Now you’ve challenged me to sharpen up my vague intuition! I realise it’s not a ‘long-tail’ curve as currently spoken these days (e.g. in https://www.amazon.co.uk/Move-Fast-Break-Things-Facebook/dp/1509847693/ref=sr_1_1?ie=UTF8&qid=1519380181&sr=8-1&keywords=move+fast+and+break+things )
I had in mind a curve shape like https://getrevising.co.uk/https_proxy/6223 - ignore the writing, just the curve shape.
The x (horiz) axis is the error and the y (vert) axis is the count of tie points (TPs) at given error. The full curve would be seen if Max error is set very high. Decreasing Max error is a vertical line that cuts off the right hand end of the curve.
Mean error is a vertical line that’s going to lie v close to the curve’s y-peak and the Median error is a vertical line somewhat to the right - higher x.
Decreasing Max error (moving its vertical cut off line to the left) pushes the other two vertical lines to the left. At very low Max error, Mean error may fall leftward off the peak and decrease rapidly down the slope. Mean error will be more resistant to decrease - may in fact increase a bit as it’s pushed leftward to the peak.
Increasing Max error (moving its vertical cut off line to the right) pulls the other two vertical lines to the right but causes a diminishing increase in Mean and Median error.
Does this correspond with reality? Seems to, in the numerous cases I’ve run. Whether they’re good or poor, larger or smaller photo sets, the Mean and Median error figures seem nearly same in case after case, regardless of Alignment settings, only affected, as I say, by very poor small photo sets, and by the Max error setting.