Hello everybody, I´m new to this forum.

I have played a game in backgammon galaxy and I don´t understand the level of play. I lost less equity than my rival and got worse level of play.

I write down the results:

Me (level 1455): Total equity lost: -0,12; Level of play: Master 4.62
Rival (level 1763): Total equity lost: -0,29; Level of play: International Master 3.92

Shouldn´t level of play be proportional to equity lost?

They should, and most of the time they do. But there are matches where they don't seem to correspond. Looks like you played one here.

Let me preface this by saying that I am not sure what I state below is accurate. So, please take it with a grain of salt. I'm only stating what I think should be true. Whether it is true or not is another story.

Level of play, I assume, not only takes into account the amount of equity lost, but the difficulty of the decisions each player has to make. I'm guessing most of the time, the decision-making difficulty for each player is close enough to the same that it isn't much of a factor in the level of play calculation; however, occasionally, the difference is more substantial and one player faces significantly more difficult decisions than the other.

Who played better, the guy who only had one or two tough decisions and lost 0.12 in equity or the guy who had a dozen or more tough decisions and lost 0.24 in equity? Honestly, I don't know, but level of play quantifies it and comes up with an answer. There are definitely indications that the person who made six times as many tough decisions and only lost twice as much equity played a better game and deserves the better level of play.

Again, I don't know if I'm right, but I'm thinking difficulty of the decisions has to play a roll in calculating the level of play for individual matches. Over time, when the law of averages catches up, maybe it doesn't need to be factored into a level of play calculation, but over the short-term, it wouldn't really be a very good indicator of a person's skill level without it.

I think I have got the solution to my problem. I have been reading how xg calculates it. The formula of level of play is (-equity lost / decisions) x 500. A decision is not made when you are in the bar and can´t enter or when the movent is mandatory. In that game I played, I stayed a lot of time in the bar without entering, so I had far less decisions than my opponent. That said, my lelvel of play (PR) was worse.

"Difficulty of decision" is purely a human evaluation and XG can't take it into account. A good human player could assign an approximate value, but a machine can't.

Well, I guess I was on the right track with decisions, anyway.

Simply dividing the equity lost by the number of decisions makes perfect sense to me now. Thanks for the update.

Note a decision is not only a not-dancing-move but a move where you can possibly (even absurdly) lose equity.

If whatever you play you have 100% or 0% (bearoff with huge advance for ex.) it is not a decision.
If whatever you play your opponent will have a double/pass it is not a decision.
But if some stupid move leads to a too good fo him, it was a decision.

Let's say your two last checkers are on the point two and one and your opponents have two remaining checkers also. 65 is clearly not a decision. 61 is because there is a legal move that doesnt win.
BUT if your opponents had 5 checkers left none of these moves is a decision because you have 100% even when playing the doomest move.

Hope it was helpful.