Update

elo.md

@@ -10,7 +10,7 @@ The Elo system was created specifically for chess (even though it can be applied
 
 Yet another shortcoming is that **ratings (including relative differences) depend on the order of games**. I.e. when several games are played between N players and we update the ratings after each game, then the ratings of all the players (and their differences, i.e. predictions the system will make) at the end will depend on the order in which the games were played -- playing the games with exact same results but in different order will generally result in different ratings. This also holds for grouping: we may update ratings after each game or group several games together and count them as one match, outcome of which will be the average outcome of all the games -- and this may affect ratings too. So the rating partially depends on something that has nothing to do with the player's skill. This may not be such a huge problem in practice, tiny differences and fluctuations are usually ignored, but eventually this IS an undesirable property of the system. Some other systems address this by always computing every player's rating based on whole history of games he ever played, which fixes the issue but also brings in more computational complexity (imagine having to recompute everything from scratch after every single game, AND having to keep the record of complete history of all games).
 
-It also must be said that **Elo is a [simplification](approximation.md) of reality**, as is any attempt at capturing skill with a single number -- even though it is a very good predictor of something akin a "skill" and outcomes of games, trying to capture "skill" with a single number is similar to trying to capture such a multidimensional attribute as intelligence with a single dimensional [IQ](iq.md) number. For example due to psychology, many different areas of the game to be mastered and different playstyles [transitivity](transitivity.md) may be broken in reality: it may happen that player *A* mostly beats player *B*, player *B* mostly beats player *C* and player *C* mostly beats player *A*, which Elo won't capture. However this is not an issue of the Elo system specifically but rather of our simplified model of reality -- any other system that tries to capture skill as a one dimensional number, no matter how advanced, will suffer the same flaw.
+It also must be said that **Elo is a [simplification](approximation.md) of reality**, as is any attempt at capturing skill with a single number -- even though it is a very good predictor of something akin to a "skill" and outcomes of games, trying to capture "skill" with a single number is similar to trying to capture such a multidimensional attribute as intelligence with a single dimensional [IQ](iq.md) number. For example due to psychology, many different areas of the game to be mastered and different playstyles [transitivity](transitivity.md) may be broken in reality: it may happen that player *A* mostly beats player *B*, player *B* mostly beats player *C* and player *C* mostly beats player *A*, which Elo won't capture. However this is not an issue of the Elo system specifically but rather of our simplified model of reality -- any other system that tries to capture skill as a one dimensional number, no matter how advanced, will suffer the same flaw.
 
 Besides mathematical inaccuracies Elo (as well as other systems in general) also comes with more potential practical problems such as creating focus on grinding (players strategically choosing weaker opponents to maximize their rating), players refusing to play in order to not lose points, removing [fun](fun.md) from games by implementing super effective matchmaking that just maximizes number of draws etcetc. Despite all the described flaws however it must be held that Elo is pretty nice and very useful, it's usually just its wrong application (for example in the mentioned matchmaking) where it starts to create trouble.