#Two numbers from the same errors
Every decision in an analysed match has a cost: the equity of the best play minus the equity of the play you made. HedgeHog turns those costs into its own score, and reports one more for comparison.
- Accuracy, also called DQI (Decision Quality Index), is HedgeHog's measure. It scores each decision by how bad its error was and averages the scores into a percentage. Higher is better. It measures how often you got it right, with the big mistakes weighted heavily.
- PR is eXtreme Gammon's measure: the average cost per decision that was a real choice, multiplied by 500. Lower is better. It measures how much you gave away. Many players already know their PR, so HedgeHog also reports its version, XR, counted by the same rules on the same scale. Backgammon error rates and PR explains it in full.
The two answer different questions, and a match where they disagree is worth a closer look.
#How accuracy is scored
Each decision gets a score from the band its error falls in. A correct decision scores 1.0, each worse band costs roughly twice as much as the one before, and the worst bands score well below zero:
| Equity lost | Band | Score |
|---|---|---|
| Below 0.010 | Correct | 1.0 |
| 0.010 - 0.020 | Minor | 0.9 |
| 0.020 - 0.050 | Inaccuracy | 0.7 |
| 0.050 - 0.080 | Error | 0.3 |
| 0.080 - 0.120 | Blunder | -0.5 |
| 0.120 - 0.200 | Whopper | -2.1 |
| 0.200 - 0.500 | Double Whopper | -5.3 |
| 0.500 or more | Double Whopper | -11.7 |
The scores of all your decisions are averaged and shown as a percentage, between 0% and 100%. A score below zero is what keeps one catastrophe from being averaged away: a single error of half a point or more cancels out about twelve correct decisions.
The percentage then gets a name:
| DQI | Rating |
|---|---|
| 90% and above | Excellent |
| 75 - 90% | Good |
| 60 - 75% | Decent |
| 40 - 60% | Poor |
| Below 40% | Very poor |
#Same equity lost, three different matches
Take three players who each lose 0.600 in total over a match of 100 decisions, 80 of which are real choices in PR's counting. Their PR is identical: 500 × 0.600 / 80 = 3.75, World Class on the PR scale. Their accuracy is not.
| Player | How they lost 0.600 | PR | Accuracy |
|---|---|---|---|
| A | Twenty inaccuracies of 0.030 | 3.75 | 94.0% |
| B | One catastrophe of 0.600, every other decision right | 3.75 | 87.3% |
| C | Seventy-five small slips of 0.008 | 3.75 | 100.0% |
- Player B made one terrible decision, and accuracy punishes it more than PR does. PR only adds the equity up, so one mistake of 0.600 is exactly as bad as twenty of 0.030. Accuracy says that a player who can make a mistake that size has a hole in their game.
- Player C is slightly off on most decisions. Accuracy scores a cost under 0.010 as correct, since differences that small are within what separates one analysis from another (next section). PR adds the slips up.
So accuracy is the sharper alarm for the mistakes that matter, and PR is a plain sum of equity lost.
#When two analyses disagree slightly
An engine's evaluation is an estimate, and two analyses of the same match, at different depths or by different engines, disagree by small amounts on many decisions. PR adds every one of those differences into its total, so it moves with them. Accuracy mostly does not: a cost that shifts by a few thousandths stays in the same band and keeps the same score, and a cost under 0.010 scores as correct whichever analysis measured it. Only an error close to a band's edge can change its score. So accuracy is the steadier number, and the one to trust when you compare analyses run at different settings.
#Which decisions count
The two numbers also divide by different decisions.
Accuracy counts every decision with a choice in it: every checker play with at least two legal plays, every cube action, and every turn on which you should have doubled. Plays where all the options are worth almost the same still count, and they always score 1.0. A match full of easy decisions, such as a long race, therefore lifts accuracy without saying much about your play.
PR counts only real choices: a checker play counts when its best and worst plays differ by more than 0.001, and a turn on which you held the cube counts when doubling was close. So PR is less flattered by an easy match, and correctly holding the cube in a close position counts in your favour.
A forced play, with only one legal move, counts in neither.
#Which one to follow
- Follow accuracy. It is HedgeHog's own score, steady across analysis settings, and one blunder cannot hide in it behind a run of easy moves. Track it over ten or twenty matches rather than one.
- Study from the error symbols. A match whose accuracy is low had a few large mistakes in it, and those are the decisions to look at first.
- Use XR only to compare with a PR you or an opponent got from eXtreme Gammon (see what a good PR is). Even then, the two are different engines' opinions on the same scale, not the same number.
Whatever you track, the errors behind the numbers are what improve your game. A routine for finding and fixing them is in How to get better at backgammon.