In Fun&Games with Sets and Subsets I wrote
We tend to think of the FBS football schedule as not being as wellconnected as basketball or baseball because fewer than half the teampairs are opponents' opponents. However, it turns out that the connections that do exist are highly robust. A few years ago in baseball there was one A↔B↔C↔D↔E chain which if broken would cause the diameter of the schedule graph to grow from 4 to at least 5. If we count the number of games with a nonzero RC for each of the 237 FBS teampairs that are 4 steps apart, we find that to increase the schedule graph's diameter by 1 we'd need to eliminate 69 games. That's over 10 percent of the schedule!but while what I wrote in the article was otherwise correct, it turns out the program that produced the report I based the statement on was not counting games as I described.
I found the error while generalizing "responsibility count" to include distances less than the schedule graph's diameter. Define RC_{n}(game) (1 < n ≤ diameter) as
x ∈ O_{[ i ]}(a) and y ∈ O_{[ j ]}(b)
distance(x,y) = n 
Now we can define a more complete measure of a game's contribution to connectivity:

The Connectivity Contribution by Game includes corrected values for RC_{4}(game) and the corresponding count of games that connect teampairs 4 edges apart. The connections are still robust, but not astonishingly so.