No, I don’t drink alcohol. However, research shows that sleep deprivation is just as bad as alcohol impairment so I have rightly titled this post as the “Sober Second Thought” after copious (11!) hours of sleep.
At any rate, this is a follow-up post on yesterday’s article, Z.
If you do not wish to read the giant wall of text I wrote yesterday, I blame you not. Thankfully, I have enclosed a tl;dr to the dilemma I encountered yesterday:
Problem: How do you compare the scores of competitors in martial arts competitions in different events (separated by age, sex, skill level and style) without re-testing such competitors in similar brackets?
“Answer”: Seeing as each competitor’s score is already a mean score calculated by averaging the scores given by several judges, and given the fact that each event has at least two competitors in it, it should be relatively simple to calculate the Z-scores of each competitor’s score by finding the mean and standard deviation of the scores in each event.
Advantages – The advantage of calculating Z-scores for each competitor’s event score makes it so that we can compare competitors across different age groups, styles and level, based on the performance of other competitors in the same event. The process of calculating Z-scores can easily be automated through Excel as long as you have a working database that can log competitor scores.
Disadvantages – The main roadblock to the Z-Score method is that we cannot assume normal distribution through the Central Limit Theorem for all the events, since not all events have at least 30 competitors in it. In an ideal world each event would be normally distributed, but I’m not going through all this to forego reality and wish for a better scenario; I’m trying to think up some tools to combat problems that I see in the competitive scene (in terms of efficiency, mind you, the current process is still fair and relatively unbiased).
So, what now?
My original hypothesis was to draft a method that would allow me to compare events without bias. However, after some careful thought I have realized that it is not the correct approach to try to remove bias from the individual events, especially for large prizes (Best All-Around, Grand Champion). This is because competitors in the “advanced” divisions deserve to have higher scores on average (9.2, 9.5, 9.7, etc) as opposed to lower scores in the novice and intermediate divisions (6.5….7.444, etc) because they have earned such scores just by being in such a bracket. To sum it up, if you’re teer-tottering and wondering if you belong in an intermediate or advanced division and end up choosing intermediate, you deserve to have a slight disadvantage in going for the grand champion or best all-around trophies, because your mentality would be that you’re “not good enough to compete in the advanced division.” Therefore, my aim to remove bias from the different events is fundamentally flawed. We WANT bias in these events.
So, seriously, what now?
Three thousand words later, you’re probably not surprised at my final conclusion: Nothing.
That’s right, we change nothing.
If the events are already biased towards giving “advanced” competitors an advantage over “intermediate” competitors, then the average scores of such competitors are already reflective of their skill and ranking over other competitors. This means that, in order to find a grand champion/best all-around competitor, all we would have to do is average the competitor’s scores (for BAA) or just choose the highest score (for GC). Besides, if we were to use the Z-Score system, competitors who were in event with very few individuals would have highly variant Z-scores (waaay better than the average or, in a scenario where the competitor is the only one in the division, a Z-Score of 0).
It’s been an interesting experience. I’m sure this will be useful for me in the future. Mostly as a good laugh when I’m 30, or an “oh wow you really are wasting time over the summer” moment when I’m in my mid-20’s. Hurrr.
Signing off,
Chris
