As a new player I'm still trying to develop a feel for how often a better player (lower error rate) should beat a worse player (higher error rate). In chess it's a very high percentage of the time. In heads-up poker it's slightly over 50% of the time. Obviously it depends on lots of factors like how different the error rates are and what score the match is played to. I found a couple of tangentially related threads (mostly on single games) but nothing directly applicable to matches. I could take a crack at actually modeling this with different levels of sophistication, but as a first pass I thought I would ask here for ballpark estimates.

Based mostly on gut feeling (or rough calculations if you've seen them!), how often would you expect:
(1) a 15-average-PR player to beat a 10-average-PR player in a match to 3? to 7?
(2) a 15-average-PR player to beat Bill Robertie in a match to 3? to 7?

As I recall Snowie used to give a match winning probability based on each players error rate. Not quite what you wanted but close. This feature was not included as part of XG.

I found one specific data point in this old article from Phil Simborg. Apparently according to Snowie PR 3.8 vs. 12.5 has a 93% win chance in a match to 3. Higher than I would have thought! But roughly consistent with me playing against XG I guess.

That seems way, way off. In a 3-point match, I would think a player playing at 3.8 would be something like 60-65% against a decent intermediate. (PR about 10-14). Take the match length up to 21 to 25 points and I think you could reach that 93% number.

I can't vouch for the correctness of this, but here's what I found:

PR to Elo:

https://www.reddit.com/r/backgammon/...th_error_rate/

Elo to winning chances based on match length:

https://bkgm.com/faq/Ratings.html

Thanks for the references! I calculated and plotted the implied win probabilities from the links that Z provided (where we assume a relationship between PR and Elo, which is more directly connected to winrate). Looks closer to what I might have initially guessed (if not somewhat closer to random) — this says PR 15 has about a 20% chance of beating PR 5 in a match to 15, for example.

60-65% was a great guess btw. According to this model PR 3.8 has a 60% win probability against PR 10, and 66% against PR 14.