Differential Equations

I hated this class at Nova.  It was my least favorite class by far, and I enjoy and have always been good at mathematics, part of the reason for why I do this blog.  This post is about score differentials throughout a game.

I am continuing to do a longer research project on the concept of ‘a run.’  The impetus for this research is two fold. First, from observations so far this year, I feel as if we have not had many true ‘runs’ (especially against any quality opponent).  Secondly, this train of thought follows along nicely with my last post about what our bench is able to provide to this team.  If our bench contains our strong defensive players who give great effort and hustle (qualities I believe you need in order to create a run and qualities which our Main 5 do not seem to have) but who lack offensive capabilities (again a quality necessary for a run but also qualities our Main 5 have), then how can you actually create a run.  It seems as if our bench and our Main 5 have 2 separate pieces of the puzzle, and we have not yet figured out a way (lineup?) that puts the two together. 

A major hurdle in this research project, one which I have thus far failed to overcome, is how should a run be defined.  I suggested above that there needs to be a combination of offense and defense, but what is the appropriate threshold.  Is it 4 successful offensive possessions (not necessarily consecutive) without allowing your opponent a successful possession?  On the opposite side of the spectrum, we could define a run as in any specific amount of time/possessions when you double the score of your opponent.  So any time we score 10 points and our opponent scores 5 or less in a stretch.  Both of these seem inadequate.  In any event I attempted to compile some data from our games hoping to find some trends that could help me create a successful definition.  In doing so I created these graphs which display the point differential throughout the game.

I plan on pursuing my research on ‘runs,’ but that will have to be for another post.  Now for the questions.  In games we win: do we create runs or simply play more efficiently than our opponent; and in losses: do we give up runs, or simply play less efficiently than our opponent?  The graphs show an interesting story so far, check them out.

NOTE:  In a spreadsheet I put in two columns the Nova score and the opponent score every time there was a point or points scored.  So the x-axis reflects how many times a score was made, and thus it does NOT reflect the time on the clock or of individual possessions.  Pretty much the x-axis is meaningless really.  The line represents whether or not we are ahead by so many points or behind, and the space where the line breaks into two lines is halftime.  I have put up 4 games.  2 wins & 2 losses.  1 win and l loss which are NOT typical games (Syracuse & Providence – doesn’t it suck that you have to say you lost to Providence?  I didn’t even want to have to type it.) and 1 win and 1 loss which are relatively normal (Georgetown & Maryland).