Why does "restrict rank" allow ? players?

[dragon-devourer]

@GreenAsJade

Are you willing to actually look at the maths?

I have already looked at the maths Here’s the evidence that I have:

Glicko-2 does not require accounts to start at 12 kyu. So why do we do that?

I agree that 1500 is arbitrary The fact that 1500 corresponds to 6 kyu basically says that if everyone is given the same starting point of 1500 and Glicko is allowed to do it’s thing, then the players that end up with this arbitrary rating of 1500 are those of a strength of approximately 6 kyu in other systems (AGA, EGF, etc.), as determined by surveying members for anchor points. Therefore, we will call this arbitrary rating of 1500 by a certain rank to give it real world meaning and that…

@dragon-devourer

Looking at the Glicko equations … the Glicko equations mean that:

• Playing stronger opponents has more potential to increase your rating than playing weaker opponents (step 3, definition of E ~ 1 / (1 + exp(mu_j)) where mu_j is opponent rating). The size of this effect is relative to your current rating (the above is actually E ~ 1 / (1 + exp(-(mu - mu_j))) where mu is player rating).
  …
• Opponents with a high deviation are weighted less favourably than opponents with a low deviation (step 3, definition of g ~ 1 / sqrt(1 + phi^2) where phi is deviation).
  …
• Winning will increase your rating while losing will decrease your rating (step 4, definition of Delta). Again, results against opponents with a high deviation are weighted less favourably.
  …

Thank you @GreenAsJade for offering those links as evidence However, these are not evidence that Glicko-2 must start at the midpoint to avoid drift. Rather, they are just evidence that this is an opinion held by a number of forum posters. Just look at these quotes (emphasis added):

@BHydden

From my understanding glicko needs a central starting point

Not evidence that Glicko needs it, just that @BHydden believes it.

@mekriff

Actually no… Glicko doesn’t NEED it, Glicko RECOMMENDS it. And the statistics when setting it up (as we are told) has more accuracy when it starts at 1500.

Not evidence that an initial value of 1500 leads to statistically more accurate ratings, just that @mekriff has heard that from someone else.

@anoek

I do think it’s the mathematically best way of placing folks quickly

Not evidence that it is the mathematically best way of placing folks quickly, just that @anoek believes it.

There is actually an important point in what mekriff was saying though. Note the use of the words “when setting it up”…

When there is a rating system update, the new system is applied retroactively to the entire game history. Therefore, all accounts need a starting value. Of course, we cannot know the historic true strength of each account at the time when they signed up. If fact, it is impossibleto know because our system doesn’t exist yet so there is no way to relate our rating scale to other systems.

But I’m not arguing to change that. That should remain as 1500 for all. This is necessary just to initialise the whole system, work out the current ratings of our current population and use anchor points (like people’s declared AGA / EGF rank) to relate our rating scale to ranks in other systems, e.g. 1500 = 6 kyu.

But now that we have an established system, what if new players join OGS? Glicko-2 says:

@Glicko-2

If the player is unrated, set the rating to 1500

But if a player is new to OGS but already has an AGA / EGF / KGS / DGS / whatever rank, then are they really “unrated”? No, they are not. We can assume their OGS rank will be close to their whatever rank, work out the corresponding rating and start them from there. Deviation and volatility would still take the default values as we don’t have any better information for that. To be clear, this would only apply to accounts created after the declared rank system is implemented and released.

And what about new accounts who don’t know their rank but can at least declare their general skill level at sign up? Are they “unrated”? Not really. If they declare they are a complete beginner, it is safe to assume their true rank is somewhere around 30 kyu. Better to start them from there, that 6 kyu, which is obviously completely wrong.

As for whether the maths says that new players that join after the system is established have to start on 1500… It does not. Actually, examination of the equations shows that it’s worse to start such players from 1500 because it is wrong in most cases, often way wrong, so alters their opponents’ ratings due to an “unexpected” result that actually could have easily been expected with declared initial rank. Although the high initial deviation reduces the impact of these incorrect initial values on other players’ ranks, having a more correct initial rating (even just right ballpark) would remove this impact completely and would be a much nicer experience for new accounts and their opponents in terms of automatically matching opponents of similar true strength.