Based on the MMR distribution of the SC2 ladder (https://i.imgur.com/ojB2Nw8.png), we can calculate the odds of a grandmaster occurring for each race, which is P(x>4860). The mean & standard deviation for each goes as follows:
The ratios of Grandmaster should then be:
P(x > 4860) / (P(ProtossX > 4860) + P(TerranX > 4860) + P(ZergX > 4860))
which is:
P
T
Z
(0.003573 / 0.010283) * 200 = 0.347*200 = 69
(0.002803 / 0.010283) * 200 = 0.27*200 = 54
(0.003907 / 0.010283) * 200 = 0.38*200 = 76
What are the actual Grandmaster statistics? I am glad you asked:
P
T
Z
56
86
45
Whatās the probability of this occurring? Thatās an easy one:
P
T
Z
2.62%
0.01%
0.01%
TLDR
Zergās representation in Grandmaster is about 40% smaller than it should be, Protoss is about 20% smaller, Terran is about 60% larger than it should be; the confidence of these results exceeds 97%, 99.99%, and 99.99% in each case respectively. Terran is drastically overpowered, Protoss is slightly underpowered, and Zerg is drastically underpowered.
I had a look, and Zerg is also the lowest represented at the low level, bronze, silver and gold. So it appears that zerg is happily average.
Another, seperate point, is the lower amount of zergs total. This points to zerg not being fun to play. I will blame it on tiring gameplay, such as creep spreading, possibly queen inject? And having to anxiously wait on larva to pop.
Hereās a cool statistic:
Diamond/plat are even distribution (60,000~ players)
Now, gold/bronze/silver: (70,000~ players)
Zerg has 24% dist.
Protoss has 33% dist.
Terran has 43% dist.
So, based on distribution alone, you are around 50% more likely to be in a low league as Terran, 25% as Protoss.
Or, putting it another way, as Zerg, you are 16% more likely to be dia/plat than gold/silver/bronze.
A Terran is 26% more likely to be gold/silver/bronze than dia/plat.
Protoss is roughly in the middle of them.
Masters has 5% less zerg, Grandmasters has 25% less zerg, but grandmasters are less than 1% of the playerbase. Who do we balance for?
Zergās mean MMR is about 100-200 higher than Terran/Protoss. I was surprised that the difference was that low.
Being overpowered would widen the variance and lower the average which is literally the exact opposite of what is observed for zerg. The problem on these forums is that people donāt know how to read a basic probability density chart.
If you have two groups of people and one group has an advantage over the other group, the variance of each group would be identical and this is crystal clear if you understand, for example, the binomial theorem. The difference in variance of the two groups canāt change as a function of the average performance level of the groups, e.g. if itās tight for one then it will be tight for the other; if itās loose for one then itās loose for the other. A difference in the variance can only occur as a result of group selection, e.g. if there is a correlation between group performance and and the skill level of the player who picks which group he wants to be in.
This creates the effect that, when a group has a disadvantage, their average performance goes up while the variance of their performance shrinks. A group that has an advantage has a lower average and a larger variance. This makes sense, intuitively, since an increase in performance lowers the skill floor, making it more accessible to more people (in particular the lower performing ones). This is saying that as the performance level of the race goes up, the performance level of the group goes down, and this happens because the demographics of the group changes as a function of the raceās performance.
Mathematically, this means that group performance varies by racial strength and group demographics, but group demographics varies by racial strength. In other words, racial performance is a derivative of both group demographics and group performance, but group demographics is also a derivative of group performance. That makes racial performance both a first and second derivative of group performance.
Plotting this over time, the first derivative (racial performance) will create an increase or decrease in group performance for a short period, but it also incites a change to another derivative (group demographics) which will quickly outweigh its own impact direct impact on group performance.
This means that average group performance goes up for a short period after becoming overpowered, but goes down long-term due to the second derivative aka demographic change. This predicts that a race that is underpowered will have a higher average and lower variance. A race that is underpowered will have a lower average and higher variance. Thatās exactly what is observed in all three cases with all three races ā each one perfectly fitting this trend.
What I am describing is known as the āLotka-Volterraā equations. They are also known as the āpredator/prey equationsā, which gives us a way to visualize this more effectively. Think of balance like rabits vs wolves. Wolves have to kill rabits to survive. So if wolves are doing well, they are by definition killing lots of rabbits. Which rabbits are the wolves killing, though? They are killing the slowest rabbits, which increases the average speed of rabbits. Itās the same exact process in effect. When a zerg gets absolutely wrecked by a terran, he quits playing or switches races. The ones most susceptible to being wrecked are the lowest skill ones, which means the average zerg performance goes up as a result of terran being overpowered.
Literally every facet of ladder data perfectly fits this description. Zergās play fewer games, are less numerous on the ladder, have higher average performance, and a tighter variance ā all predictions of the Lotka-Volterra equations.
Hmm, not sure about that, the simplest explanation to me is that Zerg must be easier to win with (below Masters). EDIT - a few days later: I wanted say Zerg should be easier at EVERY rank, but I was being nice.
Continued: I mean, itās the most logical explanation as to why so many Terrans are stuck at bronze/silver/gold. They canāt all be bad, r-right?
If wolves are eating rabbits, that would increase the average performance of rabbits, because the wolves eat the slowest rabbits, while decreasing the number of rabbits and also decreasing the variance in performance of the rabbits (the rabbits left alive will have a reliably higher average performance).
If zerg is easier to win with, Terran and Protoss would have higher performance as a group, there would be fewer Terran and Protoss than there are Zergs, and the Terran/Protoss groups would have a lower variation in their performance. None of these predictions align with the measurements. Your theory is wrong.
SC2 is a predator/prey tournament system which is very similar to many biological systems. The behaviour here is well defined. We know exactly how it works, and if it is doing something we know what it means. If you canāt understand simple āwolf eats rabbitā examples, then you should probably check out tic-tac-toe instead of SC2.
This is very strange, we are talking about casual ranks, there is no incentive for terran to try harder because they got eaten. Itās just non-sensical. The majority of zergs are at diamond rank, they all won for some reason.
What on Earth are you even talking about. This has nothing to do with ātryingā harder. Players are more likely to quit the game or race switch when they lose. People who lose more are more likely to quit or race switch than someone who loses less. If a race is underpowered it will lose more which means more quitting and more race switching. Itās the same as a rabbit dying to a hungry wolf. This is how tournament systems operate. The lowest performers are kicked out. I canāt believe I have to explain how a tournament works.
How can it be? Thereās twice the amount of terrans than zerg at low level, but only the same amount at diamond. Theoretically, it should be spread out more.
So you have a hard time separating racial performance from group demographics. That takes legit brain damage to get those two mixed up. Racial performance is the design of the game. Group demographics would be who plays what race.
Ah, so you are using the argument that terran is the ānoobā race. Perhaps, but of course thereās no proof really, and the game is 11+ years old now? Maybe.
Thatās absolutely wrong. Did you read anything I posted? The widening variance means itās played by more noobs AND more veterans, which is exactly the case with terran (highest in Bronze and highest in Grandmaster). This is the widening of the variance that I keep talking about.
Thatās a straight up lie. Blocked. The ladder data perfectly conforms to this model (and no other) with about a dozen verifiable predictions (each of which are accurate) as I detailed in previous posts. To say that there is āno proofā is a blatant lie. Literally all the available data conforms to this theory. Itās unreal that I can spend 1,000 words detailing all the ways in which this theory robustly describes the observations, and someone will waltz in here and say āof course thereās no proof reallyā. Do you have eyes? Absolutely unreal.
There are drastically more Terrans in bronze, silver and gold league (half the playerbase) and only more Terrans in Grandmaster league, slightly masters.
Zerg must be doing really well, on average.
For anyone reading, the OP is trying to assert that the majority of diamond/plat zergs are just ābetter at the gameā than the gold/silver rank terrans. No imbalance here.
The worst part about Terran hogging GM is that itās all low GM terrans so they account for 60% of your games. I also think youāre using the NA server because it fits the narrative.
This is a 5300 mmr terran. Link to any other person to ever beat a GM with 1 base swarmhost and I will delete my account and never post again. Balance is not relevant to guys like me. Iām in a different universe in terms of skill. Everyone else is stuck in the stone age while I am colonizing mars.
Accusations of bias just donāt work on me. Do you think I need help from SC2ās balance team to win? Lmao. Come to think of it, I am biased ā I want Blizzard to nerf zerg even more.