6 replies to this topic

[Silme]

Quote

Case 1: 1350 Player WINS over 1410 Player

Since the lower rated player won despite the odds against him/her, they are rewarded a much higher change in score than the higher player is. The higher player score will actually be reduced.

One variable that is set by winning or losing is the WinFlag (as seen in Figure 3). The WinFlag is a binary (true/false) value of either 1 (Player has won) or 0 (Player has lost). In this case, the WinFlag value is 1.

Let’s begin the calculation:

Old Rating = 1350
Maximum Change Allowed = +50 for a win, -50 for a loss (as seen in Figure 1)
WinFlag = 1
Probability of Winning = 0.41

1350 Players new ranking = 1350 + 50 x (1 – 0.41)
= 1380

1410 Players new ranking = 1410 – 50 x (1 – 0.41)
= 1381

A player’s rating will only go down if they are beaten by a player who has a lower rating than theirs. In this case, if the 1350 player lost, their score would not change since the Match Maker was correct in its prediction.

This is from the Matchmaking phase 3. Specifically I was wondering if anyone can clarify whether the bold/underline/italicized portion of the calculation for ELO for the higher ranked player losing is intentional?

According to the way the article is written, I would have assumed that the formula would have used the 1410 player's chance of winning, here 59% (seeing as he is, in fact, higher ranked than his opponent), and secondly, the win state value for the loser should be set to 0.

Our new equation is:
1410 - (50 * -0.59) = 1439.5 -> 1440
which is obviously incorrect, as he's gained rank for losing.

However, once we swap the minus sign, the end result is still the same, new ELO of 1381. So, either the original result is correct despite a mistyped formula or we're missing a statement that the lower ranked player always determines the values for win state and win probability for both players' adjusted ranks.

Edited by Silme, 22 January 2013 - 09:40 AM.

[LethalRose]

Read this, there will be a test friday.

http://en.wikipedia....o_rating_system

[HRR Insanity]

Silme, on 22 January 2013 - 09:39 AM, said:

This is from the Matchmaking phase 3. Specifically I was wondering if anyone can clarify whether the bold/underline/italicized portion of the calculation for ELO for the higher ranked player losing is intentional?

According to the way the article is written, I would have assumed that the formula would have used the 1410 player's chance of winning, here 59% (seeing as he is, in fact, higher ranked than his opponent), and secondly, the win state value for the loser should be set to 0.

Our new equation is:
1410 - (50 * -0.59) = 1439.5 -> 1440
which is obviously incorrect, as he's gained rank for losing.

However, once we swap the minus sign, the end result is still the same, new ELO of 1381. So, either the original result is correct despite a mistyped formula or we're missing a statement that the lower ranked player always determines the values for win state and win probability for both players' adjusted ranks.

Also read this: http://en.wikipedia....ntheses_.28_.29

Hint: Resolve the parentheses first, then the multiplier.

[Silme]

@Lethal: Thanks, didn't think to check that it might be a previously established system

@Insanity: I'm pretty sure I did my basic order of operations correctly. Perhaps I lost you where I skipped a step when I initially wrote it out, though.

PEMDAS

1410 – 50 x (0 – 0.41) : Parentheses
= -0.59

1410 - 50 x -0.59 : Multiplication (no exponents)
= -29.5

1410 - -29.5 : Subtraction (no division or addition)
= 1439.5

Edited by Silme, 23 January 2013 - 04:46 AM.

[Apoc1138]

Silme, on 23 January 2013 - 04:42 AM, said:

@Lethal: Thanks, didn't think to check that it might be a previously established system

@Insanity: I'm pretty sure I did my basic order of operations correctly. Perhaps I lost you where I skipped a step when I initially wrote it out, though.

PEMDAS

1410 – 50 x (0 – 0.41) : Parentheses
= -0.59

1410 - 50 x -0.59 : Multiplication (no exponents)
= -29.5

1410 - -29.5 : Subtraction (no division or addition)
= 1439.5

read the article again - it says ( 1 - 0.41 )
and you are doing ( 0 - 0.41 )
that's where you are going wrong

[Silme]

It's intentional, Apoc, per my original post. And per the Elo article that Lethal linked, the win state should properly be 0 for the loser, which means that (0-0.41) is correct and the dev post had a typo (they wrote '- 50' instead of properly '+ 50').

Edited by Silme, 24 January 2013 - 08:00 AM.

[Apoc1138]

Silme, on 24 January 2013 - 07:58 AM, said:

It's intentional, Apoc, per my original post. And per the Elo article that Lethal linked, the win state should properly be 0 for the loser, which means that (0-0.41) is correct and the dev post had a typo (they wrote '- 50' instead of properly '+ 50').

yes, they made a typo, either the - should be a +, or if you read it exactly as they did write it then it works out correctly... when they copied the formula, they changed the + to a - instead of changing a 1 to a 0

if you use the formula they posted, it works out correctly, they've just stated it in a different fashion to how the text suggests

to be honest, when representatives of the developers start putting math on the forums, I tend not to take them at face value on the actual math and concentrate instead on the intended outcome, and then take a look at the actual outcome

people get too caught up in math and then declare the game to be broken, however the end result in game may well be what the developers intended, even though the representative who posted the maths made a typo

Edited by Apoc1138, 24 January 2013 - 08:26 AM.