Why Six Points is About Right for What Used to be a 25-Point Penalty

I was watching the movie A Clockwork Orange the other night.  There is a scene where Malcolm McDowell, having been “rehabilitated” and returned to society incapable of defending himself, is being beat up by an old man.  He can’t even defend himself.  For some reason, it made me think of Kyle Busch.

To top off an already tough couple of weeks, Kyle’s car failed tech inspection (the front of the car was too low) after his third-place finish at Pocono last week.  NASCAR made a rare exception to their Tuesday penalty announcements due to the NASCAR Hall of Fame announcement being scheduled for Tuesday.  Monday, NASCAR docked the team 6 points and fined crew chief Dave Rogers $25,000.  Under the old scoring system, this would have been a 25-point penalty.

Six points seemed like an odd number (I know, it’s an even number – I mean odd strange).  Just out of curiosity, I graphed the new scoring system against the old scoring system (shown at right). I ignored bonus points because they are variable from race to race.  The bonus points put a little wiggle in the graph here and there (again, depending on which race), but they don’t change the overall conclusions.

The points toward the left and toward the bottom represent the worst finishes.  The last point in the upper right-hand corner represents the winner.  For most of the graph, the relationship between the old points system and the new points system is linear.  Using the handy formula y = mx+b, we can calculate that for the lower part of the graph, the slope (m) is 3 and the intercept (b) is 31.  Look to the bottom of the blog for a large graph showing the slope.

The 31 is simply an offset.  Under the old system, the lowest score you could get (assuming you were in the race) was 34.  In the new points, the lowest score you can get is 1 (1*3=3; 34-3 = 31 QED).  What we’re really interested in here is points relative to other people’s points, not points overall.  We could have taken the old system and subtracted 31 from everyone’s score and the results would have been just the same in terms of where people finished and how far away they were from the next person.  The relevant parameter here is the slope.

Notice that when you reach position 10 or so, the data start to deviate from a straight line.  NASCAR used to make progressively larger differences in points as you finished higher.  There was much more difference from 1st to 2nd than there was from 9th to 10th. That was done to try to reward drivers for finishing races.  The new scale is 100% linear and the motivation to win rather than place a comfortable second is that the last two spots in the Chase are determined by number of wins.

If you approximate a straight line going positions 10 though 2, you end up with a slope around 4-2/3.  So at the low end of the finishing order, one point in the new series is about three points in the old one.  If you look at higher finishing places, one point in the new series is about 4-2/3 points.  I drew in the slopes and made the picture bigger below to make it more evident.  You’ll notice that my straight line for the higher finishers is not a great fit due to the non-linearity.  I didn’t even try to include the winner.

Twenty-five points would correspond to anywhere from 8 points (using slope 3) to 5.4 points (or so, using slope 4-2/3).  So 6 points is on the lower end of the range, but it seems perfectly reasonable.  Too bad for Dave Rogers they didn’t scale the fine as well – he’d be ($25,000-$6,000=) $19,000 richer.