The model never observes anyone's strength. It only sees placings: who beat whom on 950 tasks. From those it fits a strength estimate, and every estimate carries a standard error, a measure of how much the data pins it down. The bell curve below is the model's honest belief about where a contestant's true strength sits.

The band you see on the ladder is the middle 95% of that curve: the estimate plus or minus 1.96 standard errors, leaving 2.5% of belief in each tail. Both curves above share one peak. Two contestants can have the same dot on the ladder while one was fitted on 54 tasks and the other on 5, and the second's band sprawls across the axis. That sprawl is not indecision; it is the model refusing to claim precision the data cannot pay for. It is also exactly why one-series contestants wobble.

The rank range in the hover tooltip comes from a simple move: slide the contestant's strength to each edge of their band, hold everyone else at their dot, and count heads above. Since it moves one contestant at a time, read it as a floor on the true wobble; letting the whole field resample at once would spread ranks further still. The full machinery lives on the methods page.