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Maybe you can understand it this way.
We are talking about the average ranking. You have solved for how many teams there would be if you split the league in half.
To solve for the average ranking, you must add all of the values together and divide by the number of values. Avg=sum of numbers/amount of numbers
You can be ranked with each number from 1 thorugh 32. 1+2+3....+32= 528
528/32=16.5
See now it works for any quantity.
3 teams 1+2+3=6/3=2 2 is the average ranking for a 3 team league
4 teams 1+2+3+4=10/4=2.5 Less than 2nd is above average, more is below average, there is no 'average' team out of an even #, so an average ranking lies in between the 2 teams in the middle
Got it yet?
You guys are having such a great discussion here that I hesitate to intrude, but this might help.
Statisticians resolve the conundrum with which you seem to be dealing by differentiating between the "Median" and the "Mean" of a distribution. The Median is the midpoint, the Mean is the average. In the 50-50 likelihood that a distribution has an even number of observations, the Median is the average of the two middlemost observations.
Taking it just one level deeper, the Median seldom equals the Mean (to use your language, the "Average" is seldom equal to the "Midpoint") unless the distribution consists of a set of identical values, which is, of course, very rare and certainly not the case when it comes to 32 NFL teams. If the Mean is larger than the median, it suggests that the distribution is top heavy; if the Mean is smaller than the median, it suggest that the distribution is weighted to the lower end.
Finally, Statisticians derive the size of the Standard Deviation around the Mean as a way of resolving the problem I think (emphasis on "think") you are trying to solve, but I'll keep this short, other than to say that relying on Means (averages) to predict or define the behavior of the elements of a distribution is a dangerous thing to do. It's called the "Flaw of Averages."
Hope that helps and, one final question: what predictions did the two of you make that led to this informative debate? They're lost many pages back.
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