It's been 10 years since I picked up a stats book and wondering what's the best tool for the job. Given 2 systems, 3 categories in each system (better, same, worse) and for each category two outcomes (a win or loss). Is there a statistical significance of a win or loss between the 3 categories?

Or to rephrase the question, treating the two system separately, if the category is either better / same / worse what is the probability of a win / loss and the significance of that probability?

To add a layer of complexity/sensitivity(?), if the categories were numbers where using the previous scenario a zero fell into the "same" category, a negative number fell in the "better" category and a positive in the "worse" category, is there a test to see if a number range or particular quartile bears any significance to the probability of a win / loss? So the next time a number falls into a particular range / quartile the probability that the result is a win / loss is x and the probability is statistically significant?

Attached the data set in question.