Fun with Excel - Equality III

In this Fun with Excel project, I am looking more at simulations than mathematical formulas. There can be drawbacks to this approach. In my latest spreadsheet, I was hoping to see my point a little more pronounced. Even so, I do think the point has become a little more clear.



In case you didn't read my last post in this series, I have been trying to show how people can stand out more as you take more into consideration. My calculations have primarily been based off of how many people have to be taken into consideration before someone better than anyone else is found.

The latest spreadsheet can be found at https://1drv.ms/x/s!Ar3VXpGA-24ugYFmaSG3o2WPOHAlKA
 The only real difference between this spreadsheet and the last is that a fourth skill has been added and the numbers have been rerun.

On the Trends tab, I have provided the result of 100000 runs. The minimum, maximum, average, and median have been included based off whether one, two, three, or four skills have been considered. I have also included a distribution table.

I apparently didn't include the raw data, but the numbers are getting larger as more skills are taken into consideration. There is even an exponential component. This should help prove my point about how people look better as you take more into consideration.

Although I am trying to avoid too much math, there is a simple component to the calculations made. Powers of two are at work. With one skill considered, there is a one in two chance that one individual will be stronger than the next. With two skills, this becomes one in four. From there, it becomes one in eight then one in sixteen.

These numbers aren't going to match due to how these numbers are calculated. For example, one skill will always result in a one because if the first isn't weaker, the second person will appear weaker than the first. As a result, there will always be signs of one individual be stronger than another if you look at two people.

This latest spreadsheet has been pushing my computer a little harder than I like. I don't want to have to wait for calculations based on five skills, so this specific sequence is likely complete. I wanted to think a little, so I didn't start with the most obvious comparisons. I will continue to use Excel to show my views on equality, but expect my next post to be more straightforward.