I get that the main goal is to show how the placement is used, but do you not use Glicko instead of Elo like the rest of the site? https://www.chess.com/article/view/chess-ratings---how-they-work
How the rating system works

ok, that a slight surprise to me. Not that I think the difference between elo and glicko is a big deal.
In any case, well explained.

so is there no difference between a 90-30-20-10 point win vs a 50-40-30-20?
correct! The goal is not to have as many points as possible, but just to have more points than your opponents.

I am really disappointed that anything ELO based was used. It is a terrible rating system. It is an estimate of estimates that penalizes players for losing to players with a weak rating, without proper consideration for their actual strength. It also penalizes players for a single mistake, if it resulys in a loss, regardless of how good their play was otherwise, and also fails to reward players for playing above their strength, when they lose to players who are far above their own rating and strength.
You have an opportunity to utilize the points and reward people for their performance, instead of letting the rating system unjustly reward and penalize.
My recommendation to you is to stop looking at the ELO system as a work of genuis and see it's failings for what they are. It has been time for something better for many years now.

I'm not going to say that the elo or Glicko or any rating system is perfect, but any system that is not result based sounds bad to me. It doesn't matter how many good moves you play if you blunder everything away with one move. If you can not produce the results, then you were just not good enough.

lol and how are you supposed to calculate performance in 4-players? how do you know if a move is good or bad? there is no such thing as centipawn loss like in chess, it simply would not make any sense
Any move, even giving your queen for free, could be a strategy

lol and how are you supposed to calculate performance in 4-players? how do you know if a move is good or bad? there is no such thing as centipawn loss like in chess, it simply would not make any sense
Any move, even giving your queen for free, could be a strategy
Feel free to read my forum in the 4 player chess club entitled"How to make this great variant of chess, more competitive"...
I would forward a link, but I am on my cell phone.

lol and how are you supposed to calculate performance in 4-players? how do you know if a move is good or bad? there is no such thing as centipawn loss like in chess, it simply would not make any sense
Any move, even giving your queen for free, could be a strategy
Feel free to read my forum in the 4 player chess club entitled"How to make this great variant of chess, more competitive"...
I would forward a link, but I am on my cell phone.
The formula is basically:
Rating = 100 * Points per move * ( 3 * wins + checkmates - losses )
A formula that does not take into consideration of the strength of your opponents, rewards players for resigning early instead of playing many moves that does not give many points and rewards players for playing out dead won positions to get as much points as possible instead of just winning as quick as possible. It also gives players with more losses than ( 3 * wins + checkmates ) a negative rating (and in that case having many points/move is a bad thing since it will make your rating worse).
The formula also values the quantity of games played. If we consider the Points per move and checkmates to be constants, then playing 2 games with one win and one loss will result in your rating to go up. If we take checkmates into account the rating will go up even more.
One more thing I want to add is that it is a bit unclear to me what wins and losses mean. The game is about points and get to 1st, 2nd, 3rd or 4th place. If wins is first place and loss is 4th place, then that basically means that the other positions does not matter.

lol and how are you supposed to calculate performance in 4-players? how do you know if a move is good or bad? there is no such thing as centipawn loss like in chess, it simply would not make any sense
Any move, even giving your queen for free, could be a strategy
Feel free to read my forum in the 4 player chess club entitled"How to make this great variant of chess, more competitive"...
I would forward a link, but I am on my cell phone.
The formula is basically:
Rating = 100 * Points per move '* ( 3 * wins + checkmates - losses )
A formula that does not take into consideration of the strength of your opponents, rewards players for resigning early instead of playing many moves that does not give many points and rewards players for playing out dead won positions to get as much points as possible instead of just winning as quick as possible. It also gives players with more losses than ( 3 * wins + checkmates ) a negative rating (and in that case having many points/move is a bad thing since it will make your rating worse).
The formula also values the quantity of games played. If we consider the Points per move and checkmates to be constants, then playing 2 games with one win and one loss will result in your rating to go up. If we take checkmates into account the rating will go up even more.
One more thing I want to add is that it is a bit unclear to me what wins and losses mean. The game is about points and get to 1st, 2nd, 3rd or 4th place. If wins is first place and loss is 4th place, then that basically means that the other positions does not matter.
Ok, now I am on my desktop and can do a better job of replying and stating my case. I will first post my OP from the other forum and then address your contentions one by one.
Christopher_Parsons
Player Efficiency Rating = { ( Total Points scored / Games played = Points per game) (Points per game / ( Moves played / Games Played ) = Points per move) ( Checkmates + ( Wins × 3 ) - Losses) × Points per move ) = Player Efficiency Rating) }
A hypothetical model:
1000/50=20
20÷(750/50)=1.33
18+(10×3)=8
8×1.33=10.64
If you wanted to multiple it by 100, to make it appear more Elo like, the rating would be 1064
This is your reply from above :
A formula that does not take into consideration of the strength of your opponents, rewards players for resigning early instead of playing many moves that does not give many points and rewards players for playing out dead won positions to get as much points as possible instead of just winning as quick as possible. It also gives players with more losses than ( 3 * wins + checkmates ) a negative rating (and in that case having many points/move is a bad thing since it will make your rating worse).
To make the accusation that my rating system would fail to consider the strength of an opponent, but standing by the ELO system which estimates and then estimates based on estimates, isn't well thought out. If a player that is 1800 ELO, but new to a particular rating pool, kicks the snot out of a 1300 in the 1800's 1st game in the system, the 1300 is penalized for losing to a 1200 player. This is even worse than any one single complaint you have made against my system, including failing to consider strength and wrongfully rewarding someone.
In my system, everyone would essentially start at zero. You have given the idea of starting at 0 or being in the negative, a negative connotation, when in reality, it is simply like the inverse of the way golf's par system works.
As for players playing for points, before going checkmate, it is already happening and will continue to happen, unless a guy realizes he can score 20 points in 2 moves for mate, or score 30 in 5 moves, and thus it would hurt his points per move average. This gives an incentive to checkmate, while still keeping the importance of points and being efficient with one's moves. It also helps to deal with people making a bunch of senseless moves in a short span, to try running out your timer.
The formula also values the quantity of games played. If we consider the Points per move and checkmates to be constants, then playing 2 games with one win and one loss will result in your rating to go up. If we take checkmates into account the rating will go up even more.
You make the accusation that my system rewards for more games being played, but doesn't ELO ? You can't climb to the top, without playing games. In my system, your rating doesn't automatically go up, if you play more games. It only will, if you perform well enough for it to go up. If you play more games and don't perform well, it will only go down, the same as in ELO.
One more thing I want to add is that it is a bit unclear to me what wins and losses mean. The game is about points and get to 1st, 2nd, 3rd or 4th place. If wins is first place and loss is 4th place, then that basically means that the other positions does not matter.
It seems to me that this is the biggest part of your problem, in understanding and accepting my system. You seem to be confused by what wins and losses are and what quality of play is, as it pertains to 4 player chess. If you score more points than everyone else, you won a victory over 3 other players. If you came in 2nd, you won a victory over 2 over players, but you lost to one player. If you came in third in points, you won against one player and lost to two players.
I find a real big hang up that people have with this game is the don't want to accept losing to someone whom they checkmated, or someone that resigned. This isn't regular chess. If you can't handle the thought of wins and loses being dictated by points, then this variant isn't for you. Perhaps they will make a variant of this that is dictated strictly by checkmate and resignation is a lose. I wouldn't like it as much. I find the points system makes for an interesting twist and dynamic. It does a better job of rewarding players for great play. I would hate to see guys who checkmate 2 others and score far more points than anyone else, lose to the last player standing.
PS edit:
I just realized while lighting my grill that, I need to rethink the win/loss structure of my formula. Thanks for pointing out the confusion you have with wins and losses. Since I agree that a win to a player or a loss to a player, is only by points and that checkmate is simply a vehicle to help get you there or remove someone from the game, I need to rethink my formula, so that there is a distinction between beating an individual or beating everyone. I think a player should be rewarded for beating everyone as individuals and as a group, in one game, as opposed to what the reward would be for beating three individuals in three separate games. I will get back to you on this. I am a busy guy.

lol and how are you supposed to calculate performance in 4-players? how do you know if a move is good or bad? there is no such thing as centipawn loss like in chess, it simply would not make any sense
Any move, even giving your queen for free, could be a strategy
I wanted to address this earlier and more specifically, but was at work and only had a cell phone at my disposal.
I would never waste my time trying to base someone's quality of play, simply by their average error and this is why. I will use a series of questions with which you can feel free to offer a rebuttal for, simply by answering.
Which engine should we use to find out what the best move is ? Would that engine be strong enough ? Are you sure ? What ply depth should we set it at ? Maybe we should run it with an infinite timer setting ? How big would the hash table need to be ? Are you sure we could find out what the best move actually is this way ? How could we even know what the quality of the play is with CP loss/average error, if we don't even know for sure what the best moves are ?
The point you make about giving away a queen for free is an interesting one, in spite of the fact that I wouldn't use CP loss / average error. After all, you could give away a few points to gain a larger number of points, to gain a checkmate and to simply stay in the game, to have a chance to gain more points, to buy time, etcetera. Considering the complexities of this game, it needs something more than what they have to reward people for the quality of their play. My system will do that and take in consideration those choices like, sacrificing a queen. In regular chess, you are only rewarded for doing this, is you beat the other guy by checkmate, his timer runs out, or you get a draw and he is higher rated. If 4 player chess, you can be rewarded in several different ways, including those.

Your rating system do not take into account the strength of your opponents. That is very simple to see, it is not part of the equation.
When it comes to negative values, the values will get more negative with more losses and more negative with a high average points/move. Do you not find it strange that getting more points per move makes your rating lower? Someone in the negative would be best at an average of 0 points/move.
The thing with your system is that not very much is needed to not lose rating. If you get third place with 0 checkmates you get 1 win and 2 losses. In the equation we get checkmates + 3 * wins - losses = 0 + 3 * 1 - 2 = 1. You gain rating points by getting to third place. If you should go +/- 0 you need to get 3 checkmates and 4th place which is quite unlikely to say the least.
My question about wins and losses was mainly there because I had a hard time to imagine that getting to third place you actually gain you rating points. It looked strange to me
Some of the major things for a good rating system to is to reward quality over quantity (usually achieved by making it equally easy for your rating to go up and down), take your opponents rating into consideration (winning against better players is a big achievement) and make it only based on results and not some other arbitrary values. If you disagree with these ideas, then I guess we have to agree to disagree.

As a side note, I don't think it is obvious at all that 1st place is the same as winning against all opponents. If I tell someone I got 3 wins in four player chess most people would think I got 1st place in 3 games and not 1st place in one game. It makes sense when calculating ratings though.

Your rating system do not take into account the strength of your opponents. That is very simple to see, it is not part of the equation.
No rating system can take into account what the opponent's rating is, until they first get a rating. In defense of my ideas, why reward someone for beating a player is a particular rating, if we don't even know if their rating reflects their actual strength ? That is why my system bases it on individual performance and not someone's performance in conjunction with someone's repute. What if they haven't played in many years and their rating is well over their strength ?
When it comes to negative values, the values will get more negative with more losses and more negative with a high average points/move. Do you not find it strange that getting more points per move makes your rating lower? Someone in the negative would be best at an average of 0 points/move. Getting more points for move should make your rating go higher. Either you or I looked at the math wrong. Why would I make better performance equal a worse rating ?
The thing with your system is that not very much is needed to not lose rating. If you get third place with 0 checkmates you get 1 win and 2 losses. In the equation we get checkmates + 3 * wins - losses = 0 + 3 * 1 - 2 = 1. You gain rating points by getting to third place. If you should go +/- 0 you need to get 3 checkmates and 4th place which is quite unlikely to say the least.
As I stated above, but you didn't directly address it, and instead restated your previous case without addressing my rebuttals above, I will say again, you helped me to realize that I needed to clarify wins against individuals and the group more clearly. As I also said, give me some time and I will rework the formula. I realize you don't necessarily know what I am thinking, and I may not have stated it well either, in mathematical terms, but it should have been more clear to you in my opinion, what I was trying to say with my formula. You seem more interested in bashing my idea than accepting that there is something better than ELO.
My question about wins and losses was mainly there because I had a hard time to imagine that getting to third place you actually gain you rating points. It looked strange to me
Some of the major things for a good rating system to is to reward quality over quantity (usually achieved by making it equally easy for your rating to go up and down), take your opponents rating into consideration (winning against better players is a big achievement) and make it only based on results and not some other arbitrary values. If you disagree with these ideas, then I guess we have to agree to disagree.

I might not have addressed everything, but I have a hard time discussing several topics about the rating system at the same time. I will admit that my first post regarding your formula was highly negative criticism. Basically I was against both which variables were used and in some regards how they were used. I will wait for your update though. One reason I wanted to be overly critical is because I don't get why you seem to have such a strong belief that you can create a better system than already exist.

I might not have addressed everything, but I have a hard time discussing several topics about the rating system at the same time. I will admit that my first post regarding your formula was highly negative criticism. Basically I was against both which variables were used and in some regards how they were used. I will wait for your update though. One reason I wanted to be overly critical is because I don't get why you seem to have such a strong belief that you can create a better system than already exist.
People give little credit to faith, but how could you accomplish anything, if you didn't first believe you could? Why are improvements to any of the things that we utilize in life ever made? There is an old saying, there is always room for improvement. If you believe that it is just that I am not capable, though the theory is plausible, so be it. I won't be last person doubted and nor are you the first to doubt me. Kepler was doubted and the son of a wealthy man, with nothing better to do, took the time to investigate his " theories" and found Kepler was right. Trying to find a reason why it is that, I have a vision for how to accomplish such an undertaking, though I am not a mathematician, to me is like trying to explain why you like your favorite color. If you must know, I am an electrician. I took tests in middle school that determined I should be an electrical engineer. I loathed the idea of sitting around drawing pictures and calculating math formulas, but the irony is, the older get, the more I enjoy it. I used to want to do physically oriented things and enjoy playing with my work, after I was doing. My physicality is waning and my mind hasn't slowed down. I had to take algebra, trigonometry, and Pythagoran Theorem, just to get into the electrical workers union program. I have a college credit from a local community college for it. I spend my days planning and problem solving circuitry built of various parts that I could use and can always see, buried behind walls, beneath floors, above ceilings, underground, etcetera. I have to plan things or imagine things from beginning to end and from end to beginning, just to see how it is best to build or solve. If I tell you I have a vision for something abstract and mathematical, I am not putting you on or just trying to get attention. I am dead serious about it.
Tell me how to calculate the wire size for a 7.5HP 480 volt 3 phase motor that will operate 350ft from the power source and in an average ambient temperature of 115 Fahrenheit?
Those are kinds of problems I have to solve on the fly to do my job, on top of the mechanical challenges for how to mount and install all of the equipment.
Update August 2018
4 Player chess uses the glicko2 rating system.
The rating calculations are still done as described below.
For teams, note that as we use glicko now, you don't necessarily gain or lose the same amount as your teammate. This is because your teammates deviation is likely different from your own, and a player's deviation should not affect anyone's rating change other than his own.
Deviation = "Confidence that the rating is accurate". The higher the deviation, the higher the change in rating will be.
Lots of players have been asking about the rating system, so here is a rundown of how it works.
4 player chess uses the standard Elo system with a few modifications. Each four-player chess game is treated as a standard chess game amongst all the players. In other words,
( Top rated player in team * (2/3) + lower rated player * (1/3) ) / 2
2. The corresponding team ratings are used to determine the difference given to the winners and losers.