Super Bowl Squares - Part 2

This post is in response to a comment made regarding my previous post on the same subject.  The suggestion was made that I only consider games since 1994 since that is when the two-point conversion was introduced.  The new distributions are shown in the charts below.  There is also a chart at the bottom that compares the previous chart with the changes to the probabilities.

The distributions did change.  Some of it I'm sure due to the introduction of the two-point conversion.  Some of it is by random chance.  And, the uncertainty has increased.  The # of games over which this data is analyzed is 3,884, a reduction from the 9,509 in the previous sample.  All else being equal, and they are rarely if ever equal, the reduction in the sample size alone creates a larger uncertainty in the estimated probabilities (technically speaking, if the sample size increases by a factor of n, then the error in the estimate increases by the square root of n).

Therefore I'm not necessarily sure that these are better estimates of the true probabilities, but it is now shown.  What we may have gained in relevance, we may have given up in the uncertainty around the estimate.