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THIS IS BEING MAJORLY UPDATED. THE REWORK BELOW WILL BE ENTIRELY DIFFERENT FROM THE FINAL REWORK, BUT THIS STILL GIVES A GENERAL IDEA OF HOW IT WILL WORK.-------------------------------------------------------------------------------------------------------------------------------------------

PLEASE give Feedback or even Review the rework if you would like. This took hours upon hours to make and optimize, so it would be really appreciated.

If you do not wish to read the entire post, which is understandable, refer to Section 1 and Section 9. These two sections give a general summary and a list of all the things this Elo rework does and doesn't do effectively.

I will add a poll when I am sure I have finished and it has been reviewed by a few others.

Also note that this is being updated over time, so there may be some mistakes or unfinished things.-------------------------------------------------------------------------------------------------------------------------------------------

• The main section titles are given in bold capital letters and are BLUE.

• The main sections go from Section 1 to Section 9, and may be referred to throughout the post.

• The sub-section titles are given in bold normal lettering and are Black.

• Important information is given in Red.• Important expressions or data is given in Italics. Then I'll Talk like this-------------------------------------------------------------------------------------------------------------------------------------------

Section 1: SUMMARY - WHY AN ELO REWORK IS NECESSARY & GENERAL IDEA-------------------------------------------------------------------------------------------------------------------------------------------

The current Elo system mainly rewards grinding games heavily as opposed to a high win percentage (more indicative of skill). So, I believe that the player win percentage should have a larger impact than it currently does. It also does not give larger Elo gains/losses for a lower amount of games played (which is necessary). For example, a player with 20 games played and a 80% win rate may be extremely good at the game, but with the Elo system in it's current state that would only get you about +100 Elo, which is not indicative of the player's true skill.

As such, I propose a new Elo system fixing "the grind". This new system would use win percentage as it's primary variable, but would still take into account the amount of games played (for example, a very low win % with only 20 games played should give more Elo than a very low win % with 100 games played since 100 games is a larger sample size).

In this rework, a mean win percentage, a standard deviation percentage, and all faction mean win percentages of the population will be used.

You will also be rewarded for having more games with factions of a lower mean population win rate (for example, Neutral Killing) and punished for having more games with factions of a higher mean population win rate (for example, Town).

The difference between Team Elo (minus yourself) and Opposing Elo will also be considered if you are Town or Mafia, but not Neutral Evil or Neutral Killing (see why in Section 3, 7th point).

Ranked Placement will require 20 games played rather than the current 10 to be given an Elo score, because it is a larger sample giving a more accurate Elo score than if the player were to only play 10 games.

The starting (and average) Elo will be set at 1500, and you will gain or lose an amount of Elo from 1500 based on how many standard deviations away from the mean you are, and also the amount of games you have played has some impact, so that too high or too low win % of a player by chance is taken into account.

That is a really good idea! And Great reasoning-------------------------------------------------------------------------------------------------------------------------------------------

Section 2: THE ELO GAIN/LOSS EQUATION-------------------------------------------------------------------------------------------------------------------------------------------

Elo Gain/Loss =

80ln(2X-35) * (new(z) - old(z)) + 1/30*(TM)*(OE - TE) + 20*((AVG% - F%)/AVG%) I cut out all of the variable explanations so the reveiw would be shorter, but I do like the equation.-------------------------------------------------------------------------------------------------------------------------------------------

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Section 3: NOTES-------------------------------------------------------------------------------------------------------------------------------------------

• The maximum amount of games recorded (X) is maxed at

200.

• It should also be noted that If a player is to reach 210 games played, only the last 200 games should be analysed (so the first 10 games do not count). This is known as the

Rolling 200 games. This is so that the Elo is more indicative of the players skill in more recent games and so their current ability as opposed to their old ability, whether it be better or worse.

• The player is required to have played at least 20 Ranked games (placement games) to be given an Elo, so this equation is only for

X>19. Since this equation is not for X<20, instead of gaining or losing Elo from game to game during your placement games, you will instead be given an Elo score on your 20th game using the formula

1500 + 80ln(X-17.5) * (z) + 20*((T)*((AVG% - T%)/AVG%) + (M)*((AVG% - M%)/AVG%) + (NK)*((AVG% - NK%)/AVG%) + (NE)*((AVG% - NE%)/AVG%)). Go to Section 6 for more information on this.

• The minimum total Elo score is 0.

• The maximum total Elo score has no set bound, but would be bounded somewhere. This bound is approximately equal to

1500 + 80ln(383-17.5) * (9.51515) = 5992, so around 6000 Elo. However, this requires a 100% win rate after 383 games, which is obviously impossible.

• The mean Elo score of any given player will be approximately the starting Elo, which is 1500 Elo.

• Differences in Opposing Team's Elo and Your Team's Elo (excluding you) are only considered if you are Town or Mafia. You are excluded from your own Team's average Elo score because if you are included and you have a high Elo, after many games you will be punished HEAVILY in terms of Elo, and if you are included and have a low Elo, after many games you will be rewarded HEAVILY in terms of Elo. As such, you must be excluded from the average of your own team's Elo score. This is why differences between opposing team's Elo and your team's Elo cannot be considered if you are Neutral Evil or Neutral Killing, because you must be excluded, but you are the ONLY member of that faction (if NE or NK). As such, differences in Opposing Team's Elo and Your Team's Elo (excluding you) are only considered if you are Town or Mafia.

• The

z-score (z) is a value showing how well you perform compared to the population of Ranked. A win rate below the population mean Ranked win percentage will result in a negative z-score leading to less Elo, and a win percentage above the population mean Ranked win percentage will result in a positive z-score leading to more Elo.

• A z-score calculator showing the percentage bracket you are in can be found here:

http://onlinestatbook.com/2/calculators ... _dist.html• For example, a z-score of 2 means you are in the top 2.28% of the Ranked population in terms of Win Percentage.

• Estimate of population mean win percentage:

47.66666%• Estimate of Town mean win percentage:

60%• Estimate of Mafia mean win percentage:

35%• Estimate of Neutral Evil mean win percentage:

30%• Estimate of Neutral Killing mean win percentage:

5%• Rough estimate of standard deviation:

5.5% (give or take 0.5%) Got It! All is in order-------------------------------------------------------------------------------------------------------------------------------------------

Section 4: CAPS/RESTRICTIONS ON ELO GAINS/LOSSES-------------------------------------------------------------------------------------------------------------------------------------------

• Refer to Example 1 in Section 5 lower down for an explanation of the below restrictions/caps.

Also note that Restriction 1 has priority over Restriction 2. This basically means gives an order for the restrictions:

1) the usual formula (80ln(2X-35) * (new(z) - old(z)) + 1/30*(TM)*(OE - TE) + 20*((AVG% - F%)/AVG%)) should firstly be used.

2) If necessary (if 80ln(2X-35) * (new(z) - old(z)) = 0), use Restriction 1.

3) If necessary (if Elo change is less than 2 for a win or if Elo change is more than -2 for a loss), use Restriction 2.-------------------------------------------------------------------------------------------------------------------------------------------

Restriction 1-------------------------------------------------------------------------------------------------------------------------------------------

• If you gain 0 Elo from the first part of the formula (which will only happen with >200 games played),

80ln(2X-35) * (new(z) - old(z)), this part of the formula will be restricted to ±20 Elo depending on whether you win or lose (+20 for win, -20 for loss). The next parts of the formula,

1/30*(TM)*(OE - TE) + 20*((AVG% - F%)/AVG%), will still be used, and so the new Elo gain/loss will be:

±20 + 1/30*(TM)*(OE - TE) + 20*((AVG% - F%)/AVG%).

However, a NK or NE loss could give a very small Elo loss, or in very rare cases, a zero Elo gain or positive Elo gain for a loss. For example,

-20 + 20*((0.5-0.04)/0.5) giving -1.6 Elo for an NK loss. To prevent these rare cases where Elo gain/loss is small/incorrect, we will cap the Elo for a loss such that it is always -2 or less, and we will cap the Elo for a win such that it will be always be +2 or more as shown below.

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Restriction 2-------------------------------------------------------------------------------------------------------------------------------------------

• If you win a game, you will ALWAYS

gain 2 or more Elo (capped).

• If you lose a game, you will ALWAYS

lose 2 or more Elo (capped).

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Section 5: EXAMPLES OF ELO GAINS/LOSSES-------------------------------------------------------------------------------------------------------------------------------------------

IMPORTANT: Example 1 (Town Win)-------------------------------------------------------------------------------------------------------------------------------------------

Let's say you win a game as Town. Your old winrate is 112/200 giving a z-score of around 1.51515, and your new winrate is 112/200 giving a z-score of around 1.51515.

NOTE: The new win rate is 112/200 because the 1st win out of the previous 200 games was also a win, so the overall winrate remains the same. If we were to have a win replace a loss, we would have a new win rate of 113/200, making the difference between z-scores much higher than usual and therefore the Elo gain is much higher. Vice versa for a loss replacing a win. However, wins replacing wins and losses replacing losses results in a far smaller Elo change due to the win rate remaining the same, and so the z-score remains the same. As such, the effects of a much higher Elo gain/loss when wins replace losses and losses replace wins is neutralised by the smaller Elo gain/loss when wins replace wins and losses replace losses.The opposing team has a mean Elo of 1650 and your team (excluding you) has a mean Elo of 1600.

Assume that AVG% (Avg win % of all factions) = 0.4766666 and F% (Town win %) = 0.6

As a result, using the Elo gain/loss formula,

80ln(2X-35) * (new(z) - old(z)) + 1/30*(TM)*(OE - TE) + 20*((AVG% - F%)/AVG%), we have:

80ln(2(200)-35) * (1.51515 - 1.51515) [i][note that this = 0] + 1/30*(1)*(1650 - 1600) + 20*((0.4766666 - 0.6)/0.4766666)[/i] = -3.5 = -3.5 Elo loss (for a win?!)

However, using necessary Elo restrictions as shown before, we see that this is not the true Elo difference in this case.

Using

Restriction 1, making the first part of the formula,

80ln(2(200)-35) * (1.51515 - 1.51515), equal to +20, we have:

20 + 1/30*(1)*(1650 - 1600) + 20*((0.4766666 - 0.6)/0.4766666) = 16.5 =

17 Elo gain. Much better.

However, if we had a significantly higher in Elo in your team than the opposing team, for example, we might get a very low or even negative Elo gain as a result. For example:

20 + 1/30*(1000 - 2000) + 20*((0.4766666 - 0.6)/0.55) = -18.5 = 19 Elo loss.

This is extremely unlikely though, since a difference in Elo of 1000 between Town and Mafia would basically never happen. However, in these unlikely cases, we use the restriction that says that you must gain at least 2 Elo gain for a win. As such, we will have a +2 Elo gain in this case. The same applies for a loss.

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IMPORTANT: Example 2 (Town Loss)-------------------------------------------------------------------------------------------------------------------------------------------

You lose a game as Town. Your old winrate was 125/200 giving a z-score of around 2.69697. Your new winrate is now 124/200 (it may be 125/200 still if a loss replaces a loss) giving a z-score of around 2.606061.

Town (except you) and the Mafia/NK/NE have the same mean Elo of 1600.

Assume: F% = 0.6 and AVG% = 0.4766666.

Using the Elo gain/loss formula,

80ln(2X-35) * (new(z) - old(z)) + 1/30*(TM)*(OE - TE) + 20*((AVG% - F%)/AVG%), we have:

80ln(2(200)-35) * (2.606061 - 2.69697) + 1/30*(1)*(1600 - 1600) + 20*((0.4766666 - 0.6)/0.4766666) = -48.08 =

48 Elo loss.

IMPORTANT NOTE: This is a higher change than it would usually be because a loss has replaced a win, due to Rolling 200. This means the difference in win rate is higher than normal, resulting in a higher change in z value from game to game, resulting in a bigger Elo change. This is neutralised however by a minimal Elo change if a loss has replaced a loss, as seen below:

If a loss were to replace a loss instead of the loss replacing a win, (meaning your new winrate is 125/200 giving a z-score of around 2.69697), the ELO loss would be:

-20 + 1/30*(1)*(1600-1600) + 20*((0.4766666 - 0.6)/0.4766666) = -25.17 =

25 Elo loss (Using

Restriction 1 in

Section 4)

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Example 3 (Town Win)-------------------------------------------------------------------------------------------------------------------------------------------

Let's say you win a game as Town. Your old winrate is 60/100 giving a z-score of around 2.24242436364, and your new winrate is 61/101 giving a z-score of around 2.31443.

Mafia/NK/NE has a mean Elo of 1450 and Town (except you) has a mean Elo of 1550.

Assume: F% = 0.6 and AVG% = 0.4766666.

Using the Elo gain/loss formula,

80ln(2X-35) * (new(z) - old(z)) + 1/30*(TM)*(OE - TE) + 20*((AVG% - F%)/AVG%), we have:

80ln(2(101)-35) * (2.31443 - 2.24242436364) + 1/30*(1)*(1450 - 1550) + 20*((0.4766666 - 0.6)/0.4766666) = 20.97 =

21 Elo gain.

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Example 4 (Neutral Killing loss)-------------------------------------------------------------------------------------------------------------------------------------------

You lose a game as NK. Your old winrate was 80/120 giving a z-score of around 3.454545. Your new winrate would now be 80/121 giving a z-score of around 3.35437.

Assume: F% = 0.05 and AVG% = 0.4766666.

Using the Elo gain/loss formula,

80ln(2X-35) * (new(z) - old(z)) + 1/30*(TM)*(OE - TE) + 20*((AVG% - F%)/AVG%), we have:

80ln(2(121)-35) * (3.35437 - 3.454545) + 20*((0.4766666 - 0.05)/0.4766666) = -24.8 =

25 Elo loss.

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Example 5 (Mafia loss)-------------------------------------------------------------------------------------------------------------------------------------------

You lose a game as Mafia. Your old winrate was 12/30 giving a z-score of around -1.393939. Your new winrate would now be 12/31 giving a z-score of around -1.628543.

Town/NK has an average Elo of 1700 and Mafia (except you) has an average Elo of 1400.

Assume: F% = 0.35 and AVG% = 0.4766666

Using the Elo gain/loss formula,

80ln(2X-35) * (new(z) - old(z)) + 1/30*(TM)*(OE - TE) + 20*((AVG% - F%)/AVG%), we have:

80ln(2(31)-35) * (-1.628543 - -1.393939) + 1/30*(1)*(1700-1400) + 20*((0.4766666 - 0.35)/0.4766666) = -46.55 =

47 Elo loss.

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Example 6 (Neutral Evil Win)-------------------------------------------------------------------------------------------------------------------------------------------

The same player as in Example 3 has won as Neutral Evil. Their old winrate is 12/31 giving a z-score of around -1.628543. Your new winrate would now be 13/32 giving a z-score of around -1.280303.

Assume: F% = 0.3 and AVG% = 0.4766666

Using the Elo gain/loss formula,

80ln(2X-35) * (new(z) - old(z)) + 1/30*(TM)*(OE - TE) + 20*((AVG% - F%)/AVG%), we have:

80ln(2(32)-35) * (-1.280303 - -1.628543) + 20*((0.4766666 - 0.3)/0.4766666) = 101.2 =

101 Elo gain.

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Section 6: APPROXIMATE OF A PLAYER'S ELO SCORE-------------------------------------------------------------------------------------------------------------------------------------------

IMPORTANT NOTE: The formula below will be used to give your Elo after your 20th game, because the gain/loss formula does not work for all games played less than 19 games (X<19). The main use of this formula is to give your Elo score after this 20th game, but it can also be used to estimate Elo score for any amount of games up to 383 games.-------------------------------------------------------------------------------------------------------------------------------------------

Approximate Elo =

1500 + 80ln(X-17.5) * (z) + 20*((T)*((AVG% - T%)/AVG%) + (M)*((AVG% - M%)/AVG%) + (NK)*((AVG% - NK%)/AVG%) + (NE)*((AVG% - NE%)/AVG%))-------------------------------------------------------------------------------------------------------------------------------------------

Where:

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• "X" is the amount of games, and is capped at

383 games.

• "z" is the z-score of the player.

• "T" refers to the total amount of Town games played.

• "M" refers to the total amount of Mafia games played.

• "NE" refers to the total amount of Neutral Evil games played.

• "NK" refers to the total amount of Neutral Killing games played.

• "T%" refers to the average winrate of Town.

• "M%" refers to the average winrate of Mafia.

• "NK%" refers to the average winrate of Neutral Killing.

• "NE%" refers to the average winrate of Neutral Evil.

• "AVG%" refers to the average winrate of all factions, which is also the average winrate of all players. For example, if the average win % of all factions is 50%, AVG% = 0.5.

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Section 7: EXAMPLES OF PLAYER'S APPROXIMATE ELO SCORE-------------------------------------------------------------------------------------------------------------------------------------------

Example 1-------------------------------------------------------------------------------------------------------------------------------------------

A player has a win rate of 60% overall (z-score approx 2.242424), and has played 20 games of which 8 games were Town, 5 were Mafia, 4 were NK and 3 were NE.

Assume T% = 0.6, M% = 0.35, NE% = 0.3, NK% = 0.05, AVG% = 0.4766666.

Using

1500 + 80ln(X-17.5) * (z) + 20*((T)*((AVG% - T%)/AVG%) + (M)*((AVG% - M%)/AVG%) + (NK)*((AVG% - NK%)/AVG%) + (NE)*((AVG% - NE%)/AVG%)), the approximate Elo score is:

1500 + 80ln(20-17.5) * (2.242424) + 20*((8)*((0.4766666 - 0.6)/0.4766666) + (5)*((0.4766666 - 0.35)/0.4766666) + (4)*((0.4766666 - 0.05)/0.4766666) + (3)*((0.4766666 - 0.3)/0.4766666)) =

1743 Elo.

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Example 2-------------------------------------------------------------------------------------------------------------------------------------------

A player has a win rate of 40% overall (z-score approx -1.393939), and has played 40 games of which 25 were Town, 7 were Mafia, 5 were NK and 3 were NE.

Assume T% = 0.6, M% = 0.35, NE% = 0.3, NK% = 0.05, AVG% = 0.4766666.

Using

1500 + 80ln(X-17.5) * (z) + 20*((T)*((AVG% - T%)/AVG%) + (M)*((AVG% - M%)/AVG%) + (NK)*((AVG% - NK%)/AVG%) + (NE)*((AVG% - NE%)/AVG%)), the approximate Elo score is:

1500 + 80ln(40-17.5) * (-1.393939) + 20*((25)*((0.4766666 - 0.6)/0.4766666) + (7)*((0.4766666 - 0.35)/0.4766666) + (5)*((0.4766666 - 0.05)/0.4766666) + (3)*((0.4766666 - 0.3)/0.4766666)) =

1172 Elo.

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Example 3-------------------------------------------------------------------------------------------------------------------------------------------

The same player as in

Example 2 still maintains the same winrate of 40% (z-score approx -1.393939), but has now played 350 games of which 26 games are NK, 23 games are NE, 100 games are Mafia and 201 games are Town.

Assume T% = 0.6, M% = 0.35, NE% = 0.3, NK% = 0.05, AVG% = 0.4766666.

Using

1500 + 80ln(X-17.5) * (z) + 20*((T)*((AVG% - T%)/AVG%) + (M)*((AVG% - M%)/AVG%) + (NK)*((AVG% - NK%)/AVG%) + (NE)*((AVG% - NE%)/AVG%)), the approximate Elo score is:

1500 + 80ln(350-17.5) * (-1.393939) + 20*((25)*((0.4766666 - 0.6)/0.4766666) + (7)*((0.4766666 - 0.35)/0.4766666) + (5)*((0.4766666 - 0.05)/0.4766666) + (3)*((0.4766666 - 0.3)/0.4766666)) =

872 Elo.

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Section 8: ELO TIERS (May change)-------------------------------------------------------------------------------------------------------------------------------------------

Bronze: 0-1099Silver: 1100-1799Gold: 1800-2099Platinum: 2100-2349Diamond: 2350-2599Master: 2600-2799Saviour: 2800+-------------------------------------------------------------------------------------------------------------------------------------------

Section 9: THE UPSIDES & THE POSSIBLE DOWNSIDES-------------------------------------------------------------------------------------------------------------------------------------------

• BIGGEST STRENGTH: Far less based on grinding Elo. There is a higher rise/loss in Elo with a lower amount of games played, and while still considering the amount of games played as a stabilising "k" factor, the main factor is the win rate of the player. This should be the case, this is the thing that shows the players skill, especially after a larger amount of games played.

• BIG STRENGTH: The higher rise/loss in Elo with a lower amount of games allows the player to know how well they are performing early on. This is not the case with the current Elo system, where MANY, MANY games must be played to even see some slight indication. This is one of the huge flaws of the current system, and this rework entirely solves it.

• Considers almost all factors, including things such as Your Faction's and Opposing Factions' Elo (if Town/Mafia), increases in Elo due to large amount of NK/NE/Mafia games (due to low faction win %), loss in Elo due to larger amounts of Town games (due to high faction win %) and the amount of overall games played.

• Self-sufficient, since it is based on faction win percentage. This formula would not have to be updated if balance changes were to be made affecting the faction win percentages.

• "Rolling 200 games" allows for an Elo rating showing players ability in the most recent 200 games as opposed to all games played. This allows for an indication of the players recent skill (where they may improve or get worse) rather than older games. This also makes trolling/gamethrowing have a significant impact on Elo, perhaps deterring people from gamethrowing.

• Elo changes from game to game are generally much higher and more exciting than the current ones. This may be another deterrent for trolls/gamethrowers.• BIGGEST WEAKNESS: This Elo system would not allow for a player having games with players of similar ability every single game. This is because this rework uses win rates, and so assumes the mean win rate of the average player over time will average out to the overall average win rate of the Ranked playerbase. If the average win rate of the players you play with is higher or lower than the average, this will not be the case. As such, if players were to be ranked with those of similar ability constantly, a significant change from the average Elo score would be hard for any player, resulting in the majority of players being very close to the average Elo (1500).• HOWEVER, a ranking system can still be applied (see Section 8 above).• Very complex and intricate. Perhaps quite hard to implement into the game as a result.• HOWEVER, the higher amount of complexity allows for a more accurate Elo rating and overall skill indication.• Very small and very large Elo gains/losses with more than 200 games played due to larger changes in win rates from game to game.• HOWEVER, this cannot be fully fixed due to the cutoff point of 200 games, and there HAS to be a cutoff point at some place, else the multiplier for games played will become too high, and also Rolling 200 would become impossible if there is no cutoff. Although it seems like a downside, it really isn't all that bad. Limitations/caps have been placed on Elo gains/losses to prevent small or incorrect Elo gains/losses (see Section 4).All is really cool. Definently support this-------------------------------------------------------------------------------------------------------------------------------------------

Thank you for reading! Let me know if I have made any errors and/or I am missing information, or if you simply want to share opinions and ask questions, or anything really. Thanks!

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