RealGM PC's board All-Time ranking as of early 2023: how much of a hivemind is there?

[WestGOAT]

Expanding on the previous topic discussed in viewtopic.php?f=64&t=2261392, here is a small update as I previously missed one poster. Based on the rankings by average scores, LeBron's overall ranking is being skewed by two posters, which could be somewhat controversial here . In this post, I propose a solution to handle such cases using a popular statistical technique called principal component analysis (PCA). This technique was previously also mentioned by zimpy27.

Firstly, here is the latest all-time ranking, black line is the median, while the grey dashed line is the average score. Player rankings are sorted by average score. I tried making the individual markers unique for each poster, but it did not work out.

Spoiler:

I was inspired by Squared2020 heatmaps and created one myself to provide another overview of the rankings for each poster.

Spoiler:

Here is a more color-blind friendly version.

Spoiler:

PCA is a dimension-reduction technique that involves a combination of linear algebra and statistics. In this case, I tried summarizing the rankings of each player (48 in total) in two latent variables, also known as principal components (PC1 & PC2).

Spoiler:

Using multivariate statistics, we can draw a confidence ellipse (the red dashed line above) that indicates that four posters are statistical outliers. Based on this, we can exclude these posters more objectively compared to simply cherry-picking, which would lead to the following subsequent rankings:

Spoiler:

Any opinions on these rankings, and whether some posters should be excluded at all? Personally not a big fan of it, as long as posters are being genuine and not trolling their rankings should be included. Otherwise, this place could turn out to be an echo-chamber. On the other hand, we all know trolling and being on the internet goes hand-in-hand and LeBron vs Jordan rankings can get out of hand

It is possible that some people sabotaged others, so in the future, I will suggest people lock their sheets after providing their rankings in the google docsheet as I'd def would like to update the ranking at the end of the season. While I'm not a big fan of excluding outliers in general, if needed, I think PCA could be a reasonable method. However, it's not entirely objective as setting thresholds to consider something as an outlier is somewhat arbitrary as well.

Link to the aggregated raw data:

Spoiler:

https://docs.google.com/spreadsheets/d/1PA-VH7RbT-kJ7r3vzY1P5x_TkzkNTXu9eHEuiE5VHhc

shout out to:

.

.

[rk2023]

Thanks for investing the time and effort in a cool project, the data visualization came out really nice and robust!

For the question highlighting this thread: I think groupthink and inate anchoring biases / preconceived notions can be present in any context of real-world and not just a board like the player comparisons one.

Maybe the answer is a yes then, but I don’t feel comfortable saying this due to considerations that (1) this is generally a more intelligent and ready to debate community than most sectors of sports fandom, and (2) keying in on similar criteria (opposed to magazines/TMT giants/entities cited in the original T-30 consolidations) would likely lead to less of a range in how we view a given player on an all time scale.

[zimpy27]

Expanding on the previous topic discussed in viewtopic.php?f=64&t=2261392, here is a small update as I previously missed one poster. Based on the rankings by average scores, LeBron's overall ranking is being skewed by two posters, which could be somewhat controversial here . In this post, I propose a solution to handle such cases using a popular statistical technique called principal component analysis (PCA). This technique was previously also mentioned by zimpy27.

Firstly, here is the latest all-time ranking, black line is the median, while the grey dashed line is the average score. Player rankings are sorted by average score. I tried making the individual markers unique for each poster, but it did not work out.

Spoiler:

I was inspired by Squared2020 heatmaps and created one myself to provide another overview of the rankings for each poster.

Spoiler:

Here is a more color-blind friendly version.

Spoiler:

PCA is a dimension-reduction technique that involves a combination of linear algebra and statistics. In this case, I tried summarizing the rankings of each player (48 in total) in two latent variables, also known as principal components (PC1 & PC2).

Spoiler:

Using multivariate statistics, we can draw a confidence ellipse (the red dashed line above) that indicates that four posters are statistical outliers. Based on this, we can exclude these posters more objectively compared to simply cherry-picking, which would lead to the following subsequent rankings:

Spoiler:

Any opinions on these rankings, and whether some posters should be excluded at all? Personally not a big fan of it, as long as posters are being genuine and not trolling their rankings should be included. Otherwise, this place could turn out to be an echo-chamber. On the other hand, we all know trolling and being on the internet goes hand-in-hand and LeBron vs Jordan rankings can get out of hand

It is possible that some people sabotaged others, so in the future, I will suggest people lock their sheets after providing their rankings in the google docsheet as I'd def would like to update the ranking at the end of the season. While I'm not a big fan of excluding outliers in general, if needed, I think PCA could be a reasonable method. However, it's not entirely objective as setting thresholds to consider something as an outlier is somewhat arbitrary as well.

Link to the aggregated raw data:

Spoiler:

https://docs.google.com/spreadsheets/d/1PA-VH7RbT-kJ7r3vzY1P5x_TkzkNTXu9eHEuiE5VHhc

shout out to:

.

.

Awesome.

Yep, taking many lists and then doing a PCA followed by an average rank from those lists in the 95% confidence interval is the best way to get a decent consensus GOAT list.

If you could collect lists from people that put real effort in to their list then you will get the best quality list.

I think your final list is only reliable up to top 24 as you probably wouldn't accept in rankings with more than 20% missing values.

[zimpy27]

Some heirarchical clustering analysis could be amusing to show how closely certain posters think while also seeing how players are closely linked across many lists.

[penbeast0]

Interestingly enough, I think your analysis is focused on those posters who DON'T fit the hivemind simile in their rankings.

I do think there is something of a group think that goes on here (I think it's less pejorative than hivemind) as many of us read and are influenced by each other's analysis. I'm don't think that's a bad thing.

[csh 19792001]

Expanding on the previous topic discussed in....

Outstanding, nuanced, seminal work here, Sir. Outstanding!!!!!!

One of my (initial/visceral) takeaways is, not a single person voted for Wilt Chamberlain as GOAT. I find that fairly insane, honestly.

[OhayoKD]

Expanding on the previous topic discussed in....

Outstanding, nuanced, seminal work here, Sir. Outstanding!!!!!!

One of my (initial/visceral) takeaways is, not a single person voted for Wilt Chamberlain as GOAT. I find that fairly insane, honestly.

joining up with the 3rd or 4th best player in the league and then losing to a retiree player-coach will do that

[AEnigma]

Great work. Feel a bit bad for Iggy because he at least was sincere lol, but some correction is probably appropriate if trying to find a normative ranking.

You do need to correct the Patrick Beverley one though.

[uberhikari]

Correct me if I'm making a mistake.

Has anyone looked at G35's rankings on the heat map? He has LeBron at 23, Duncan at 21, Kareem at 8, Mikan at 4, Doncic at 16, Walton at 7, Jokic at 15.

Those numbers are extreme outlier rankings.

[rk2023]

Correct me if I'm making a mistake.

Has anyone looked at G35's rankings on the heat map? He has LeBron at 23, Duncan at 21, Kareem at 8, Mikan at 4, Doncic at 16, Walton at 7, Jokic at 15.

Those numbers are extreme outlier rankings.

Yeah. That’s my guess as to why WestGoat added the further data visualizations of the circle/network of voters that had him far away from the group and of the adjusted averaged filtering out them and one other voter.

[uberhikari]

Correct me if I'm making a mistake.

Has anyone looked at G35's rankings on the heat map? He has LeBron at 23, Duncan at 21, Kareem at 8, Mikan at 4, Doncic at 16, Walton at 7, Jokic at 15.

Those numbers are extreme outlier rankings.

Yeah. That’s my guess as to why WestGoat added the further data visualizations of the circle/network of voters that had him far away from the group and of the adjusted averaged filtering out them and one other voter.

Thanks for pointing that out. The numbers were so crazy that I wrote that before I finished going through everything.

[70sFan]

Awesome job, looks really good and easy to comprehend.

Maybe it's a result of group thinking, but I like this list up to 25th spot. It's very good.

[Dutchball97]

This makes it look like my favorite drink is water and my favorite color is gray. Seems like the guy ranting against groupthink was the real hivemind all along lol.

Either way great work though, very clear visualization and some interesting thoughts here. I'd be careful with labeling people as outliers though as some of the posters close to the edges have very interesting insights despite having somewhat unconventional rankings. I still believe the best way to combat "troll" lists is the requirement of an explanation with your votes like we do for the top 100 project. Sure you can still make something up but it's often much easier to spot whether someone is trying to skew a ranking or just has a legit different opinion that way.

[f4p]

This makes it look like my favorite drink is water and my favorite color is gray.

the confidence oval is a harsh mistress.

[LA Bird]

Credit to OP for going through all this work to handle outlier cases which were clearly troll attempts but the results were still skewed by those votes in the end. For example, if we look at the votes for LeBron and Kareem,

LeBron: 1x14, 2x10, 3x3, 4x2, 6, 12, 23
Kareem: 1x2, 2x12, 3x15, 4, 6, 8

It is obvious most ranked LeBron over Kareem. In a direct H2H comparison, 24 out of 32 voted for LeBron over Kareem. But because LeBron had two haters who left him out the top 10, he ended up behind Kareem overall in average rankings. I am not saying we have to throw those two votes out but there is clearly something wrong with the vote counting method if the opinion of just two voters can override the vast majority.

(Don't know who will be running the top 100 project this time but I would recommend the H2H vote counting method I used in the peaks project to avoid manipulation like this. It's quite intuitive and there is already a script to tally up the votes automatically.)

[70sFan]

I will never understand manipulation attempts in such projects. Some people take the results way tok seriously, without focusing on what actually matters.

[WestGOAT]

Some heirarchical clustering analysis could be amusing to show how closely certain posters think while also seeing how players are closely linked across many lists.

That's actually a cool idea to further expand on! Thanks for the suggestion!

Credit to OP for going through all this work to handle outlier cases which were clearly troll attempts but the results were still skewed by those votes in the end. For example, if we look at the votes for LeBron and Kareem,

LeBron: 1x14, 2x10, 3x3, 4x2, 6, 12, 23
Kareem: 1x2, 2x12, 3x15, 4, 6, 8

It is obvious most ranked LeBron over Kareem. In a direct H2H comparison, 24 out of 32 voted for LeBron over Kareem. But because LeBron had two haters who left him out the top 10, he ended up behind Kareem overall in average rankings. I am not saying we have to throw those two votes out but there is clearly something wrong with the vote counting method if the opinion of just two voters can override the vast majority.

(Don't know who will be running the top 100 project this time but I would recommend the H2H vote counting method I used in the peaks project to avoid manipulation like this. It's quite intuitive and there is already a script to tally up the votes automatically.)

The initial results are indeed with the 4 statistical outliers (those outside the red confidence ellipse) included, at the end of the post I provided the adjusted overall rankings excluding them:

Spoiler:

Here is an updated version of the 1st graph:

Spoiler:

So the PCA can help adjust against the skewing, but as you can see this can also be somewhat arbitrary depending on how strict the red confidence ellipse is drawn.

[WestGOAT]

Btw would you guys be willing to rank at least 50 players at the end of the season, or even 100 ?

Would be great to have a more exhaustive list!

[rk2023]

Btw would you guys be willing to rank at least 50 players at the end of the season, or even 100 ?

Would be great to have a more exhaustive list!

I’d be down to chime in and participate while trying to get to 50, would be a fun community project I feel like (sans a few trolls sabotaging votes). I take it new participants not on the original spreadsheet are welcome?

[Texas Chuck]

I will never understand manipulation attempts in such projects. Some people take the results way tok seriously, without focusing on what actually matters.

JJ Barea is a top 15 all-timer or I riot.