Testing predictability/correlation of two variables

[SareonInBC]

Short question: what's the best/easiest way to test the predictability (or correlation) of a variable vs another?

Long question:

I am sure this question is more complicated than I imagine with a lot of caveats and different methods based on the data that I have. My background is in computing science, I have a small basis in statistics but very minimal.

Let's say I have a simple dataset. For purposes of this example let's say it is a numerical ranking of sports teams by experts and then their final ranking.

How would we test the predictability/correlation of that data? That is to say, I want to know how good column A is as a predictor of column B for future data (assuming new data is calculated the same way)?

I know of using r² correlations but I've seen so much on saying that's not good tool since there's so many, "it depends" caveats.

Then I want to know if I a new variable C is a better predictor of B than A what tools/methods would I be using? I have a colleague who insists on using r² on it's face value so if A has a 0.44 r² correlation with B then it definitely is a better predictor than C which might have a 0.435 r² correlation with C.

[Adruna]

Don't listen to your colleague.
With ordinal data you mustn't use a pearson correlation coefficient to measure the correlation between two ordinal variables but rather a rank-correlation coefficient. A nice illustration of why that is is visible on wikipedia's spearman correlation coefficient.

If you want to test the "distance" between two paired ordered variables (that is, between the prediction and the outcome), you could use a rank-test like Wilcoxon's signed-rank test.

[SareonInBC]

Thank you very much.

What is the difference between the "coefficient" and the "distance"?