Blog Post #2 - To Function, or Not to Function

Stewart Hiles


Part 1:

Alright, what better way to show a function than to tweak an existing example from class and tailor it to my interests!  Using data compiled from the NHL’s website, I’ve decided to look at the goals scored by Corey Perry of the Anaheim Ducks since his debut at my home town in the 2005-2006 season.  Note that these are only regulation goals, excluding goals made during playoffs.  Also excluded are goals made last season, as the series was atypically shorter.

X (Season)                                          Y (Goals Scored)

2005-2006                                            13

2006-2007                                            17

2007-2008                                            29

2008-2009                                            32

2009-2010                                            27

2010-2011                                            50

2011-2012                                            37

This data represents a function because each input (the season played) can only ever have one output value (number of goals scored).  It is physically impossible for Corey Perry to have two different sets of recognized goals for any given season.

Clearly, this graph is non-linear.  While there is an overall trend upwards, the rate of change has not been consistent from any one point to the next, as well as the presence of steep declines.

To explain:

The ROC for this particular graph is:

37-13 / 2012-2006  =  24 / 6 =  4

While this matches with the first given interval between the 2006 season and the 2007 season.

17 – 13 / 2007 – 2006 = 4/1 = 4

Clearly, we can see that, visually, the rate of change is not constant. 

This is not a mathematical model.  There is no way Corey Perry’s performance can be explained by a simple y=f(x) model, using y as the number of goals and x being the year he plays.  There are too many factors that go into any players performance in a year:  too many to possible list, but several common sense ones should come to mind.  While advanced math may roughly guestimate short-term performance, such an all-encompassing prediction of a players goals would be ridiculous and futile. 

Part 2: 

http://www.chp.ca.gov/switrs/

The California highway patrol lists the recorded traffic accidents every year on the roads in California, in addition to the causes of each death.  When looking at the aggregated data, we can see that this is not at all a function.  Any death could’ve been caused by overlapping reasons that another death was recording having.  If a driver was listed as being drunk and driving without front headlights, and another was listed as driving without one headlight yet was talking on the phone, there really is no correlation at all between the two deaths.