Average of Opponent's Score/Rank on Profile

[saaimen]

Map Ranks works for Explorer also but not Safari.

Which is *not* good for me

Now back on topic... You think Lack or anyone is actually watching this thread ? Not a lotta response...

[chipv]

Map Ranks works for Explorer also but not Safari.

Which is *not* good for me

Now back on topic... You think Lack or anyone is actually watching this thread ? Not a lotta response...

No, but it was a good excuse to let IE users know they have scripts they can actually run...

[saaimen]

I know your post made sense, as this is an open forum and not a private conversation (though now it seems like one ), don't worry.
As for the second part of my post... What do you think?

[chipv]

I know your post made sense, as this is an open forum and not a private conversation (though now it seems like one ), don't worry.
As for the second part of my post... What do you think?

Sincere apologies for deviating off-topic.

Moderators will have seen this thread so it will be dealt with along with the hundreds of other suggestions made.

If you're not satisfied with the responses on this thread then maybe it's because the suggestion is not explicit enough.

To further its chances, there needs to be a complete set of steps to generate the number and then very importantly
how to represent that number because as it stands it is not a fraction so cannot be merely represented as a percentage.

[FarangDemon]

I think I'm going to go for BaldAdonis' proposal and put it into Map Rank

Proposal:

Only count players who have been beaten. This will give a measure of strength and I guess can be called Strength ratio.

So Strength ratio = ratio of average rank of defeated opponents / target rank at game end time.

I will not be counting terminator kills that do not result in a win.

Any last minute amendments welcome.

(Not counting losses)

Chipv, I just took a look at your Relative Rank metric. Nicely done and thank you. I got a N/A for some maps that I did win. Maybe it doesn't do teams?

1) Is relative rank not implemented for losers because the point is to see where someone's points come from and you only get points for winning a game?

Because it could be implemented for every player in every game, because (A/B) / (A/C) = C/B

2) How is relative rank calculated? Are you averaging the ratios of target player's score to opponents score? Averaging ratios is usually not done because the result skews large: ratios of 2/1 and 1/2 average to 1.25, ratios of 2/3 and 3/2 average to 1.08. (I tried to do it myself in a project once, but my boss told me it was not a good idea, so now I understand.)

Might I suggest changing the metric to be median opponent relative rank - this translates into something readily understood as: half of all target player's opponents were below the given score ratio,

OR

a percentage based on discrete events, i.e. each event is either a one or a zero, depending on whether or not the opponent's score was greater than 2/3 the target players score (or some other cutoff you deem appropriate). Then we have a metric readily understood as "percentage of opponents whose score was greater than 2/3 target player's score".


3) So will CC change their code to track the relative ranks of every player's previous 100 opponents? That is what is required in order to implement this on the CC site, which is the goal. I think we need to use this metric to create a 2nd scoreboard that only shows players that tend to play their peers.

[chipv]

I think I'm going to go for BaldAdonis' proposal and put it into Map Rank

Proposal:

Only count players who have been beaten. This will give a measure of strength and I guess can be called Strength ratio.

So Strength ratio = ratio of average rank of defeated opponents / target rank at game end time.

I will not be counting terminator kills that do not result in a win.

Any last minute amendments welcome.

(Not counting losses)

Chipv, I just took a look at your Relative Rank metric. Nicely done and thank you. I got a N/A for some maps that I did win. Maybe it doesn't do teams?

Uninstall associated preferences and try again. It does everything.

1) Is relative rank not implemented for losers because the point is to see where someone's points come from and you only get points for winning a game?

It does losers - the above quote is redundant as I solved the problem. (Only tricky for terminator games)

Because it could be implemented for every player in every game, because (A/B) / (A/C) = C/B

It's much more complicated that this as it turns out.

2) How is relative rank calculated? Are you averaging the ratios of target player's score to opponents score? Averaging ratios is usually not done because the result skews large: ratios of 2/1 and 1/2 average to 1.25, ratios of 2/3 and 3/2 average to 1.08. (I tried to do it myself in a project once, but my boss told me it was not a good idea, so now I understand.)

For each game the relative score is extracted from the log. This is a direct function of the relative rank at game end. Terminator is more complicated but this has also been calculated. The relative ranks are then summed and divided by the number of players to give an average relative rank.

Might I suggest changing the metric to be median opponent relative rank - this translates into something readily understood as: half of all target player's opponents were below the given score ratio,

OR

a percentage based on discrete events, i.e. each event is either a one or a zero, depending on whether or not the opponent's score was greater than 2/3 the target players score (or some other cutoff you deem appropriate). Then we have a metric readily understood as "percentage of opponents whose score was greater than 2/3 target player's score".

I don't think either of these is a satisfactory stat. Relative rank is easy to understand - it's the average relative rank of your opponents played.

3) So will CC change their code to track the relative ranks of every player's previous 100 opponents? That is what is required in order to implement this on the CC site, which is the goal. I think we need to use this metric to create a 2nd scoreboard that only shows players that tend to play their peers.

This will be a long wait.

[lancehoch]

Farang, the N/A for relative rank may also be due to missing game logs. Since the point transfers were lost, you cannot see what the relative rank was on those games.

[FarangDemon]

I don't think either of these is a satisfactory stat. Relative rank is easy to understand - it's the average relative rank of your opponents played.

After thinking about it, I agree with you that a mean of ratios like the one you have is a better metric than those other metrics I suggested. It is much more straightforward. But in order to get rid of the skew, it should be the geometric mean and not the arithmetic mean because we are dealing with ratios and not actual amounts. To find the geometric mean you take the nth root of the product of the n numbers.

http://www.math.toronto.edu/mathnet/questionCorner/geomean.html

Averaging ratios skews large. It is not a huge deal but it is inaccurate and actually makes someone look less guilty of farming than they actually are.

If I play a guy 1.2 times my score and then play a guy that is my score divided by 1.2, I'd expect the aggregate relative rank metric to say that on average I play a guy at my level. I'd expect the same outcome for me as for a guy that plays someone 1.5 times his score and then plays someone that is his score divided by 1.5. But by averaging the ratios I would have (1.2 + 1/1.2) / 2 = 1.04 and he would have 1.08. A guy playing a guy half his score and then a guy double his score ends up with 1.13. These guys should all have the same aggregate relative rank score. It skews up.

Here is a good example:

Opponent 1 2 3 4 5 6 7
Rel Rank 0.29 0.29 0.29 0.29 0.29 0.29 2.0

Mean 1-6 1-7
arithmetic 0.29 0.53
geometric 0.29 0.38

Pretend a colonel farmer has farmed 6 cooks. Then he plays a Field Marshall just once.
This shows how a farmer's arithmetic mean skyrockets but the geometric mean does not skew.

Geometric mean can be calculated several ways - one way uses logarithms and one way uses roots, but they get the same result. Maybe the easiest way is to multiply all the values together and then take the nth root of the product. The other method is to take the average of the log of every number and then raise e to this power. But they produce the same result and it does not skew like the arithmetic mean does.

[FarangDemon]

Are you using 1/2 as the cutoff for the "noob farmer" designation? I think that makes sense.

Here is the huge question.....

Are you thinking about installing a feature in the next edition of MapRank that would look at the top n players of the scoreboard, calculate their mean opponents' relative rank (whether you implement arithmetic mean or geometric mean) and then compile a ranked listing consisting only of those whose mean opponents' relative rank is above 1/2? Or maybe even let the user type whatever cutoff they want...

You would be a hero for doing this.

[chipv]

I don't think either of these is a satisfactory stat. Relative rank is easy to understand - it's the average relative rank of your opponents played.

After thinking about it, I agree with you that a mean of ratios like the one you have is a better metric than those other metrics I suggested. It is much more straightforward. But in order to get rid of the skew, it should be the geometric mean and not the arithmetic mean because we are dealing with ratios and not actual amounts. To find the geometric mean you take the nth root of the product of the n numbers.

http://www.math.toronto.edu/mathnet/questionCorner/geomean.html

Averaging ratios skews large. It is not a huge deal but it is inaccurate and actually makes someone look less guilty of farming than they actually are.

If I play a guy 1.2 times my score and then play a guy that is my score divided by 1.2, I'd expect the aggregate relative rank metric to say that on average I play a guy at my level. I'd expect the same outcome for me as for a guy that plays someone 1.5 times his score and then plays someone that is his score divided by 1.5. But by averaging the ratios I would have (1.2 + 1/1.2) / 2 = 1.04 and he would have 1.08. A guy playing a guy half his score and then a guy double his score ends up with 1.13. These guys should all have the same aggregate relative rank score. It skews up.

Here is a good example:

Opponent 1 2 3 4 5 6 7
Rel Rank 0.29 0.29 0.29 0.29 0.29 0.29 2.0

Mean 1-6 1-7
arithmetic 0.29 0.53
geometric 0.29 0.38

Pretend a colonel farmer has farmed 6 cooks. Then he plays a Field Marshall just once.
This shows how a farmer's arithmetic mean skyrockets but the geometric mean does not skew.

Geometric mean can be calculated several ways - one way uses logarithms and one way uses roots, but they get the same result. Maybe the easiest way is to sum up all the values and then take the nth root of the sum. The other method is to take the average of the log of every number and then raise e to this power. But they produce the same result and it does not skew like the arithmetic mean does.

Sorry for the delay in response.

I think you have a good point here, let me have a think about it.
The gm <= am so we will get a lot more farmers as you say...

[FarangDemon]

please note I accidentally wrote "sum" instead of "product" in that last paragraph. I just edited it and it should read:

"Maybe the easiest way is to multiply all the values together and then take the nth root of the product. "

Geometric mean = nth root of the product of all values ( where n = how many values )