Hello,

I've been testing out some data analytics on recently grabbed data, so I wanted to answer a very simple question. What maps do you play to farm pp effectively?
This study is based on players who have played quite a few ranked maps and have had good success in obtaining a high score even though the star rating was high, vice versa.

Results here have some limitations, I'll list them down before you get your hopes up:

1. Only maps that have been ranked from Jan 2015 ~ Oct 2018 are included
2. Loved maps aren't included (They skew the data too much)
3. DT isn't included as well (Limitation of osu!API)

That's most of the easier to explain limitations, here's the results, I believe these are accurate to a high degree, but I wouldn't say these are perfect, take it how you will.

What do the predictions mean?
Mean it's predicted that, with the current top 100 player scores, the star rating will be that value. There are 2 methods of calculation, hence there are 2 different predictions.

All Results in a PDF

All Results in a Google Sheet

Use Filter View to change the filters!
Data -> Filter Views... -> Create Filter View

You can mess with the filters with this button.
Don't worry, it won't destroy any of the original data.

Want to know how it was calculated?
Here's the Research Document

Have some improvements/criticism to share?
Feel free to comment below on what you think can be done better.

Thanks for reading.

not at all surprising that the most undervalued maps for 4k are sv heavy, a mechanic completely ignored by the sr calculator, while the most overvalued maps are jumptrill heavy

interesting to see nonetheless

Your analysis fits, for each player, a curve that estimates the "alpha" (score/star_rating) given the star rating of each play. In theory, this curve should be decreasing (score is decreasing with star rating, and you are dividing by star_rating on top of that).

Deviations from that curve allow finding which maps are too hard or too easy to get a score despite their star ranking, assuming the a 3 degree polynomial fit is flexible enough to fit the data according to the theory. I think that in this case it is better to use a non-parametric fit to the data instead of the polynomial. For example, an isotonic regression assumes less things about your theoretical curve https://en.wikipedia.org/wiki/Isotonic_regression

pp is directly proportional to a piecewise linear function of score (the function goes from 0 to 1, with 0 slope below 500k score, 0.3/100000 slope in the 500k-600k range, and the slope decreases by 0.05/100000 for each 100k range), and directly proportional to star_rating^2.2.

This means, if you are interested in finding a map that gives too much or to few pp for its star rating, deviations from the theoretical curve of X amount of score in a high star_rating map, are more important than deviations of X amount of score in low star ratings maps; the score range the score is also has an effect (for example, differences in the 900k-1M range are less important than differences in the 700k-800k range).

In theory, for a single player, the pp vs star_rating curve should be quasi-concave. For low star rating, it should give low pp values, since the star_rating is too low for the player to represent their skill. The value should keep increasing with star_rating until the difficulty of the map is too high for the player to make a decent score. I think finding deviations from this theoretical curve is more relevant for findings maps that are overrated/underrated.

Full Tablet wrote:

Deviations from that curve allow finding which maps are too hard or too easy to get a score despite their star ranking, assuming the a 3 degree polynomial fit is flexible enough to fit the data according to the theory. I think that in this case it is better to use a non-parametric fit to the data instead of the polynomial. For example, an isotonic regression assumes less things about your theoretical curve https://en.wikipedia.org/wiki/Isotonic_regression

That is true, I assumed a 3 degree since it just "looked" like it would fit, isotonic regression seems to fit a lot more in this study though since I'm not looking for projected values outside the data set. I'll do a comparison of it

Full Tablet wrote:

pp is directly proportional to a piecewise linear function of score (the function goes from 0 to 1, with 0 slope below 500k score, 0.3/100000 slope in the 500k-600k range, and the slope decreases by 0.05/100000 for each 100k range), and directly proportional to star_rating^2.2.

I feel like it's a bit of a stretch to use a piecewise func since I'm doubting the accuracy of it, I'll however make use of the star_rating^2.2 relationship, that one will deem very useful for me

Full Tablet wrote:

This means, if you are interested in finding a map that gives too much or to few pp for its star rating, deviations from the theoretical curve of X amount of score in a high star_rating map, are more important than deviations of X amount of score in low star ratings maps; the score range the score is also has an effect (for example, differences in the 900k-1M range are less important than differences in the 700k-800k range).

That is true, I wasn't really looking at "normalizing" the head and tail of the deviations since I wasn't confident on how certain score relate to difficulty faced by the player. I ended up with more of a non-comparable result between the negative and positive values, but they are still inter-comparable between their polarities.

Full Tablet wrote:

In theory, for a single player, the pp vs star_rating curve should be quasi-concave. For low star rating, it should give low pp values, since the star_rating is too low for the player to represent their skill. The value should keep increasing with star_rating until the difficulty of the map is too high for the player to make a decent score. I think finding deviations from this theoretical curve is more relevant for findings maps that are overrated/underrated.

This is a much neater comparison than what I was doing, removing the need of having extra variables, I'll definitely look into it.

Thanks for the feedback!

ITT: Stats nerds.

But seriously, the results already look pretty much the way I expect them to. It will be interesting to see what works well for refining things though.

I have added something much more interesting and easier to engage in. Here are the changes:

1. Changed Prediction to Star Rating (less abstract)
2. Added Isometric Prediction alongside Polynomial Prediction
3. Added to Google Docs and csv format (in GitHub) for ease of usage

You can use Google Docs and add your own filters with:
Data -> Filter Views... -> Create Filter View

It's more customizable that way

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Apologies for removing some of the PDFs, the procedure to creating these PDFs automatically is giving me a headache.

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Special Thanks again to Full Tablet for the feedback, this is much better now

Mostly checks out. Empress [SC] does not feel easier than Speedcore [Extra]. Burn this moment into the retina of my eye being harder is debatable.

Seems like around 4.9 stars would be my limit.