#One number for how well you played
An error rate is the average amount of equity you gave away per decision. Every decision in an analysed match has a cost: the equity of the best play minus the equity of the play you made, which is zero when you found the best one. Add up the costs, divide by the number of decisions, and you have an error rate.
The best-known one is eXtreme Gammon's Performance Rating, or PR: the average equity lost per decision that was a real choice, multiplied by 500. Because so many players quote their PR, HedgeHog reports its own version of it, XR, counted by the same rules on the same scale, so the two can be compared. HedgeHog's main score is a different one, accuracy. A PR of 5 means that on an average real decision you gave away 0.010 of a point. Lower is better, and 0 would be perfect play by the engine's own judgement.
#What a single error costs
The same cost decides the symbol a decision gets in the analysis. In HedgeHog the ladder is:
| Symbol | Name | Equity lost |
|---|---|---|
?! | Inaccuracy | 0.020 - 0.050 |
? | Error | 0.050 - 0.080 |
?? | Blunder | 0.080 - 0.120 |
??? | Whopper | 0.120 - 0.200 |
???? | Double Whopper | above 0.200 |
Anything under 0.020 is not flagged at all. At that size the play is a matter of taste, or of the engine's own uncertainty, and marking it would drown the ones that matter.
The thresholds are in equity, so they mean the same thing for a checker play and a cube action, in the opening and in the bearoff. One blunder of 0.100 adds as much to your total as five inaccuracies of 0.020, which is why a few large errors usually decide a PR.
#Which decisions count
The divisor matters as much as the total. Dividing by every roll of the match would reward a match full of forced moves and obvious races, so PR counts only the decisions where the choice was real:
- a checker play, when the best and the worst legal plays differ by more than 0.001 (a forced play, where the dice leave one legal move, never counts);
- every cube action you took: each double, each take and each pass;
- a turn on which you held the cube, when doubling was close, within 0.200 of not doubling, unless you were so far behind (No double and Double/Take both below -0.500) that the cube no longer mattered;
- a turn on which you should have doubled and rolled instead.
Every error you made is in the total, whether or not the decision it came from is in the divisor. So a match full of close decisions divides the same errors by more, and a match full of easy ones by fewer.
#Money games and matches on one scale
In a money game an error is measured in points. In a match it is measured in match winning chances, converted to EMG: at the score and cube of the decision, losing a single game counts -1 and winning one +1, and gammons are worth what the match score makes them worth. An error at 2-away 4-away and an error in a money game of the same EMG size are errors of the same size, so a whole match adds up into one PR. How the conversion works is in Equity in backgammon.
#What a good PR is
XR is on eXtreme Gammon's scale, so it reads against the labels that program gives a PR:
| PR (and XR) | eXtreme Gammon's label |
|---|---|
| Below 2.5 | World Champ |
| 2.5 - 5.0 | World Class |
| 5.0 - 7.5 | Expert |
| 7.5 - 12.5 | Advanced |
| 12.5 - 17.5 | Intermediate |
| 17.5 - 22.5 | Casual Player |
| 22.5 - 30.0 | Beginner |
| Above 30.0 | Distracted |
Treat it as a band, not a grade, for three reasons.
- It depends on the engine. A PR is a distance from what the engine thinks is best. A stronger engine finds mistakes a weaker one agreed with, so an XR and a PR share a scale but are two engines' opinions, and two numbers are strictly comparable only when the same engine measured both.
- It depends on the depth. A deeper analysis sees further and finds more. Compare numbers measured at the same depth.
- One match is noisy. Some matches are full of close, difficult positions and some are straightforward races. Your PR over one match says as much about the positions you were dealt as about your play. Ten or twenty matches say much more.
#PR or accuracy
HedgeHog's own score for a match is accuracy: how often you got a decision right, with big mistakes weighted heavily. It moves less than PR when two analyses disagree by small amounts, and a single blunder shows in it more clearly. How the two compare, and why they can disagree about the same match, is in Accuracy versus PR.
#Luck is not in it
PR and accuracy measure decisions, never dice. Losing a match to a lucky sequence does not make either worse, and winning one with a string of doubles does not make either better. They move only when your play does. A routine for improving them is in How to get better at backgammon.