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.