On the topic of "islands", I wonder more about the mathematics of it. Like in a population the size of the FargoRate database, what would constitute an island? Would it be a social graph of players in the system and have played each other and have zero connections to the rest of the tapestry of players? How do you analyze that. By the size of the island? I have to imagine there's a fair number of 2-player islands where their only games in the system was a single Salotto match they played against each other. Maybe you throw that island out because it's size 2? Maybe you throw it out because no player in that island has an established rating. How many islands are there size 3? Size 4? How big does the island get in the FargoRate database? Would you be able to say there are zero islands size 20 or 50?
And lets get realistic. Maybe we assume in an island of 20 that someone played at least one game outside the island. So what now constitutes an island? Is there a mathematical attribute you can apply to the island for its overall connectedness? How much connectedness does it take for it to no longer be an island? Is 5 players having each played 20-30 games outside the island sufficient? Is that a static number to anchor the island into the larger tapestry? Or is it proportional to the size of the island? I'm assuming 5 players playing 20-30 games outside the island is a stronger connection than 1 player playing 150 games outside the island. Is there a mathematical way to assigned connectedness of the island that accounts for the diversity of connections. I imagine if those 5 players played all 20-30 games against the same person then that's not as strong as if they played their games against a good variety of players at different ratings. So realistically, any island we have will have fuzzy edges to it. Does that make identifying islands impossible? Or are there algorithms that can do it?
If someone poses a hypothetical of a remote town with 70 players (or less). Fairly stable. Few enter or leave. Maybe 1 team goes to nationals and plays others but most everyone else stays home. Almost nobody travels to other areas to play in regional tournaments. Could FargoRate find if that situation existed in their database? Could they prove demonstrably that it does not exist in their database? If it does exist, could FargoRate attribute a confidence score to how globally anchored those players ratings are? If so, I think that would make for an extremely interesting video.
And lets get realistic. Maybe we assume in an island of 20 that someone played at least one game outside the island. So what now constitutes an island? Is there a mathematical attribute you can apply to the island for its overall connectedness? How much connectedness does it take for it to no longer be an island? Is 5 players having each played 20-30 games outside the island sufficient? Is that a static number to anchor the island into the larger tapestry? Or is it proportional to the size of the island? I'm assuming 5 players playing 20-30 games outside the island is a stronger connection than 1 player playing 150 games outside the island. Is there a mathematical way to assigned connectedness of the island that accounts for the diversity of connections. I imagine if those 5 players played all 20-30 games against the same person then that's not as strong as if they played their games against a good variety of players at different ratings. So realistically, any island we have will have fuzzy edges to it. Does that make identifying islands impossible? Or are there algorithms that can do it?
If someone poses a hypothetical of a remote town with 70 players (or less). Fairly stable. Few enter or leave. Maybe 1 team goes to nationals and plays others but most everyone else stays home. Almost nobody travels to other areas to play in regional tournaments. Could FargoRate find if that situation existed in their database? Could they prove demonstrably that it does not exist in their database? If it does exist, could FargoRate attribute a confidence score to how globally anchored those players ratings are? If so, I think that would make for an extremely interesting video.