Conquer Club

joriki wrote:

MrBenn wrote:Why not just display the 'Average No of Opponents' next to the Win Percentage?

I'm not sure whether you meant opponents or players (the latter being one more), but neither would give the right results -- if you wanted to go in that direction, you'd need the average of the reciprocal of the number of players:

If someone plays an equal number of two-player games and eight-player games, they'd be expected to win 4 out of 8 two-player games and 1 out of 8 eight-player games, for a total of 5 out of 16 games, or roughly 1 out of 3. The average number of players (or opponents), which is 5 (or 4), would lead you to expect 1 out of 5 (or 4). The average of the reciprocals of the numbers of players, 1/2 and 1/8, on the other hand, is 5/16; this is just another way of expressing Timminz' proposal: the expected win percentage.

MrBenn wrote:Expected win = 1 / Average No of Players

The expected win percentage is not the reciprocal of the average number of opponents; it's the average of the reciprocal of the number of opponents. That difference is important, as the above example shows.

The expected win percentage is certainly a simple and useful alternative to my proposal. They both have advantages. In itself, the expected win percentage is a more direct measure; everyone will immediately understand what it means, whereas a "two-player equivalent" percentage is a bit more indirect. On the other hand, the two-player equivalent percentage gives you one number you can use to compare players, whereas with the expected win percentage, you need to first compare that number to the actual win percentage, and then compare that comparison against the corresponding comparison for the other player, which is a bit more indirect. So once one has understood what the two-player equivalent percentage means, it offers a more direct comparison.

Considering this, I would suggest that all three percentages be displayed: actual win percentage (#games won/#games played), expected win percentage (sum over reciprocals of player numbers/#games played), two-player equivalent win percentage (#opponents beaten/(#opponents beaten + #games lost)) (appropriately taking team games into account in each case)

Are you deliberately complicated? It took me a long time to get the gist of what you're saying...

You are right - the average of the 'winning probablilty' for each game is different from '1 / average number of players'. Apologies for my error

Instead of displaying the 'Expected win%', why not display the comparator? [can't think of a good name - I'll call it 'Win Rate']
Let's say that a player has the following stat:

Games: 2791 Completed, 1271 (46%) Won

If they only played 1v1 games, their expected win would be 50%, so we could display:

Games: 2791 Completed, 1271 (46%) Won. Win rate = -4%

If they only played 6p games, their expected win would be 16.6%, so we could display:

Games: 2791 Completed, 1271 (46%) Won. Win rate = +29.3%

If it so happnes that this player plays mostly 1v1 games, they might have an expected win rate of 46%, so we could display:

Games: 2791 Completed, 1271 (46%) Won. Win rate = ±0%

Factor in the adjustment to team games (so that a 6p trips game gives an expected win of 50% not 16.6%), and it's sorted.

MrBenn wrote:Are you deliberately complicated? It took me a long time to get the gist of what you're saying...

No, I'm just trying to be precise. Sorry if I'm not doing a good job of making myself clear.

MrBenn wrote:Instead of displaying the 'Expected win%', why not display the comparator?

Because that's not a good indicator. If someone only plays eight-player games, their expected win percentage is 12.5%. If they win 2.5% of their games instead, they're doing very badly, much worse than someone who plays only two-player games and wins 40% of them, but both would have the same difference between actual and expected win percentages. On the other hand, if the eight-player player won more than 62.5% of the games, the win rate would be greater than 50% and could thus never be achieved by the two-player player. It wouldn't help to form the ratio instead, either, since the eight-player player could achieve a ratio of up to 8 and the two-player player could only achieve a ratio up to 2.

I'd like to make a suggestion. I don't have unlimited time to analyze new proposals that seem to ignore the results of the thread so far and start out with "hey, why don't we do X instead". Many of these have not addressed the problem that I was trying to solve in this thread and that I believe the thread already solved a while ago. I'm all for having lots of different statistics, and I certainly don't want to prevent anyone from getting their favourite statistic displayed. But that's not what this thread was for. I would kindly ask anyone who has yet more proposals for what sorts of statistics could be included in the profile to put them in a separate thread, and to restrict this thread to a discussion of the ideas that have been developed in this thread.

To summarize:

The original proposal to calculate the ratio #opponents beaten/#games lost, or the logarithm of that, was abandoned in favour of calculating the ratio #opponents beaten/(#opponents beaten + #games lost), which has the advantage of being readily interpretable as a percentage, namely the percentage of games that someone playing only two-player games would have had to win to get the same ratio of #opponents beaten to #games lost. Thus, 0% means always losing, 100% means always winning, and 50% means winning as many games as would be randomly expected; > 50% is good; < 50% is bad. Team games would be taken into account by counting each team as one player.

It was then proposed to also display the expected win percentage to compare the actual win percentage against it, where the expected win percentage is the average of the reciprocal of the number of players.

It was also proposed to display the difference between the actual and expected win percentages; I argue above why I don't think that would be useful.

I would appreciate if subsequent posts to this thread would focus on discussing these proposals, or any new proposals specifically designed to yield a statistic that would as far as possible reflect player strength independent of the number of players per game.

There is no outstanding counterargument for the final proposal for the two-player equivalent percentage so
along with the modifications to encompass teams outlined earlier, that should stand.

I'm not in favour of the expected win percentage personally but not dead against either.
As has been said before it's an intuitive personal guage
(so you can see if you're doing as well as the mathematical average)
but cannot be used to compare with other players either by subtraction or division and still be independent of the number of players
because the range depends on the number of players.

So it falls outside the scope of the purpose of this particular thread in my opinion even though it's a good idea.

Last but ironically it may be the most important is to actually give the calculation a meaningful name.
The name needs to be something people will want to get used to looking at and comparing.

I'm just a little hesitant with how intuitive this model actually is (compare with expected win percentage)

chipv wrote:Last but ironically it may be the most important is to actually give the calculation a meaningful name.
The name needs to be something people will want to get used to looking at and comparing.

Quite true.

Unfortunately, "two-player equivalent win percentage" is unlikely to cut it

How about "beat ratio" or "beat percentage"? Since what it compares is how many players/teams you beat and how many players/teams you were beaten by.

Some other ideas: {pair/binary/match/duel/1-on-1/one-on-one/two-player} {ratio/percentage} (though "two-player percentage" without "equivalent" would probably be misleading since it sounds like the percentage of two-player games you've won)

Or, in a different vein, "standardized win percentage" or "normalized win percentage".

I think I like "beat ratio" and "standardized win percentage" best.

Whatever it's called, it should link to a page that explains it in detail, including the two-player equivalent interpretation. I could write the text for that.

The rank calculation is accepted without question as I think this will be given time and a concise name.

To further its chance of being used it needs to complete.

For example

two-player equivalent win percentage (#opponents beaten/(#opponents beaten + #games lost)) (appropriately taking team games into account in each case)

is not precise enough - you can make a formula that takes teams games into account automatically (see above).

If you do not agree with my suggestion, then by all means propose one and produce a single forumla.
This will have a higher chance of being implemented in my opinion.
(appropriately taking team games into account should be provided in the final formula).

lol seem that im only 1 which think the winning percentage is great. I dont want them to be changed:(

Androidz wrote:lol seem that im only 1 which think the winning percentage is great. I dont want them to be changed:(

This should be additional, not a replacement, don't worry!

Seems like a sound suggestion.

chipv wrote:

Androidz wrote:lol seem that im only 1 which think the winning percentage is great. I dont want them to be changed:(

This should be additional, not a replacement, don't worry!

Great:D

Chip - when's this going into Map Rank?

C.

How's about

"Opponent victory ratio".

C.

Ok, I've put this in Map Rank... and just about to make available.

I want to divide the percentages into classes to give people something to shoot for.

Can I get some suggestions, please?

e.g.

0% Bunny
1 - 25 % Petty Thug
26 - 50% Murderer
51% - 75% Serial Killer
76% - 99% Warmonger
100% - Angel of Death

Ok, this is pretty macabre, but still...

chipv wrote:Ok, I've put this in Map Rank... and just about to make available.

I want to divide the percentages into classes to give people something to shoot for.

Can I get some suggestions, please?

e.g.

0% Bunny
1 - 25 % Petty Thug
26 - 50% Murderer
51% - 75% Serial Killer
76% - 99% Warmonger
100% - Angel of Death

Ok, this is pretty macabre, but still...

Loving the names!!

C.

chipv wrote:Ok, I've put this in Map Rank... and just about to make available.

I want to divide the percentages into classes to give people something to shoot for.

Can I get some suggestions, please?

e.g.

0% Bunny
1 - 25 % Petty Thug
26 - 50% Murderer
51% - 75% Serial Killer
76% - 99% Warmonger
100% - Angel of Death

Ok, this is pretty macabre, but still...

The names might be a bit harsh for the younger players but I like them

possibly change "bunny" to "you should just quit now"
Also since you changed it to victim, maybe change the percentage to 0 - 5%

Ok, this is in Map Rank called Kill ratio.

Any amendments to the ranges and names for the kill ratio levels welcome in the map rank thread.

joriki, if you want to make a special post for instructions on the calculation, by all means do so and let me know please.

I think you guys have way to much time on your hands.

joriki et al, this formula is proving troublesome in practice.

#opponents defeated / (#opponents defeated + #games lost)

decreases faster with games lost than it increases with opponents defeated.

This means that it is very difficult to bring your percentage back up again once you lose a few games.

I am having to add extra levels to make level achievements more easily attainable.

The number of opponents defeated to maintain a certain percentage r is

(#losses * r) / (100 - r) where 0 <= r < 100 (for r=100, #losses = 0 anyway)

For example

For a 95% ratio you need 19 kills per loss.
For a 90% ratio you need 9 kills per loss.
For a 80% ratio you need 4 kills per loss.
For a 50% ratio you need 1 kill per loss.

So take the win/loss ratio. This is far easier to maintain / recover after loss.

Still pondering.

Many apologies for taking so very long to reply. (I guess that disproves joesdad's conjecture that I have too much time on my hands )

I'm afraid I don't understand the problem you're describing. 90% is an extremely good rating -- it seems reasonable that you should have to have a lot of kills per loss to get that. I agree that the levels you set up (nice names, BTW ) are probably not optimal because it's hard to get above 75% or below 25% -- how about 0-20, 20-40, 40-60, 60-80, 80-100? But I guess you've probably figured something out in the meantime.

It's not true that the score "decreases faster with games lost than it increases with opponents defeated". In fact, #opponents defeated / (#opponents defeated + #games lost) is just one minus #games lost / (#opponents defeated + #games lost), or equivalently one-half times (#opponents defeated - #games lost) / (#opponents defeated + #games lost) plus 1, so it only appears on the surface that the two counts play different roles in the formula, they actually play symmetric roles; if you've lost 5 games and defeat your 8th opponent your score increases just as much as it decreases when you've defeated 5 opponents and you lose your 8th game.

So it seems to me that it's just that it's quite difficult to get very far away from 50% (in either direction), and thus we need a sufficient density of levels near 50%, but I don't think this has anything to do with losses counting more than defeated opponents or it being unduly difficult to recover from losses.

chipv wrote:For example

two-player equivalent win percentage (#opponents beaten/(#opponents beaten + #games lost)) (appropriately taking team games into account in each case)

is not precise enough - you can make a formula that takes teams games into account automatically (see above).

If you do not agree with my suggestion, then by all means propose one and produce a single forumla.
This will have a higher chance of being implemented in my opinion.
(appropriately taking team games into account should be provided in the final formula).

Sorry, I should have said that I agree with your formula for team games; "appropriately taking team games into account" was supposed to refer to something like your formula, but I see that I forgot to write that explicitly; I was just treating that as a part of the problem that seemed to be solved or at least easily solvable and that wasn't where the disagreements lay.

Agreed all round, joriki.

The calculation is already included in Map Rank. Thanks very much for your suggestion and discussion, a pleasure!

Map rank is fantastic. Why isn't it integrated into the site?

Thanks joriki for heading up this interesting discussion and everyone else who has contributed

I think joriki's formula [opponents defeated / (opponents defeated + games lost)] has a lot of potential to replace our win% but I'm also attracted to [wins / expected wins].

Take this scenario:

Player A won a 3-player game and lost a 3-player game
Player B won a 3-player game and lost a 8-player game



Yes, expected_win% has a flaw in that playing smaller games limits your potential. You can only reach 200% if you stick to 1v1. You will never reach 800% unless you've only played (and won) 8 player games. Different players have different limits, but does that not reflect the fact that you have more to gain and lose by playing larger games?

However, joriki% has an apparent flaw in that both players got the same score, even though Player B's 8-player loss should be considered as less of a loss than Player A's.

Thoughts?

EDIT: An interesting relationship exists between these two metrics. When joriki% = 50%, expected_win% = 100%

EDIT: Although it also gives different players different potentials, e_i_pi's Players Beaten Per Game formula [opponents defeated / games played] is very easy to understand, and could be considered. But it also suffers from the same apparent flaw as joriki%...

lackattack wrote:Thanks joriki for heading up this interesting discussion and everyone else who has contributed

I think joriki's formula [opponents defeated / (opponents defeated + games lost)] has a lot of potential to replace our win% but I'm also attracted to [wins / expected wins].

Take this scenario:

Player A lost a 3-player game and won a 3-player game
Player B lost a 3-player game and won a 8-player game

Code: Select all

          joriki%   expected_win%
Player A    67%        150%
Player B    67%        218% 

Yes, expected_win% has a flaw in that playing smaller games limits your potential. You can only reach 200% if you stick to 1v1. You will never reach 800% unless you've only played (and won) 8 player games. Different players have different limits, but does that not reflect the fact that you have more to gain and lose by playing larger games?

However, joriki% has an apparent flaw in that both players got the same score, even though Player B's 8-player loss should be considered as less of a loss than Player A's.

Thoughts?

EDIT: An interesting relationship exists between these two metrics. When joriki% = 50%, expected_win% = 100%

EDIT: Although it also gives different players different potentials, e_i_pi's Players Beaten Per Game formula [opponents defeated / games played] is very easy to understand, and could be considered. But it also suffers from the same apparent flaw as joriki%...

Very good point.

I was just playing around with some numbers and may have stumbled upon an interesting solution.

The metric can be a percentile as to how your performance (total wins) compares to the performance of a player that wins according to expectation (1/2 of 2 player games, 1/3 of 3 player games, etc) playing the same types of games as you.

Say a player plays two 3-player games. Expectation is:

2-0 = 0.11
1-1 = 0.44
0-2 = 0.44

If a player has 2-0, he is playing at the 88th percentile.
If a player has a 1-1, he is playing at the 44th percentile.
If a player has a 0-2, he is playing at the 0th percentile.

If a player plays a 3-player game and an 8-player game:

2-0 = 0.04 96th percentile
1-1 = 0.38 58th percentile
0-2 = 0.58 0th percentile

So the player that is 1-1 from a 3-player game and an 8-player game gets 58th percentile as compared against the 44th percentile of the player with a 1-1 who played two 3-player games.

If a player plays two 3-player games and an 8-player game. Expectation is:

3-0 = 0.01 99th percentile
2-1 = 0.15 84th percentile
1-2 = 0.44 39th percentile
0-3 = 0.39 0th percentile

A player that wins x 8 player games will have a higher percentile than a player that wins x 2-player games, because the probability of winning an 8-player game is lower. In fact, a player that wins 6/6 2-player games will have the same percentile as one who wins 3/3 4-player games and a player that wins 2/2 8-player games. Because (1/2)^6 = (1/4)^3 = (1/8)^2

Note: This method would give the same percentile to players that played the same types of games and won the same amount, regardless of which of those games they actually won. So two guys could get the same score for winning an 8 man and losing a 3 man OR losing the 8 man and winning the 3 man. Some might object to this on gut instinct but to object to giving same scores would mean to advocate giving different scores, and I would find it difficult to objectively determine which player should be punished more than the other.

Note: Most percentiles are based on how your score compares to all other test takers' scores. This percentile is not based on other actual players' scores, but is based on the expected distribution of scores from an imaginary player that plays identical games as you and that has the same chance to win as his opponents do in any given game. So if you get a 55th percentile, that means you did better than 55 out of 100 imaginary players who played the same games as you and who were equally likely as their opponents to win any of those individual games. These scores could then be aggregated across all players and true percentiles could be computed for every player, i.e. percentiles representing how their win percentiles compare to all other players.

Very interesting. I think "farang%" might have the best qualities then:

* Goes from 0% to 100% (well, I suppose 99% is max) where 50% is "average"
* Weighs in difficulty of wins and difficulty of losses

Downside #1: Hard to compute. Can anyone derive a formula or algorithm for this?

Downside #2: Hard to explain. Can anyone take a stab at explaining this consisely in plain English?

FarangDemon wrote:Note: This method would give the same percentile to players that played the same types of games and won the same amount, regardless of which of those games they actually won. So two guys could get the same score for winning an 8 man and losing a 3 man OR losing the 8 man and winning the 3 man. Some might object to this on gut instinct but to object to giving same scores would mean to advocate giving different scores, and I would find it difficult to objectively determine which player should be punished more than the other.

I don't think we should worry about this.

Couldn't we simply take basic win %, and use opponents instead of games? [opponents beaten]/[opponents played]. This way, winning 8-player games is still better than winning 3-player games, but if you win enough 1v1's, it works out the same.

So in lack's above example, Player A (who won a 3-player and lost a 3-player) would have 50%. Player B (who lost a 3-player and won an 8-player) would have 77.8%.

I've come into this thread a little late and only skimmed, so excuse me if this has been suggested before...