To answer a potential follow up question: “How does a rating get update?”
Based on match results. Suppose the top 2 teams teamed up to play these middle 2 teams. The match predictor gives Red a nearly 90% chance of winning:
If Red, does in fact win, all 4 teams would have a small ratings change. Both Red teams would have their mean go up slightly and both blue teams would have their mean go down slightly. All 4 teams standard deviations would also get smaller, producing a “thinner” distribution because this was a largely expected result.
If Blue wins, both Blue teams would go up, by more than what they would have done down if they lost (likely about 9 times more, to account for their likely 1 win out of 10 matches). Similar for Red. In this case, all 4 teams’ standard deviations would likely also go up, creating a fatter distribution because of the fairly unlikely result.
If the matchups were more equal (1 of the top teams paired with 1 of the middle teams on each of Red and Blue), leading to a 50-50 prediction, then the winners and losers would all go up or down slightly, and all 4 would have their standard deviations go down.
Edited - Updated the distribution image to highlight in light-blue the area showing Blue’s 10% of winning. Basically showing both Blue teams need to perform significantly better than “normal” and both Red teams performing significantly worse than “normal”