1. Go strength is fairly universal. Meaning: If you've developed your skills at go, where ever you go, you will be playing at similar strength, and you can perceive other players as stronger or weaker than you're. When comparing your subjective experiences of different opponents with other players experiences of the same opponents, there should be a strong rank correlation, which can be hypothesized to be explained by difference in skill.
2. Go strength is based on several componentsMeaning: Your skill of the game is not made from a single factor, but it has several factors which create a fairly static average performance. For an example your memory functions when performing long reading exercises can be compared with other players, your ability to benefit from time per move may have a difference in comparison to your opponent. As another example, you may have quicker executive functions while reading. You may perform an interference series at quick speed. There are lots of factors. I don't claim to know which ones matter most. The claim here is that there are several of them.
3. Go strength has a fairly low degree of oppositionExplanation: Your strength components oppositon to the components of other players don't have a strong degree of opposition, your expectancy of winning is rather derived from your universal stregth, than the opposition of your strength components and opponent's strength components, but these factors modulate your winning expectancy.
Sidepoint: This is part of strength universality claim, as the inverse of universal strength is local strength, strength based entirely on circumstances. So strength is fairly universal and has a low degree of opposition. But it's still worth a distinct point.
If there were competing schools of strategy/tactics, then perhaps there could be a stronger degree opposition, but that's not really the case, as far as I understand. However it's not that the seperate schools would simply induce opposition, rather it's both, if there were opposition, it would create a logical platform to support competing schools, so their absence is evidence against high degree of strength opposition. The components themselves may have some degree of opposition, but it may blend with the players. (You should think of playing 9x9 or 19x19 as an example but they're not
really the same game)
But still some players will be better at life and death, others will better at strategy, wholeboard thinking. The relative value of this components changes the opposition. Players also optimize to their own strongpoints with their own play, even if they would be bad at it. As as sidepoint, the components maybe correlated with each other, so there's factor which causes lots of components (like high overall or general intelligence). Notice that the flocked components reduce he effect of opposition instead of increasing it.
4. Go strength is quite strongly uniformMeaning: That if there is a difference between players strength, it can be quantified in such a way, that you can find a consistency between different ranks. This is what it means in a more concrete example: Let's generate a player A with static strength. Then let's reach to the pool of players, and find one who will have a 80% winning rate against player A. Let's call him player B. Now let's use the same value and find player C, who can beat player B at 80% winning rate. It is obvious that these players can be found, but what's not obvious that if A,B,C and have this relationship, then we can estimate the winning rate between players A and C. That is what uniform strength means in this context. So the claim is Go strength is fairly uniform, which allows the possibility consistent ranking systems from low to high strength. However there is, as far as I know, asymmetry. Outcomes become less random as players get stronger. This expectation can also be derived with the following interference: If really low strength means making lots of mistakes (closer to randomness), and really high strength means making very accurate and closer to optimal moves, then the degree of randomness decreases as players get stronger. This is hugely important because it changes the skill distance between player A and B in respect to B and C, even if they exist, which also means different ratios for A and C.
However the game of go is capable of supporting the handicap system fairly well. This is strong evidence for stongly uniform go strength, but not for absolute uniformity, which is in my opinion practically impossible.
Time as factorPlaying the game with different time settings is hard to fit into this perspective, because in my opinion, the game is not the same if you change the time settings, but it's complicated. And right now I don't feel like trying to analyze this any further.
Alright these are the main claims about go. Now to ranking systems. Some ranking systems may be more flawed than others in that they're less good at really estimating players winning expectancy or finding the most appropriate relative rank for a player. They may have these different aspects of go strength incorrectly included in their mathematics, which may cause slight distortions in the ranks. For an example you might find that there's a longer distance between 3d and 4d on some server than there is on some other server. Or you might find that there's a tiny percentual difference between winning changes with handicap stones in relation to otherwise.
In addition to this playerbases are different. Tygem is rather an asian server. Go is also a more popular game in the eastern countries. That means the player population can be expected to be less specialized at go, as in less a niche group (not necessarily strength-correlated niche) and players might be more casual. This might translate into the strengths of the playerbase. Even the time of day may be a factor.
It might be hard to directly compare different servers even if they had identical ranking systems. However they don't have identical ranking systems, which makes the comparisons even harder. Rank labels are not equivalent to player strength, but you could assume they are strongly correlated, but not by labels with the same name. So you could make a general statement like the ones made in this thread, that (with DAN ranks) KGS rank = Tygem Rank + 2, so 1 DAN kgs would be 3 Dan tygem. You can expect this claim to be somewhat consistent, if it's based on collected data, but you should expect some kind of error margin, which may appear in the form of distorted uniformity so you might not find the same distance between the ranks at all levels (like high dans might have a longer distance between them), or simply congruence (like low 1 dan, high 2 dan) if you're not making claims more specifically.
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