Statistics of British Open winners after the 2nd round

We are now in the second round at the British Open and players are scrambling to make the cut.  An analysis the the scores of the previous winner since 1980 provides some interesting results and trends.  Here are some of the trends that I have noticed.

The average combined score is 137 and the median is 138 but this represents only 10 winners out of 30.  But from the graph below you can see a wide range of scores.

Similarly the average score for the second round for the eventual winner is 68 but the spread is quite large.

More interesting though is the graph showing the number of eventual winners and how far they led or behind the leaders they were.  Again there is a fairly large spread but 19 winners either lead by a shot or were within 3 shots of the lead.  Not a great correlation but something to note.

My conclusions from this analysis is that there is no real strong correlations here.  Players are scrambling to make the cut which can lead to variable scoring.  However it does appear that players that are leading by more than 2 shots have trouble holding on to the lead while trailing by more than 4 is too much of a deficit to overcome.  But as we all know exceptions do happen!