Will the Gen-6 Car Affect the Number of Cautions?

 Cautions, Edwards Carl, math, Racing, Tony Stewart  4 Responses »
Jan 252013
 

I love the Gen-6 car.  Not as much as I love the Nationwide cars (but that’s got more to do with what I drive than it does the cars).  The big question is whether the decrease in cautions is going to be changed because of the new car.Let’s start (as we usually do) with the new car.

Graph4Let’s start (as we usually do here) with the data.  I’ve tabulated the data for cautions for the last twelve seasons and found that cautions have been decreasing since 2005, as shown,  for both the Nationwide and the Sprint Cup series.

In order to compare the two series and to compare between seasons within a single series, I’ve plotted the number of cautions per 100 miles.

In 2012, the Sprint Cup series had 1.57377 cautions per 100 miles.  They drove 13725 miles total, so that was 216 cautions total.

In 2012, the Nationwide series had 2.23969 cautions per 100 miles.  They drove 8240 miles, with comes out to 189 cautions — essentially the same number of cautions per mile they had last year.

Conclusion #1.  If the Nationwide drivers had driven the same number of miles as the Sprint Cup drivers, they would have had 307 cautions.

You’ll notice that I’ve drawn lines through each set of data.  They aren’t just a best fit by eye – I actually did a non-linear least-squares fit that determines the line that goes closest to all the points.  The data are decidedly linear and, more importantly, there aren’t any bumps or jump in, say, 2008, when the COT (which I guess is now the Gen-5 car) was introduced, or in 2011 when the Nationwide car was changed.  The data remained pretty consistent.

Conclusion #2.  Cautions are not affected much by the car that’s being driven.  Sure, I expect there to be some driver errors when a car doesn’t handle the way the driver expects it to behave; however, these guys catch on really quickly, so that’s going to be maybe 5 cautions.  Five out of 216 is like 2.3 percent, which is well within the error in the fit parameters.

Why are the cautions decreasing?  I’ve gone into this before, but I believe it is essentially because the drivers have a lot more experience now than they did in previous years.  There are a lot of veteran drivers in the Cup series right now, and I calculated that if you add up all the races run by the current crop of drivers, they have run a total of about 1000 more races in 2011 than they did in 2005.  That’s a whole lot of experience, and it’s distributed amongst the drivers.   Compare just two drivers:  Tony Stewart had run 248 races in  2005 and at the end of 2012, had run 500.  Carl Edwards had only run 49 races in 2005 – compare that to the 301 races he’d run as of today.  (I am only counting points paying races.  If you could somehow quantify the number of practice laps, time testing, etc., I think that would only make my argument stronger.)

So, in short, I don’t expect there will be any significant change in cautions because of the new car — up or down.  What do you think?

 

Is There Really a Second-Place Curse?

 Clint Bowyer, Dale Earnhardt Jr., Denny Hamlin, Edwards Carl, Jeff Gordon, Jimmie Johnson, Kasey Kahne, Keselowski Brad, Kyle Busch, Mark Martin, Martin Truex Jr, math, Tony Stewart  No Responses »
Dec 072012
 

One of the commentators after the final race in Homestead mentioned that Jimmie Johnson should be happy he finished in third because it allows him to avoid the “dreaded second-place curse”.
Anytime someone says something like that, it makes me wonder whether there really is a curse, or whether that person had just been talking to Carl Edwards.  So I analyzed a little data and guess what… there really IS a second place curse.

I used data from the last twelve years — from racing-reference.info, bless them!  After trying a couple of different approaches to making the data easy to visualize, I ended up with something a little more complicated than I would have liked.

Bear with me – it’s not as yucky as it looks.  I have plotted on the horizontal axis the place in which a driver finished in the first year listed, which we’ll call “X”.  I then calculated the change in positions of the same driver the next year (X+1) and plotted that on the vertical scale.  So the first set of data has X = 2000 and X+1=2001.

  • A positive number on the vertical axis means that the driver finished better by that many places in the following year. For example, +5 means that the driver finished five places better the next year than they finished the year before.
  • A negative number on the vertical axis means they finished worse the next year. A -5 means they moved down five spots in the final standings.

I went through and removed any special cases — like Mark Martin running full time one year, but not the next, Busch brothers missing races (that’s a different kinds of curse), people retiring, etc.  The graph below summarizes the top 16 finishing places and the change in final standing over the last twelve years.

There’s an obvious statistical implication:  If you finish second, for example, you have only one place to move up and forty one places to move down.  You’re either going to win the championship next year, become second again, or move down.  The probability is that you’re going to finish worse than second.

To look at the data in a slightly different way, I plotted it the same way they plot the daily activity of the the stock market:  the symbol shows you the average.  One line extends up to the maximum increase in position and one line extends down to the largest drop in position.

 

The first-place curse

In fact, if we’re going to call dropping in the standings a “curse”, then there is clearly a first-place curse that affects everyone except Jimmie Johnson.  Mose drivers who win the championship one year inevitably finish worse the next year.  When I say ‘drop in points’, it’s not a huge drop:  nine places was the most anyone who finished first dropped.

The average first time finisher fell almost five positions.  That’s including four consecutive ’0′s due to Jimmie Johnson.  If we exclude Jimmie just because what he did was really unprecedented (and unlikely to be duplicated), the average first-place finisher falls almost seven positions the next year – about the the same as the second-place driver.

The second-place curse

Second place shows a very similar story, only worse.  There is only one case in twelve years in which the second place finisher one year won the championship the next year.  That was Jimmie Johnson.  Whoops – Rick pointed out my mistake.  It was 2001 -2o02 and the driver was Tony Stewart!  On average (including Jimmie), the second place finisher finishes about seven positions lower the next year.

The three biggest drops in point standings (-15, -13, -11, -9 and -7) are due to Martin, Edwards, Biffle, Edwards and Hamlin.  There are no extenuating circumstances like crew chief changes, owner changes, etc. on which to blame the drops.  Four out of five of those drivers were all driving for Roush at the time… maybe there’s a Roush curse?

The bad news for Jimmie Johnson… and everyone else who made the chase

Here’s the bad news for Jimmie:  Yes, he avoided the second-place curse; however, no third-place driver has gone on to finish first or second the next year.  The best they’ve done was to match their third-place finish.

Yep, perhaps there’s a third-place curse as well, as third-place drivers finish an average of three places lower the following year.

In fact, you don’t find a finishing position in which there is an average probability of bettering your finish until 7th place.  On the graph above, you can see that the majority of finishes were improvements, although without one -11 change, it would be a much more positive number.  After that, it’s an oscillation between slightly better and slightly worse.

A caveat of this data analysis is that the Chase sort of messed things up going out past 10 because a driver in the Chase can’t finish lower than 10th, even if he misses races or otherwise would have fallen much lower without the Chase format.

 

Degrees of Difference: How is Martinsville like Fontana?

 Auto Club Speedway of California, Martinsville, math, Talladega, Texas Motor Speedway, Trigonometry  1 Response »
Oct 252012
 
DLPTXTrackBanking

I love getting questions from readers because I always worry that the geeky stuff I find interesting is only interesting to me.  I love it even more when they not only give me a question, they also supply part of the answer!  This one has to do with the degrees of difference between Martinsville and Fontana.

Michael J. Clark asked a really good question about Martinsville and Fontana:

Why does Fontana (banking in the turns is 14 degrees) seem to have such higher banking than Martinsville (banking in the turns is 12 degrees)?  I would think the 2 degrees more that Fontana has wouldn’t look so dramatically different than Martinsville, but it really does.  I’m guessing it has to do with the fact that Fontana’s turns are about 10 car-widths wide (my estimate) compared to the turns at Martinsville, which seem to be about four car-widths wide.

Great question and another example (like race cars seemingly speeding up when spinning into the grass) of how our perceptions are often subjective.

We always talk about Martinsville being a “flat track”, which is sort of unfair.  It’s flat compared to Talladega and Daytona, but there are still twelve degrees of banking in the turns.  Nothing like a little trigonometry at the racetrack – what does twelve degrees look like?  Let’s start with some definitions so we’re all talking about the same things.

Track width is measured across the track surface and forms the hypotenuse of a right triangle.

Any right triangle can be described by the lengths of any two sides, or the length of one side and one angle.  Remember SOHCAHTOA? You can (finally!!) use your trig to reverse engineer the racetrack.

One degree isn’t really all that large.  A banking angle of one degree means that in order to get a rise of one foot, you need to have a run of about 57 feet.  One degree isn’t very much, as shown in my figure below.

The top picture shows what a banking angle of one degree would look like, with the rise of 1 foot and the run of 57 feet.

The bottom picture is a scale drawing of Martinsville Speedway, which has a track width of about 55 feet (although I think it is a little narrower in the corners).  The banking angle is variously given as 11 degrees or 12 degrees.  I’m using 12 degrees here because that’s what the official NASCAR site says.  Given the hypotenuse (track width) and the banking angle, I can back calculate to show that the rise is about 11.4 feet and the run is about 54 feet.

Now to Michael’s question.  The diagram below shows scale drawings of the banking at Martinsville and California and (just for comparison) Talladega.  I’m using the best numbers I can find on the web.  If someone has more accurate numbers, please let me know.  Kudos, by the way, to Talladega for having one of the best webpages of track data.

Michael has great instincts – the track at Fontana is two-to-three car lengths wider than Martinsville.  This means that the rise is seven feet (one Brad Daugherty) higher than Martinsville at the edge of the track. That increase in rise makes the banking look steeper because you’re looking up a greater distance.

(You always hear that Talladega is five stories tall.  I’m not sure what they’re counting in that calculation because I get 26 feet, which is pretty far short of five stories unless you have very short stories.)

In addition to the greater width, you also have to remember that there’s a huge difference in overall scale.  Martinsville was the second track I visited while writing The Physics of NASCAR – the first was Atlanta.  Martinsville was the track that made me love short tracks.  You get up close to the action and even though they’re not going 200 mph, when you’re that close to them going 100 mph, it seems really fast.  Short tracks are a great challenge to the crew chief (and the driver) because suspension movement is so much more important than aerodynamics.  And, of course, tempers seem to be proportional to the track length of the track:  at Martinsville, they are both really short.

But you have to realize just how much smaller Martinsville is than the California track.  The straights at Martinsville are 800 feet, while the backstretch at Fontana is 2500 feet.  Martinsville is .524 miles, which is 2777 feet.  If you unrolled the Martinsville track, you could just about fit the entire thing on Fontana’s backstretch.  The picture below is my attempt to make a to-scale drawing of the two tracks.  The banking at Fontana looks huge compared to the banking at Martinsville not only because the track is wider at Fontana, but also because the track is simply bigger.  When you look out into the turns, you simply see a lot more asphalt.

Side note:  The featured picture in the post at the top shows me trying to stand up on the 24-degree banking at Texas Motor Speedway, just to give you an idea of how steep 24 degrees actually is.  This was while we were shooting the Science of Speed video series.

So that’s the difference between the tracks at Martinsville and Fontana.  I’m told there is absolutely no comparison between their hot dogs.

Thanks for the question, Michael!  Questions (and suggestions for the Sirius radio “NASCAR Mythbusters” segment) are always welcome.  Click on the ‘contact’ tab above to send me an email.

I’m heading out to Joliet, IL to give my  Science of Speed talk at Joliet Junior College Friday October 26th at 7:00 p.m.  More information on how to get there can be found on my appearances page.  My talk is aimed at the average NASCAR fan and focuses on why it’s a lot harder to drive fast than most of us think.  Most people leave the talk with even more respect for what professional racecar drivers do.  I promise no pop quizzes, so please come on out and meet me!

 

 

The Reason for Decreasing Cautions

 Bristol Motor Speedway, Cautions, Consipracies, Martinsville, math, Texas Motor Speedway, Uncategorized  4 Responses »
May 262012
 

This was the first year that most people noticed a decrease in the number of cautions, but (as I’ve pointed out), 2012 is merely the latest in a six-year trend of decreasing cautions.  The same downward trend is evident in the Nationwide Series.  This year is perhaps notable for it being so extreme.

I’ve plotted the cautions per 100 miles (the best way I’ve found to compare changing race lengths and different tracks) for Cup races so far this year at right.  The plot shows the minimum and maximum values for each track, with the average shown by an open square.  The red square shows the cautions for 2012.  At California, Bristol, Martinsville, Texas, Kansas, Talladega and Darlington, the 2012 value is the lowest value in the last six years.

The data clearly shows the trend:  The question, of  course, is why?

Given that it’s happening in both Nationwide and Cup, that sort of eliminates issues like the introduction of new cars (either COT or the new Nationwide car), the Chase Format, etc.  What was left to investigate?  How about the drivers?  A number of commentators has suggested that drivers were just “better” now.  But how do you test this?

I started by deciding that experience and quality could be indicated by number of races run and number of races won, respectively.  I decided to compare 2005 (which had the highest number of cautions) with 2011.

My criteria for including drivers was that the driver had to have run more than 15 races during the season.  That kept the focus on the full-time drivers.  I totaled two quantities for the drivers that made the cut:  the total number of career laps they had run in the Cup Series (including the season in question) and the total number of career races they had won in the Cup Series.

Year 2005 2011
Races run 11109 12180
Races won 485 485

The drivers who spent the most time on track in 2011 had about a thousand (1071 to be precise) more races worth of experience:  with roughly 25 drivers included that’s an average experience level of 40 races, or almost a full season per driver. The number of wins was exactly the same.

I looked into the details as to what had really changed between 2005 and 2011.  We lost a lot of experienced drivers from active competition:  Dale Jarrett, Ricky Rudd, Rusty Wallace, Sterling Marlin, Kyle Petty, Michael Waltrip, and Ken Schrader for starters.  Their places were taken by drivers just starting out:  From 2005 to 2011, Kasey Kahne went from 72 races run and 1 win to 288 races run and 12 wins.  Kyle Busch went from 42 races and 2 wins in 2005 to 257 races and 23 wins in 2011.  Jamie McMurray didn’t make the active list in 2005, but in 2011 had 230 races and 6 wins.  Even the folks we think of as veterans, look at Tony Stewart: from 248/24 to 464/44, and Carl Edwards: 49/4 to 265/19.

Even drivers who haven’t won races have run a lot more races and gained a lot more experience:  Dave Blaney (200 races by 2005 vs. 397 races by 2011).

So I started thinking about the average experience of the drivers.  I made histograms of the number of drivers who had run some number of races, as shown at right and below.  They are plotted on the same vertical scale for easy comparison.

In 2005, 10 drivers had under 100 races worth of experience.  In 2011, only 5 drivers had 100 races or less on their resumes.  (One of those five was the 2011 Daytona 500 winner.)  In 2005, 27% of the drivers had fewer than 100 races under their belts, while in 2011, the figure was only 12%.  Yes, we lost a lot of really experienced driver with more than 600 races under their belts, but the younger, newer drivers also gained a lot of experience over those five years.

I’m not sure you learn as much from the races won.  There were 12 drivers with no wins in 2005 and 11 in 2006.  But there was only one driver who had won one race in 2005 and eight who had won one race in 2011.

There were plenty of people making the aggrandized claim that the reason cautions are decreasing is “these are the best race car drivers in the world”.  I’d make a slightly less aggressive conclusion and say that NASCAR has much more experienced drivers now than they had in 2005 and that’s why the number of cautions has decreased.

There are (as always) caveats.  Having watched the Nationwide race at Charlotte and poor Travis Pastrana causing multiple cautions, it would be interesting to go back and look at whether the drivers I didn’t count in this survey had more wrecks than the regular drivers.

 

Cautions: A Historical Downward Trend Over the Last Six Years

 Cautions, math, NASCAR  4 Responses »
Apr 242012
 

OK, I know I promised the next post was on engines, but I got sidetracked…

Being the data geek that I am, I was really curious if the decreasing number of cautions was specific to this year.  It’s not:  Cautions have been decreasing since 2005,as the graph below shows.  The squares are the cumulative number of cautions per 100 miles, obtained by adding up all the cautions in a season and dividing by the total number of miles in the races.  (This is a more accurate number than total cautions, given rainouts, shortening races and different venues from year to year.)

The straight line is a linear regression, with a R-squared of 0.87, which is pretty good.  The grey box in the lower right hand corner is what the fit predicts the number of cautions should be if the trend continues.

Of course, someone is wondering what happened before 2005. The trend was totally opposite.

My rationale for going back to 2001 is that this was the first 36-race season.  Not a great reason, but that was pretty much it.  The peak number of cautions was in 2005.  What happened in 2006 that sent the number of cautions down?

 

 

Why You Can’t Predict Anything Based on the First 10 Races

 Martinsville, math, New Hampshire, Richmond, Talladega, Texas Motor Speedway  1 Response »
Apr 202012
 

The plot below shows the cumulative number of cautions per mile since 2007.  I’m using number of cautions per100 miles to 1) make up for races that were not run to completion; 2) compensate for green-white-checkered finishes; 3) compensate for tracks that have shortened races; and 4) compensated for changing order in which tracks are visited.

Cautions per 100 miles can be thought of as follows:  If the cautions per 100 miles is 1.6, then the number of cautions for a 500 mile race would average (1.5*500/100) = 6.

The results are sort of interesting:

Things to notice:

1)  All of the final values for cautions per 100 miles end up between 1.8 and 2.4, even though the values at the start of the year ranged from 1.4 to 3.1.

2)  The data for the first 10 races changes wildly with each race.  The data don’t start to converge toward their final values until at least 15 races into the season.  I suspect that if you plotted a drivers’ standing in the points as a function of number of races, you would see the same behavior.  Why?  As the total number of miles run increases, the number of cautions in a race is increasingly small compared with the total number of  miles run.

3)  Despite the decreasing fluctuations, there are still quite a few noticeable jumps upward.  When I saw them, I immediately thought:  Ah – there’s Bristol.  But closer inspection showed me wrong.  The big troublemakers are Richmond and Martinsville, which together account for the largest number of upward jumps.

4)  There seems to be a significant difference in caution rates from 2008/2009 to 2010/2011.  Anyone want to venture guess as to what is responsible?

 

Are Cautions Really Going Down?

 Atlanta Motor Speedway, Cautions, Martinsville, math, New Hampshire, News, Talladega, Texas Motor Speedway  No Responses »
Apr 182012
 

I honestly cannot help it – scientists are naturally skeptical.  If you make an assertion, I will have to question you on what data you have that supports it.  This is second nature to the people I work with, but I realize it is damned irritating to non-scientists (aka “normal”) people.

So when I started reading everywhere that “cautions were down 35%”, I had to go look into it.  This is a preliminary post – more detailed analysis will follow as soon as I’ve read my students’ final projects and gotten comments back to them.

First, let’s talk statistics.  Reliable statistics require large numbers.  It drives me nuts when people extrapolate from the first few races of the year.  You can’t claim much on the basis of five data points.  Even the top quark required seven (if I remember right – they did get more after they announced they’d found it).

The stock market fluctuates up and down.  Everyone except people who are thinking about retiring ignore the short-term fluctuations and focus on the long-term trends.  What do the data say about cautions in NASCAR?

I picked five tracks to analyze in this first round:  Martinsville, Texas, Talladega, New Hampshire and Atlanta.  The first four represent a range of track types, while the last was chosen to see whether the cautions were “cookie cutter-like”.  I first plotted the number of cautions as a function of year for all the tracks together.  If cautions are decreasing, we should see a general trend downward.  Here’s what I got:

Not much of a clear trend, huh?  If anything, it looks like the overall trend (since 1950) is going up.

Thinking it might be unfair to use really old data, I decided to focus on 1997-2012.  I plotted all five tracks on their own graph for just those years.  I’m sorry for the color – those are the defaults on Origin.  I will change them when I do a full post.

What do you think?  I might buy a downward trend for Texas, but it’s hard to make that argument for the other tracks. Martinsville went from 18 in the last race of 2011 to 7 this year – that’s a 61% drop right there — but if you compare it to the Spring race (and an argument can be made for comparing Spring to Spring and Fall to Fall), that race had only 11 cautions.  That’s a drop of 36.3%.  there is a wide gap between those two figures.

Just for fun, I took the historical data for the three tracks with long records.  Here they are:

As I said, I’ll follow this up with more extensive analysis, but I wanted to get the data out there ASAP.

 

How Likely are You to Win the TNT Million Dollar Challenge?

 Daytona, math, Probability  No Responses »
Jun 292011
 

TNT is offering a million dollars to anyone who picks the top ten drivers – in order – at any of the six races they broadcast.  You have up until 25% of the race has been run to lock in your selections, which means up to mile 100 at Daytona this weekend.   How likely are you to win?

You have a 1 in 43 chance of picking the first driver correctly.  There are now 42 drivers left and you have a 1 in 42 chance of picking the second driver correctly.  When you calculate the probability of doing two things, you multiply the probabilities.  It makes sense that there ought to be less probability of picking two numbers in a row than of picking one, right?  So the odds of picking two drivers in the right order is 1 in (43 x 42) or 1 in 1,806.

Continuing this pattern…

# picked in right order

 Calculation Chances are …
1 1 in 43 1 in 43
2 1 in (43 x 42) 1 in 1806
3 1 in (43 x 42 x 41) 1 in 74,046
4 1 in (43 x 42 x 41 x 40) 1 in 2,961,840
5 1 in (43 x 42 x 41 x 40 x 39) 1 in 115,511,760
6 1 in (43 x 42 x 41 x 40 x 39 x 38) 1 in 4,389,446,880
7 1 in (43 x 42 x 41 x 40 x 39 x 38 x 37) 1 in 162,409,534,560
8 1 in (43 x 42 x 41 x 40 x 39 x 38 x 37 x 36) 1 in 5,846,743,244,160
9 1 in (43 x 42 x 41 x 40 x 39 x 38 x 37 x 36 x 35) 1 in 204,636,013,545,600
10 1 in (43 x 42 x 41 x 40 x 39 x 38 x 37 x 36 x 35 x 34) 1 in 6,957,624,460,550,400

That’s one in 6.9 quadrillion to get all ten in the right order.

Is Picking Them in Order Harder?

What if TNT had just said you had to get all ten, in no particular order?

If you look at ten numbers, there are ten ways of picking the first number, nine of picking the second, etc. That multiplies out to there being (10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1=) 3,628,000 different ways of organizing ten numbers in every which way possible.

If TNT had decided that you only needed to get the drivers right, but not the order, your chances would increase to a whopping 1 in 1,917,334,783.

But there aren’t Really 43 Drivers Capable of Placing in the Top Ten…

OK, in reality, the odds are a little better.  The calculation above assumes that the finish is a totally random event and we know that it’s not because there are 7-9 start and parkers.  Realistically, you’re picking from maybe 35 cars (8 S&Ps), so the odds for getting all ten in the right order if you’re only picking from 35 drivers are 1 in 818,441,006,423,040. or 1 in about 818 trillion.

But there aren’t Even Really 35 Drivers Capable of Placing in the Top Ten…

Yeah, the husband tried to make the argument that you’re really only choosing from about 17 or maybe 20 drivers.  Five words:  Regan Smith and Trevor Bayne.

Just for comparison…

Odds of being struck by lightning are 1 in 576,000.
Odds of being killed by lightning are about 1 in 2,320,000
Odds of a meteor landing on your house: 1 in 182,138,880,000,000

So you’ve got a better chance of a meteor landing on your house than winning that million dollars.

Often for promotions like this (free televisions if it snows 10 inches on New Year’s Day!!), a company will take out an insurance policy.  They’ll pay some amount of money to hedge against paying more.  The people at the insurance company who figure out how much to charge them use these types of calculations to figure out the risk.  I’m guessing TNT wouldn’t want to pay much of a premium because the odds are clearly in their favor.  But it’s a great promotion.

Does this mean you shouldn’t play?  Heck no – TNT isn’t charging you to enter, so get your best guess together and see if you can beat the odds.

RANDOM NOTES

Look at this cool project from Clemson and DuPont to take middle and high school teachers to the racetrack and teach them about science!  Way to go, Tigers.

The probability of becoming a saint is estimated at about one in 20 million, but if you’re Jacques Villeneuve, the odds rise to one in a flying pig.

Gratuitous link to The NASCAR Insiders just because their Wednesday Q&A is always worth checking out – it is a blog I always learn something from!

Daytona this weekend – read all about drafting vs. bump drafting, why you’re likely to see two but not three cars drafting together, why NASCAR limits radiator pressure to try to keep the two-car draft to a minimum, and why drivers shift to the right to get air to the engine if they’re turning left.  Or take a look at the Science of Speed video on drag and drafting.

 

100 Million vs. 78 Million is not the Numbers Question for FOX vs SPEED

 math, Media, NASCAR, Uncategorized  3 Responses »
Jun 212011
 

The NASCAR pundits have again simplified a complex situation.  Incorrectly.

(Of course, at least they got the network right!  I got FOX and ESPN confused.  This is the problem with a 60-hour a week job and trying to blog about something utterly unrelated in the meantime.  My excuse is that I have a $3.5 million proposal due this week.  The same math holds, regardless of whether it is FOX or ESPN. Thank you Michael!)

The NASCAR Net is a-twitter since FOX floated a trial balloon about moving races from ESPN FOX to SPEED.  I’ve heard the argument over and over, in print and on radio that this is a bad idea because EPSN FOX is in 100 million homes and SPEED is in “only” 78 million homes.  They argue this would be a decline of 22 million potential viewers.  The question not being asked how many of those 22 million ESPN FOX watchers are actually potential viewers?

Point number 1:  Diehard NASCAR fans are going to find the race on television wherever it is.  Rabid fans are going to get whatever cable package they need in order to watch races, or they’re going to find a local sportsbar that carries the race.  Casual and incidental viewers are the ones that will make a difference in numbers.

Point number 2:  A very small fraction of households receiving a network watch it.  The highest rated race of 2010 on ESPN was August Pocono, with 6.3 million viewers.  Let’s assume an average of 2 people per household, so if ESPN is in 100 million households, that corresponds to roughly 200 million viewers.  ESPN pulled in 3.2% of the viewers who had the option of watching the August race at Pocono.

SPEED is in 78 million households, so assuming the same two people on average per household, there are 156 million potential viewers.  If SPEED captured the same 3.2% of their possible viewers, that would be 5.0 million viewers.  The difference is 1.3 million viewers — if you are willing to ignore point 3.

The numbers for FOX – let’s leave out the Daytona 500, which was 13.3 million and I bet FOX isn’t going to move that – are similar.  The highest rated race was April Talladega, with 8.45 million viewers.  Out of the 200 million possible eyeballs, that’s 4.2%.  4.2% of SPEED’s viewing audience is 6.55 million viewers, so again, we need an increase of about 1% to match FOX’s numbers.

Point 3:  Consider the demographics of FOX viewers vs. SPEED viewers.  SPEED is a motorsports channel.  I would think you’d be more likely to get a motocross fan to watch NASCAR than an average television viewer.  Which network is more likely to promote the race during other shows?  Which network is more likely to have the schedule freedom to do extended pre- and post-race shows?  All SPEED would have to do to equal the viewership from ESPN would be to attract 0.86% of the remaining viewers and about 1% to equal the viewership from FOX.  We’re really talking more like a difference of 2 million than 22 million.

There are many factors besides numbers, but numbers aren’t as big a factor as some are trying to make them out to be.

Just for fun, here are some stats for ESPN and SPEED viewership. They are from 2006-2007, but that’s the latest I have easy access to.

Category ESPN SPEED
Men 69% 80%
Women 31% 20%
18-34 28% -
35-54 39% -
55+ 33 -
18-49 - 69%
25-54 - 63%
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Why Six Points is About Right for What Used to be a 25-Point Penalty

 Inspection, Kyle Busch, math, Rules  2 Responses »
Jun 152011
 

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.

Graph of Old Points System vs. New Points SystemSix 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.

Plot of Old vs. New Scoring System with Slopes shown