How to analyse an endgame quickly? I am a relatively new player (less than 1 year, ungraded) but I feel I have made good progress so far. I am playing competitively with players in the 1300-1500 region and would like to continue my improvement.

Middle game is my strong point for sure, I am able to muddle through some common openings and get into a complex middle game quickly, as that is where I am strongest. But I can't get over the hurdle that more experienced players seem to be able to instinctively recognise if an endgame is won, drawn or lost.

I want to spend my efforts in understanding common endgame patterns and how to handle them. Here is an example of a position I found myself in recently as white. My opponent felt it was a draw but it took me a long time to agree.

[FEN "8/5kp1/5p1p/4p3/nB1pP3/1b1P1P1P/5KP1/2N5 b - - 0 1"]


My question

Other than simply playing more games and gaining more experience, are there any patterns I should be looking for in an endgame such as the example given, so I can more easily determine if a position is won/drawn/lost?

Note: I see a number of similar questions being asked, and the general responses tend to be "practice more, here's a book/website of endgame positions for you to analyse". I'm looking more specifically for people who can explain endgames in a bit more detail, I'm not afraid of a bit of maths.
There are all kind of endgames, so it is a bit difficult to generalize, but still there are a few things that are relevant in many cases.

Just like in the middle game you can evaluate the position based on for instance:


material (this is often the most important)
piece activity
weaknesses in pawn structure


Unlike in the middle game "king safety" is often irrelevant as with reduced material it is difficult to get mated and in fact the king often plays an active role in defending/attacking pieces.

If material is equal (as in this example), in many cases you can only win by promoting a pawn. The goal is then simply to create a passed pawn and push it to the other side of the board. To do this, you can either capture opposing pawns or make use of a pawn majority (basically, with the support of your own pawns to walk passed the opponent's pawns). So you should focus on how to create a passed pawn (and of course how to prevent your opponent from doing the same).

In order to improve your endgame technique you should also familiarize yourself with the most common endgames, such as:


mating with K+Q vs K, K+R vs K, K+BB vs K
winning or defending K+P vs K
various endgames with pawns on both sides
K+R and pawn(s) vs K+R (and pawn(s)). This is a very common endgame, but also very difficult to play properly. Perhaps too difficult at your current level.


Also you should know typical themes that appear in endgames like:


zugzwang
corresponding squares
triangulation
stalemate




With this in mind, regarding your example, you note that:


material is equal
opposite colored bishops (which tend to be more drawish)
symmetric pawn structure 
blocked pawn chains
pawns on squares of the same color as the opponent's bishop (i.e. they can be attacked by either player. If the pawns were on the same color as the players' bishops, the position would be even more drawish as pawns would be even harder to attack and there would be an additional defender for the pawns (the respective bishop).
weak pawns on d3, g2 and g7


In order to win this position either side would need to create a passed pawn. Because of the symmetrical pawn structure it is difficult to achieve this by pawn breaks except for special situations like this. This leaves as the only option to somehow create a passed pawn by capturing enemy pawns.

How to do this? The most likely candidates for capture would be the weak pawns on d3, g2, g7, however these are easily defended by the king and if necessary the other pieces such as the knight on c1. Also note that it is not really possible to activate the kings (i.e. march the black king to somewhere around c3 or the white one to a more active square), because (i) white/black would have lots of time to attack and win the g7/g2 pawn and subsequently all the other pawns in the chain and (ii) the knight+bishop block the entrance on the a-b-c files (white covers the squares c4, b4, a3, b3 and black the squares c3, b3, b2, a2).

So it seems fairly impossible to just capture the weak pawns and also it seems impossible to create another weakness or passed pawn on the kingside through a pawn break. The last thing I'd check is if there is a possibility for a sacrifice (e.g. white could sacrifice a piece for two pawns on d4. However with the pawns being rather far from the promotion square it seems unlikely to succeed.

An agreed draw would be natural in this position, however at your level there is nothing wrong with playing on in order to practice and it is not impossible to make mistakes in this position. A plan for white could be to play g3 followed by f4 which could lead to another weak pawn on e5 (after capture fxe5 fxe5). Still with correct play it should be a draw.