Linear regression of pro level performance

General Discussion
1

Linear regression of pro level performance using symmetrical matchups as a baseline for asymmetrical matchups.

Data:

https://i.imgur.com/EicftOv.png

Each dot is a pro player. The X axis is their Elo ranking in their mirror matchup (TvT, PvP, ZvZ). Y axis is their Elo ranking against Zerg. Two players with an equal Elo ranking will have a split 50/50 win-rate. If a player has a higher Elo ranking, their win-rate goes up according to the difference in skill. It’s a very accurate system built on the real data of the actual games played in the pro scene. If a player has a given Elo rank, it’s because that’s what their performance history says.

Trend within the data:

Looking at 1 or 2 or even 10 data points it can be very hard to tell what is actually going on. That’s why in this graph, it’s the whole pro scene - every pro player who has been active in 2020. As you can see from the yellow line, a clear trend has emerged: for a given TvT Elo, Terrans have a higher TvZ Elo. Using linear regression, this can be represented by the equation:

TvZ = TvT Elo * 1.08 + 15.3.

What this means is that for a player with any given TvT Elo, he will have 8% more Elo vs Zerg plus a flat bonus of 15.3 on top of that. Remember, that’s the actual trend inside the actual data of the actual pro scene. Why would Terrans have better performance in an asymmetrical matchup than their symmetrical one? Put simply, the asymmetry of TvZ gives terran an advantage.

Visualizing the data in another way:

https://i.imgur.com/yXkHwZO.png

Here is every pro Zerg’s ZvT & ZvZ Elo, and every Terran’s TvZ and TvT. The regression is the “moving average”. As you can plainly see by the regression lines, Terrans are constantly punching above their skill level in TvZ.

Win-rates:

What does this equate to in terms of win-rates? Well, it depends on the skill level you are talking about. We will use the Elo algorithm for calculating win-rates based on rating differences, detailed here:

https://en.wikipedia.org/wiki/Elo_rating_system#Mathematical_details

If the average skill level is zero, then the Elo rank difference will be:

TvZ = 0 * 1.08 + 15.3
TvZ = 15.3.

15.3 Elo vs 0 Elo equates to a 52/48% win-rate split. But, remember, Terrans get a bonus 8% on top of that, so how does a Code S level Terran perform? Let’s punch in the numbers:

TvZ = 775 * 1.08 + 15.3
TvZ = 852.3

775 vs 852.3.

That’s a total of +77.3 Elo. That would split a win-rate 61/39% vs an equally skilled Zerg. To help visualize this, here is a chart that shows how a Terran’s win-rate inflates vs Zerg based on his TvT Elo ranking:

https://i.imgur.com/UvXyAQ4.png

Conclusion.

This is a huge deal. Terran is straight up better than Zerg, with a flat +15.3 Elo or +2% win-rate vs an equally skilled Zerg opponent. Terran becomes increasingly better than Zerg by a factor of +8% after that, which varies the win-rate by skill, and at the Code S level provides a whopping +11% win-rate vs an equally skilled Zerg opponent. It isn’t an isolated incident - it’s the entire pro scene.

Why doesn’t this align with the win-rate metrics of Aligulac? It is simple: these models are based from the frame of reference of equally skilled players, while the win-rates in Aligulac are a mash of a bunch of different players with differing skill levels.

Also, PvZ is balanced although it slightly favors Protoss.

9 Likes
2

Lmao. Terran Cry Force has nothing to say when the facts are laid out before them. They are out of arguments. Terran is undeniably better than Zerg when an Terran has a 61% win-rate vs an equally skilled Zerg.

10 Likes
3

Your data points and the source please?

4

http://aligulac.com/periods/latest/

1 Like
5

Yeah, where do you get the elo for each player?

6

The active player ratings are VERY clearly listed here:

http://aligulac.com/periods/latest/

The whole database can be downloaded here:

http://aligulac.com/about/db/

1 Like
7

Do they have elo inside directly? Or do you just calculate them?

8

Aligulac uses Glicko while I’ve used Elo in this analysis. The results would be roughly the same. Glicko is a version of Elo. The differences are nuanced.

1 Like
9

So do you have the Glicko version?
Comparing to the mirror matchup is genuinely a decent idea.

10

Here is the top 10 terrans according to Elo:

Maru
Cure
INnoVation
Clem
TY
HeRoMaRinE
uThermal
TIME
souL
SpeCial

Here is the top 10 according to Aligulac’s Glicko:

INnoVation
Maru
Cure
Clem
TY
HeRoMaRinE
uThermal
Dream
(11th) Special

The differences are very nuanced. There is no advantage to Glicko over Elo.

11

I mean the plots. It’d be nice to see.

12

You want the actual data?

http://www.sharecsv.com/s/52d5aa043469b5f31143a7b2a6324714/Players%20-%20All.csv

13

I mean the linear regression with straight lines, like your first plot.

14

Generate a graph with the data and tell it to generate a linear trend line. Microsoft Excel or Google Sheets or OpenOffice can do that for you. A CSV file is a plaintext file that is easy to import into basically any data management program.

1 Like
15

Err, don’t you have the codes already. I am kind of too lazy to do it.

16

I don’t really understand your axis. It’s the difference between what ?

For example that Protoss player which has a negative elo in miror MU (PvP) ? and a negative elo vs Zero ? what does that means ? He is just worst than the other players in that sample in miror and in PvZ ?

17

The X axis is their mirror elo. So in the case of a Protoss it would be their PvP elo. In the case of a Terran it would be their TvT elo. In the case of Zerg it is their ZvZ elo. The Y axis is their elo vs Zerg. ZvZ is Zerg’s mirror, so it’s a 1:1 ratio.

If the game is balanced, a player with X elo in their mirror matchup, which has no imbalance, should be roughly equivalent to their Elo vs Zerg, so it should be roughly 1:1. That is the case for ZvZ and ZvT, PvP and PvZ, but not for TvT and TvZ. Terrans perform about 8% better in TvZ than in TvT.

It’s easier to visualize in the secondary chart:

https://i.imgur.com/yXkHwZO.png

ZvT and ZvZ follow each other closely. TvT is well below TvZ and this exaggerates with skill. If we added PvP & PvZ to this chart, it would look similar to ZvT/ZvZ.

18

I stopped reading after the first paragraph, let me guess: Terran is OP and if you wins with Zerg, you’re a godly genius.

3 Likes
19

See, I’m actually more than willing to explore the idea that Terran might be OP in the current Season (though I think that’s likely the map pool), but not with a doofus that argued that Terran having 1 player in the Ro8 PROVED that Terran was OP). People like that can’t be reasoned with and are either trolling or are too stupid to realize that they discredit themselves at every turn.

2 Likes
20

If you aren’t the God of bias, then I don’t know who is.

11 Likes