- Revenge ~ 14.97
- EHUG ~ 5.54
- ISG ~ 3.04
Finally, I guess the most important (and to me, most revealing), is the “chance to win overall”, the biggest prize in this qualifier is a spot into TI4, and this final table breaks down the teams which statistically win it the most frequently (within the Monte Carlo simulation). North American Rejects dominates in overall win %, sitting just shy of 60%. It’s pretty close between TeamLiquid and Sneaky Nyx Assassins for 2nd place. NAR is 5-2 against SNA and 3-0 against Liquid. It’s a lot closer between Liquid and SNA with SNA being 1-2 down in that matchup, but both teams have similar Elo scores (both current, and averages over the last month). This leads me to think that the (statistically likely) losers bracket between SNA and Liquid will be quite exciting, but probably irrelevant as it seems likely that both will lose to NAR in the Grand Finals.
Chance to win overall:
- North American Rejects ~ 59.07
- Sneaky Nyx Assassins ~ 18.98
- TeamLiquid ~ 18.02
- CNB ~ 1.64
- TOP5 ~ 0.85
- Revenge ~ 0.58
- SP ~ 0.35
- BANearth ~ 0.34
- uG ~ 0.13
- EHUG ~ 0.04
- ISG ~ 0.0
So, this was part one of this qualifier prediction series. I may publish an update after the group stages are done, with more recent statistics and maybe some cheeky changes to my qualifier predictions. Feel free to ask any questions here, or on Reddit ^
As with almost every statistics-orientated article in Dota 2, thanks to Martin from DatDota for the amazing statistics that DatDota provides.
EDIT: A few people have been asking about how I handle team roster changes from a statistical perspective. The short of it is that I leave their team ratings intact, and allow their rating to tend towards their true skill over time. This means that predicting Revenge (amongst others) is quite hard, with such recent team changes.