Nov 222013

Now that the season is over, it’s time to look through the statistics from the year.  One big story this year was Danica Patrick’s rookie season in Sprint Cup.  She didn’t set the world on fire:  One top ten, one pole, five laps led and only thirteen lead lap finishes put her in 27th place for the season.

Tony Stewart, when asked about Danica’s rookie year, said that he saw ‘potential’.  Potential tends to be an ephemeral thing and numbers geeks like me strive to put a quantitative slant on everything, so I thought I’d look at the numbers and see if there was anything we could glean from comparing different driver’s rookie year stats.  With thanks again to the folks at for the numbers, here goes.

I didn’t include stats like average starting position or poles because, frankly, you don’t get a championship that way.  I focused on how drivers finished.  The graph below shows the percentage wins, top five and top tens for a number of drivers, ranging from champions to drivers still proving themselves and, yes, two of our rookie-of-the-year competitors.


I think it is fair to conclude that the best drivers in the series – the multi-time champions like Johnson and Stewart – were just good from day one.  Finishing almost 60 percent of your races in the top 10 in your first year is pretty darned impressive.  The guys who looked like champions in their first year usually became champions (or came pretty close).

But the converse doesn’t hold.  A slow start doesn’t preclude the possibility of your becoming a champion.

If you look at the graph above to find a driver whose rookie year is comparable to Danica’s, you inevitably land on Brad Kezelowski.  His rookie stats weren’t that different than Danica’s.  She had one top-ten, he had two.  Neither had any top fives or wins.  They both had a pole.

So maybe there’s something that average statistics, like top tens and top fives don’t tell you.

Digging Deeper:  Histograms


A histogram plots the frequency of occurrence – for example, how many times a driver finished within each particular range of finishing positions.

I chose this kind of analysis because it’s the next step up from an average finishing position.  You can take two drivers with the same average, and one could finish 17th every race, while the other alternated between winning and crashing out in the first lap.    Someone once told me that ‘averages hide a multitude of sins’ .

I broke the finishing positions into five-position segments, but I broke out wins separately.  The histogram to the right shows Jimmie Johnson’s finishes for his rookie (2002) season.  The bar corresponding to ’35′ on the chart at right shows that Jimmie Johnson had four finishes between 35th and 39th that year.  The bar corresponding to ’5′ shows that Jimmie had 14 finishes between P5 and P9.   Johnson had an average finish of 13.5 and finished 5th in the standings that year.

Stewart1999The histogram for Tony Stewart’s rookie season (1999) looks a little different than Johnson’s in the details, but (like Jimmies) it’s skewed to the right-hand side of the plot (meaning more good finishes).   Stewart had an average finish of 10.3 and finished 4th in the standings.

And then we come to Kezelowski, who had an average finish of 22.4 and finished 25th in the standings.  Unlike Johnson and Stewart, who have significant bars for top fives and wins, there are no bars for Kezelowski.  He had a few bad finishes, but he consistently ran between 25th and 10th, with more of the finishes being on the higher end of that range.


Which brings us to Danica.  Even though she finished in 27th place (only two behind Brad in his rookie year), the statistical distribution of her finishes looks much different than Keselowski’s.


The mode of a group of numbers is the number that appears most often.  It’s the most probable outcome – and the highest bar in these histograms.  Brad has a pretty even spread between 30-10, but Danica has a pretty significant peak at the 25-29th place finishing positions.  She had a lot of finishes in the 25-29, while Brad was almost equally likely to finish 10th as 30th.

How Drivers Change

The big question, of course, isn’t how anyone did last year – it’s how they’re going to do in the future.  If there were some magical algorithm that allowed an owner to predict that, if they put three years of development into a driver, he or she would pay off, they’d have no problems deciding who to keep and who to let go.

I was curious about how drivers changed.  If you start off good, there isn’t much room for improvement, right?


This histogram compares Jimmie Johnson’s finishes in 2002 with those of this year.  He’s got fewer bad finishes and increased the number of wins, top 5s and top 10s.  Bad finishes are tricky because in a sport like this, you can get a bad finish through no fault of your own if you get caught up in someone else’s accident.  I haven’t looked at it in detail, but my first glance suggests many of the bad finishes for drivers who don’t have a lot of bad finishes are at the short tracks and the superspeedways, or they’re due to equipment malfunctioning, like a motor or transmission giving out.

What about Brad, whose rookie year wasn’t quite as promising?

KezTimeThis histogram compares Brad’s rookie year, 2010 with his championship year, 2012.  Look at the difference in finishes in just two years.  With the exception of a very few bad finishes (one was Daytona) every finish was 19th place and up.  What happened in those two years?  Some experience.  A new crew chief with whom Kezelowski seems to have really bonded.

What Does it All Mean?

If a driver starts off with a slew of top 10s in his first year, the chances are very high that driver will continue to run at the top as his or her career progresses.   You cannot, however, make the converse argument:  a driver with a weak rookie year may — or may not — become competitive.  We’ve seen some good drivers from other series come to NASCAR and struggle.

There are many factors that go into winning:  you have to have most of them to run well.  Sometimes something like changing crew chiefs, owners or even being in the final year of a contract will radically change how a driver runs.  Look at Joey Logano when he moved to Penske, or Matt Kenseth when he moved to Gibbs.

Now… that isn’t to say that there aren’t some clues that might tell you whether a driver is destined for greatness or mid-pack purgatory.  We’ll dive deeper into the data next time.



Nov 142013

Hard to believe it’s winter, but we got our first snow already. Here’s the news of the week.

  • It’s holiday shopping time – great idea for your gearhead: magazine subscriptions.
  • Despite hoping for a down-to-the-last-lap Homestead finale, all the stats geeks cite a pretty high probability Johnson takes it all.
    •  36 Races notes that Johnson has a 91% chance of winning the championship, but also that Harvick has a 3% chance of taking home the title.
    • Focusing more on who wins the Homestead race, PitRho has an interesting first choice for your fantasy team:  Parker Kligerman.
  • @nascarnomics looks NPR’s “esteemed commentator” Frank DeFord’s assertion that NASCAR fan numbers rose as speed increased and now that we’re only getting marginal increases in speed, that explains the declining attendance.  He analyzes attendance vs. pole speed and the results are very interesting.
  • F1′s all aflutter about the ugly noses on the 2014 car.
  • Have you ever seen a string theorist interviewed by a cat?  If not, you really should.

And in my news, I’m busy getting things ready for the end of the NASCAR season.  Whole lot of interesting stats I’ve found looking at the year as a whole.  Those’ll be coming up soon…


Nov 012013

Concussions were big news in a week where no one actually got one.

NASCAR announced a new policy on concussions :  Starting in 2014, all drivers will be required to have a baseline test at the start of the season.  NASCAR will be using the ImPACT (Immediate Post-Concussion Assessment Test) , which I discussed back when Dale Jr had his concussion and had to sit out a couple of races.  The ImPACT test has been widely used already in NASCAR and NASCAR did quite a bit of education to the drivers and teams about the test, how it originated, and why they are doing this.  Unlike the NFL, which has consistently denied that concussions were serious or needed attention, NASCAR is taking this seriously.

Brad Keselowski doesn’t like the new policy. And, as is his style, he made no bones about his unhappiness with the new policy.

“Doctors don’t understand our sport. They never have and they never will. Doctors aren’t risk-takers. We are. That’s what makes our sport what it is and when you get doctors involved, it waters down our sport.” (via USA Today)

One aspect Keselowski didn’t like was the lack of a firm number coming out of the test.  Without one, he said, the test was “a waste of time.”

“It’s just another subjective field for doctors that don’t understand our sport… This is not the field for doctors. Let them play in their arena and I’ll play in mine.” (via USA Today)

Sigh.  I remember being twenty nine and thinking I knew everything.

Let’s just review for a moment.  ‘Concussion’ denotes a range of damage to the brain that results from blunt trauma.  Your brain sits on your spine, but it’s not rigidly held in place.  Cerebrospinal fluid surrounds the brain and cushions it as it moves.  There’s only so much cushioning that fluid can do.  If you get hit hard enough, the brain hits the skull and the cells that make up the brain can be damaged.  Brain cells are essentially electrical components.  If you throw a radio or a television and damage the components inside, it won’t work.  Same thing goes for your brain.

We don’t have a good way of figuring out how much your brain is damaged at present because we can’t open up someone’s head and look for the equivalent of a bruise.  Much like psychological illnesses, we have to piece together symptoms and deduce the cause from the symptoms.  Someone who is concussed may or may not lose consciousness and may or may not suffer from symptoms that include ringing in the ears, headaches ranging from mild to blinding, intolerance to light and sound, and a host of other things.

In most illnesses, the patient wants to help the doctor figure out how to make him or her better.  In a concussion, patients sometimes hide symptoms because they are afraid (as I suspect Mr. Keselowski is) that they are going to be prohibited from doing what they love. Racing IS different than stick-and-ball sports:  if the quarterback on a football team gets a concussion, the team can still make the Superbowl.  If the driver gets concussed and has to miss races, his or her season is over.  It is nearly impossible to make the championship if you miss a race.  Imagine if Matt Kenseth or Jimmie Johnson were told mistakenly that they had a bad concussion and they couldn’t race.  You have no guarantee you’ll ever get back to that position again.  I get that.

Having said that, the idea that racers are risk takers and therefore the rules shouldn’t apply to them is pretty absurd.  Take a look at the articles Matt Crossman wrote about concussions in the NFL for Sporting News.  There are men in their forties and fifties who can’t read because they can’t focus for more than a few minutes, men with sleep disorders that cause them to wake up and find they are choking their wife, men who say that, if they knew what playing football was doing to their brains, might have decided not to play, or to retire earlier.

Think of a concussion as analogous to a broken bone.  The bone needs time to mend.  If you get in another accident and the bone is still weak, you stand a high probability of damaging your body in a way that can’t by fixed.  There is nothing physical that prevents Brian Vickers (who is taking blood thinners to deal with blood clots) from driving.  He said “I can drive fine.  I just can’t crash.”  The blood thinners are doing their job, but if he were to have an accident and start bleeding, the blood thinners would decrease the blood’s ability to clot.  It’s the same thing with a concussion. It might not impair your ability to drive; however, it puts you in a very bad position if you have another accident.

This is why doctors have spent years developing ways to determine whether someone is concussed that is more objective than asking the patient how they feel.  ImPACT tests six areas:  verbal and visual memory, visual motor speed, reaction time, impulse control and symptom score.  It’s a half-hour computer-based test that flashes numbers and letters and asks you to remember colors or sequences.

And the reason they don’t use numbers is that you don’t measure people against some ideal standard.  Everyone’s brain works differently.  Some people have better reflexes than others.  Some people are better are remembering numbers than others.  What is important is how your brain changes after a concussion.  Without a baseline test, there’s nothing to compare the test to if you do have an accident. Likewise, there’s no magical ‘cut off’ where a doctor is going to say “You can’t race”.  They’re going to be able to show you your scores in various areas at the start of the season and then how those scores have changed after an accident.  Then the doctor is going to make a recommendation.  The driver, the owner and NASCAR then have to come to a decision about whether the driver races or not.

We all take risks.  Drinking alcohol has risks.  You decide whether those risks are worth the rewards.  The same should hold with concussions.  A person has the right to know what the risks are – then they have to make decision about what risks they are or aren’t willing to take.  Leaving aside the obvious cases in which a driver’s condition might endanger other people, there’s a broad range of possibilities left.

Keselowski also argued that we simply don’t know enough about concussions to have tests.  That’s also remarkably ill-informed.  Yes, we don’t know everything about concussions, just like we don’t know everything about depression, heart attacks and why we have appendixes (appendices?).  But the evidence overwhelmingly suggests that concussions have much farther ranging impacts than we thought.  A brand new study out this week shows that NFL players benched due to concussions have altered brain connections.  They used functional magnetic resonance (fMRI) imaging to study the brains of people while they did tasks.  fMRI detects oxygen.  Since your brain draws blood to the parts that are being used the most, you can tell what areas of the brain are active using MRI.

The study compared football players who had been benched due to at least one concussion with age-matched college graduates and gave them tasks, like given two different arrangements of colored balls, how many moves would it take to change the arrangement from one to the other.

They found very small differences between the two groups.  Only when the number of moves became large did the football players perform significantly below the non-football players.  But – they found that the areas of the brain that were being used were different between the two groups.  The different areas of football players’ brains didn’t interact as much as the non-football players.  This was particularly strong in the frontal lobe, which is the part of the brain being used for planning, organization and attention.  In essence, this study showed that although the two groups performed the same, it took the football players much more brain power to do it.

It’s a limited study and needs follow up, but it sure is interesting because the harder the task, the harder the brain is going to have to compensate.  And these were people who had one concussion.

The other reason I didn’t want to let Mr. Keselowski’s comments go is that we do have evidence that concussions in younger people could be more impactful (sorry, couldn’t think of a better word) than in older people.  The Institute of Medicine released a report this week on the science of youth concussions.  Thousands of young people play football, soccer, hockey and serve in the military – all places with a higher risk of concussion.

Concussions are potentially serious and everyone’s tolerance for risk is different.  But we need to make sure people have enough information so that they make wise decisions.


Oct 312013

My weekly roundup of math, statistics and science-related motorsports stories… and a few things that maybe are more notable for their lack of speed.

And I’ve just updated my appearances page with trips to Minneapolis, Montana, Albuquerque and Texas next Spring!

Oct 102013

Been a busy week – went out to Cincinnati over the weekend, then Vermont for a couple of talks.  More on that and my visit to Thunder Road later!


Sep 272013

Dover is a fascinating track – twenty-four degrees of banking, but only a mile in length.carturning  A student approached me with a question:  Higher-banked tracks generate higher centripetal forces – so why doesn’t the track banking appear in the equation for centripetal force?

I’ve talked about centripetal forces in detail before, but let’s have a quick reminder.   I tie a string to a tennis ball and swing it at constant speed in a horizontal circle around my head.  Assuming I am coordinated enough not to hit myself in the head with the tennis ball (don’t laugh – it happens), the reason the ball goes in a circle is because of the string.

The string exerts a force on the ball.   At every moment, the ball tries go straight and the string forces it to turn.  The direction of the force the string exerts on the ball is along the string – which means it is always toward the center of the circle.  Centripetal literally means “center seeking”.

Just like the tennis ball, a car needs a force to make it turn.  The amount of force depends on the mass (weight) of the car, the speed of the car and the turn radius of the track.


As my student pointed out, the degree of banking doesn’t even show up in this equation.  All this equation tells you is that you need more force:

  • to take a tighter turn
  • to turn a heavier car
  • to turn faster

The numbers are interesting, in part because they are so big!  Every track in the NASCAR circuit has different parameters, so we have to do a different calculation for every track.  Here’s the numbers for Dover


Teachers:  You can download metric and English unit version of this figure, along with some fun science facts about Miles the Monster.

The Numbers

Using a typical weight for a Gen-6 car (3300 lbs of car and 180 lbs of driver), we can figure out how much force it takes to make a car turn.  (Disclaimer: Parts of this table are from my previous blog.  But I did double check them and added this week’s track – Dover.)

Track Turn radius
Turning Force
Talladega 1000 180 6,848 1.97
200 8,456 2.43
Richmond 365 180 20,636 5.93
100 6,370 1.83
Bristol 242 100 9,606 2.76
Dover 500 130 7,858 2.26

We can see from this:

  • Even though Talladega is a higher speed track, the g-forces are comparable to smaller tracks – because Talladega has wide, sweeping turns.
  • Speed in the turns is limited at a small track like Richmond – the turns are very tight and you’d need a) an unrealistic amount of turning force and b) the g’s would be so high that the drivers would be likely to pass out.
  • Look at how much a 2o mph increase in speed increases the g’s experienced at the track.


The ‘G’ is quite possibly the most misunderstood unit in racing.  A ‘G’ measures acceleration, not force.   We use ‘G’ because the unit is equal to the acceleration of any object due to Earth’s gravity.

You are standing (or sitting) and the ground (or your chair) is exerting a force upward equal to your weight.  As a result, you do not accelerate up or down.  If the chair were to spontaneously disappear, you would accelerate toward the ground.

We use the unit ‘G’ just like a unit like ‘dozen’.  I can express anything in terms of dozens:  a dozen eggs, a dozen jellybeans or a dozen beers.  Likewise, we can use the unit ‘G’ to express the acceleration of anything.  I can measure the acceleration when you step on the gas after stopping at a red light in ‘G’s.   I can measure the acceleration you feel on a rollercoaster in Gs.

Just for reference, most amusement park rides top out at about 3G; however, some roller coasters go up to 4G (SheiKra Rollercoaster at Tampa) or 4.5G (e.g. the Titan Rollercoaster in Texas).

Although Earth’s gravity pulls down (toward the center of the Earth), I can use the unit ‘G’ to measure acceleration in any direction:  up or down, back or forth, or sideways.  Drag racers experience accelerations of about 5G backward at take off.  When you’re turning at constant speed, the acceleration is sideways (which engineers call ‘lateral’).


Please don’t use the term “G-force”.   It’s wrong because a ‘G’ is a unit of acceleration, not force.  When you experience ’3Gs’ of acceleration, the force you experience is the number of G’s times your weight.

Compare Danica Patrick (who weighs about 100 lbs) with Ryan Newman  who (according to Yahoo! Sports) weighs 207 lbs.  They both experience 3 ‘G’ in a turn.  That means Danica experiences a force of 300 lbs, while Ryan experiences a force of 621 lbs.  (Their cars, which weigh the same, experience the same force.)

If they experience such different forces, why do we use ‘G’s?  Because the ‘G’-value doesn’t depends on who or what is accelerating. It’s the same number.  You may remember that force = mass x acceleration.  If you take the mass out of the equation above, you have the formula for centripetal acceleration.

But What About the Banking?

As I noted above, the equation for centripetal force doesn’t address banking.  Banking doesn’t directly enter into the equation;  it’s just mass, speed and turn radius.

BUT:  A banked track lets you go faster around the turns.  If Dover were flat, you would still experience 2.26 ‘G’ at 130 mph – but you wouldn’t be able to go 130 mph in the first place.  The greater the banking, the higher speeds around the corners and thus greater G-values; however, a high-banked track with very wide corners could conceivably have lower ‘G’-values than a relatively flat track with really, really tight turns.  It – like so much of racing – is a tradeoff.

Related Posts:

Why Concrete Races Differently than Asphalt

Why Turning is Hard


Sep 082013


So instead of talking about a couple great races this week, we’re focusing on restarts.  Again.  Everyone, from pundits to drivers, is questioning  NASCAR’s decisions to not call penalties on the critical restarts of both the Nationwide and the Sprint Cup races.

The rule is that the leader of the race controls the restarts.   Lines on the racetrack walls delineate a box.  The leader may choose to start the race (that is, accelerate) anywhere within the box.  If he/she has not by the time the cars reach the end of the box, then the flagperson starts the race.

NASCAR:  Balls and Strikes

The problem is that this creates subjectivity.   NASCAR has made exceptions when they’ve deemed that the leading car spun its wheels and thus it was okay that the leader didn’t cross the line first.  I’ve already written how, if one car spins its wheels, a car going at constant speed can look like it’s accelerating when it really isn’t.

Another problem is that the drivers  look at the lines on the wall from different perspectives since they are in either the inside or outside lanes – you could get a sort of parallax error.

Robin Pemberton addressed the restart issue in the driver’ meeting before the Richmond Sprint Cup race.  NASCAR’s position is that restarts wouldn’t be an issue if the drivers would just obey the spirit of the law and “do it right”.  In the absence of common sense from drivers, Pemberton warns, it leaves NASCAR with a subjective decision:

“As many of you may have some questions on restarts tonight, I would remind you there are a few things we still have to have a judgment call on, OK?” he said. “There are balls and there are strikes. Sometimes you don’t like the call; sometimes we don’t even like the call we have to make.”

HT to Nate Ryan at USA Today

Why Technology is a Bad Idea

There have been a number of suggestions on how to solve the restart problem, ranging from telling NASCAR to “do a better job” to using an in-car technology that would simultaneously tell all the drivers to ‘go’ at the same time.

In-car technology has been used in a number of other series – but not for restarts and there’s a good reason why.  Everyone accelerating at exactly the same time works perfectly – if everyone starts accelerating at the same time and accelerates at the same rate.

What if the guy behind you is quicker on the gas than you are?   The green light goes on and he accelerates right into the back of your car.

And do you really want a driver watching a light in the car instead of the car in front of them?

Add to that the potential for tech problems (It’s not that unusual for a driver to have a radio not work properly during a race) and you’ve got the makings for The Big One at every restart.

What Would Albert Do?

NASCAR could  turn for advice on this issue to Albert Einstein, who said, simply:

“Everything should be made as simple as possible, but not simpler.”

In other words, don’t create a ton of fancy gadgets and dohickeys when a couple of gallons of paint would work.  Don’t make it a subjective call when it  doesn’t have to be.  There are no subjective calls about who exits Pit Road first, are there?

As a first attempt to solving the problem, let’s just paint a line across the track and make it the drivers’ problem.  The nose of the leader’s car has to pass the line first.   An overhead camera (or a side mounted camera similar to the one used to show the exit of pit road) would be a definitive arbiter of “strikes and balls”.  If the first car isn’t the first past the line, there’s a penalty in store for the second-place driver.

An overarching principle in NASCAR has been that intent doesn’t matter.  From speeding on pit road and fines for rules violation, NASCAR doesn’t car if there’s a legitimate reason why you broke the law.  You broke it.   Your tachometer wasn’t calibrated correctly?  Tough.  Your shock broke and your car was too low in post-race inspection?  Sorry.  We drew a line and you crossed it.  (Okay, we have to admit that sometimes NASCAR draws some pretty fuzzy lines sometimes – but this doesn’t have to be one of them.)

There’s nothing subjective to who gets off pit road first.  Yes, you could probably use  transponders to determine who reaches the finish line first – but fans can’t see it.  That just leads to people complaining that NASCAR is manipulating the race to ensure that (insert driver name here) wins.

A line and making the decision based on which car crosses the line first transfers the hassle from NASCAR to the drivers.  Sneaky drivers (you know who you are) will try to out-psych their competitors – but I guarantee you it is going to backfire on them sometimes.   Sometimes, you’re going to be stuck in second place next to someone who is horrible on restarts.  He/she spins their tires and you beat their car to the line.  You’re just going to have to be more careful when you’re next to someone who doesn’t restart well.

It was heartbreaking to see Brian Scott fail to win the Nationwide race Friday night – it would have been his first ever win and he had such a dominant car.  You never know when you’re going to get a car like that again.   On the positive side, I bet he pays a lot of attention to the physics and the psychology of restarts in the future.  When he gets to Cup, he’s going to be even more of a challenge.  You know he’s not going to forget this for a long time.

Aug 302013

There are a lot of things people say in NASCAR that have been said for so long that nobody really thinks about where they came from – or if they’re true.

As you get older, you get more and more sensitive to generalizations people make about getting old.  I can’t tell you how many times I’ve  heard someone says that drivers get slower (or don’t win as much) as they get older.  I started wondering if that was actually true.

The thing about data is that you have to think about what it means.  For example, what does ‘slow down’ mean?  Qualifying speed?  Well, you don’t get points for qualifying first – we’re really talking about being successful at racing.

What racers really care about is winning – and if you can’t win, at least running consistently well.  So I decided a good measure of  ”success” would be wins,  top fives, top tens and rank at the end of the year. I used data from to consider career statistics for drivers and look for patterns.

Given that time is finite, I picked some representative drivers.  I wanted drivers with long careers, so I had data points at either end of the age spectrum.  I wanted champions, so Johnson, Gordon, Kenseth, Stewart were obvious.  I added Dale Jarrett because he had a long career and – hey, I just like Dale Jarrett, OK?  I also wanted some youth, so I added Kyle Busch, Kasey Kahne and Carl Edwards.  I added Ryan Newman because he made a big splash the first couple years of his career and Jeff Burton because (in addition to a long career), he’s had a really interesting career.  Finally, I added Mark Martin because – well – he’s been around forever.

The Data

Jarrett_WinsT5T10withAgeLet’s look at Jarrett’s data first.  The number of wins is in blue, top fives in red and top tens in green.  I’ve indicated the year he won the championship with an arrow (which represents his best year in terms of top fives and tens, but not his best year in terms of number of wins.  Also worth noting:  He didn’t run full seasons his first three and his last two years.  But even if you ignore those, there’s a pretty clear pattern of improvement and then tailing off.

Stewart_WinsT5T10Jarrett started driving in 1984 at age 27 – the same year Kyle Busch was born.  Today, drivers get into the Cup series a little younger.

Tony Stewart didn’t start Cup until he was 28, though, so you might expect him to have a similar profile to Jarrett.

Not at all!  Stewart has been remarkably consistent over his Sprint Cup career.   The two arrows show Stewart’s first and last championship years.  The third was at age 34.  Stewart doesn’t seem to have any peaks or valley, even when he changed teams.   Jimmie Johnson’s numbers look very similar to Stewart’s.  Kenseth’s is a little more up-and-down, but again, there aren’t noticeable peaks.  (I know, I should have done Kurt Busch to see whether this is a mark of a champion!)  I’ll get there…

Each of the other drivers have similarly different (?) graphs.  Newman peaked at age 25 and he’s been up and down since then (with a slight upward trend since he joined SHR.)  Edwards is very up-and-down.    Martin’s is a little complicated because he had a couple years he didn’t drive all the races. Even so, there’s a broad peak from about age 30 to age 40 and everything after that is pretty oscillatory.

Burton_WinsTop5sTopTens_AnnotatedHere’s one of the complicating factors, though.  Look at the data for Jeff Burton – he’s got two peaks and they are very clearly divided by the year where he switched from Roush to Childress.  Similarly, Kasey Kahne’s numbers show a big upswing when he started driving for HMS.

And then there’s Jeff Gordon… I spent a lot of time trying to overlay life events on his graph – could you correlate performance to marriage, divorce, birth of children.  In short, no you can’t.  Gordon shows a broad peak from age 22 to age 28-29 and it’s been a little disappointing since then.  There is the occasional very good year (six wins in 2007), but it’s mostly down from his heyday.  Since he has the same equipment as Jimmie Johnson, it’s hard to make an argument that it has to do with the company falling down on technology.  Sorry – wish I had better news there.

Umm… So… You Gonna Tell Us Anything Useful?

This, of course, raises the important question of “How are you going to come to any type of conclusion if everyone’s graphs look very different?”

Which is a very good question.  I played around with the data and I finally came up with an idea.  What if I take a bunch of drivers and simply add together how many wins were had by drivers that were aged 21, 22, …?  I did that.

Then I realized that was stupid.  Why?  Because that’s really measuring how many drivers of each age there were.  It looked very Gaussian and that’s what made me smack my forehead and realize I was being stupid.  What I had to do was find the average number of wins:  How many wins by 28-year olds divided by the number of drivers in my sample who were 28 years old.  Now this has some promise…


There’s still a lot of scatter in the data (I haven’t had time to increase the numbers of drivers), but two clear trends emerge.  The top graph is a plot of the average wins per driver vs. driver age.  Jeff Gordon is messing things up a little with his 13 wins in 1998.  He won just about 40 percent of all the races that year.   But still – if you look at the winner for a given race, the odds suggest that he or she will be younger rather than older.  The outlier at age 50.  That is Mr. Martin.  He won five races that year and I only have data for one other 50-year old driver.

The lower graph shows the number of top tens (blue) and top fives (red).  Those numbers are both surprisingly flat until you hit about 40 years old, at which point they start going down.

Now you have to be careful – this tells you the behavior of a group.  It doesn’t tell you the behavior of any one particular driver.  When doctors tell you things like survival rates for cancer, they don’t tell you you have a 50% chance of being cured.  They tell you that, out of people like you, 50 percent of them are cured.  Your individual rate could be 10 percent or 90 percent.  Of course, that’s not something we can measure.

Just like we can’t measure luck – if you get taken out by an inexperienced driver, that really doesn’t have anything to do with your age.


Now there’s the big question.  It is a fact that our reaction rates slow down as we age.  But we also gain experience, which may allow us to make better decisions.  The relatively flat profile of a driver like Stewart doesn’t seem to indicate any decline over the years.  The Stewart of his first championship is just as good as the Stewart of his second or his third.

As Silly Season progresses, teams are going to be more likely to look for a younger driver (like Kyle Larson) than take a chance on a veteran like Bobby Labonte.  The older you get, the more you have to prove yourself.

NOTE: My friend Josh Browne pointed me to another stats blog that covered some of the same ideas – this is a great blog and should be of interest to racing geeks everywhere!


Jun 212013

In sports car racing, the only discernible change the viewer sees when it rains is that the normal “slicks”  (which have no treads) are changed out for rain tires.  Thus the calls for NASCAR to develop a rain tire good enough to allow us to continue races, even when it rains.

The surface of slicks (shown at left; from the Goodyear site) are flat sheets of rubber that maximize how much rubber is gripping the road at any given time.  The contact patch (the part of the tire in contact with the road) for a NASCAR tire on a Sprint Cup car is about the size of a man’s size 11 average width shoe — which isn’t all that much considering that those four tiny patches of rubber are responsible for producing 200 mph speeds.

The number that tells you how grippy your tires are is called the coefficient of friction:  The higher the number, the grippier the tire.  For regular car tires, the coefficient of friction between dry asphalt and rubber ranges from 0.7-0.9, depending on the specific surface.  When you make the asphalt wet, that can decrease the coefficient of friction down to 0.25-0.50.  (These numbers are all ranges because the specifics – the type of asphalt, how old it is, the oil content, the specific type of rubber, etc. all affect the coefficient of friction.)  For race tires on dry asphalt, we’re looking at coefficients of friction between 1.1 and 1.3 — or so I’ve been told, because tire companies keep that type of information under wraps.

TiresContactAs I’ve tried to show at right, water gets between the tire and the road, which decreases friction and thus decreases grip.  All you need is a very, very thin layer of water and you lose your grip.  You’ve probably heard the term hydroplaning – there is a plane of water between your tires and the road.  The faster you drive, the smaller the contact patch area and thus the faster you drive, the more likely you are to start hydroplaning.

Rain tires are made with grooves (as shown below) – just like  tires made for passenger cars.  The grooves point away from the center of the tire in the middle.  The pressure of the tire presses the water away from the flat spots and into the grooves.  The grooves give the water a way out from under the tire.

The Nationwide series at Road America will have rain tires on hand, but the Sprint Cup Race at Sonoma will not.  People have always wondered why you would do this for one series and not for the other.

Reasons to Race in the Rain

1.  The fans.  How many people spend all year anticipating a race, only to have the race postponed and they can’t stay for the following Monday because they have to work or have other obligations?  There’s a lot to be said for making sure that races are run the day they are scheduled.

Reasons Not to Race in the Rain

1.  Windshield Wipers.  When it starts raining, I’m guessing the first thing you do is to turn on the windshield wipers.  On a race car, you have to have a motor and a post available on the car so that a wiper could be mounted.  That’s not so difficult, but the teams can’t really head out to Auto Zone and buy windshield wipers.  The wipers would have to stand up to high speeds.  Ever gone through the dryers at a car wash and watched your windshield wipers get pulled off the windshield?

Another issue is that the windshield wipers would be much trickier to use effectively at high speed.  Remember that you go about a football field a second at 200 mph.  The rear tires of the race cars throw up a huge amount of spray – the windshield wipers would have to run pretty fast.  If you’ve ever reached for your wiper speed control and found that it was maxed out, you know that there’s a limit as to how fast the wipers can go and still be effective.  Sometimes, there’s just too much water coming down to remove.

Finally, if you’re going to use tear offs, you’ve got to have a wiper material that works with tear offs.  I don’t see how you can eliminate tear-offs unless you were positive it would rain the whole time — and even then, the rain isn’t going to wash all the track debris off your car.

2.  The Swiffer Effect.  Remember Carl Edwards at Montreal in 2008 with a Swiffer mop trying to clear the fog from the inside of his windshield when they tried to race in the rain there?  When the air is moist, it will condense on any cold surface.  Glass tends to be much colder than other parts of the car because glass is a good thermal insulator.  When it’s moist, you get a thin layer of fog on the inside of your windshield.

A defogger uses heated air to increase the temperature of the glass so that the water doesn’t condense on the glass.  You need a heater, ductwork and a blower.  Most passenger car systems also pass the air through a dehumidifier so that you’re not making the problem worse by increasing the moisture content.

3.  Brake Lights.  Coming over the Cumberland Pass this morning, I encountered a lot of fog in the mountains.  It’s beautiful, but really hard to see through.  In Maryland, people turn on their hazard blinkers when the weather gets like that so that you can see them more clearly.  Race cars don’t even have brake lights.  In the afore-mentioned Montreal race, Joey Logano wrecked under caution when someone stopped in front of him with no warning.  Not only do race cars not have hazard lights, they don’t even have brake lights.  If we give the drivers brake lights, they are likely to start playing mind games with each other using the brake lights, so perhaps that’s an area we don’t even want to go.

4.  The Fans.  I was at Petit Le Mans in 2009 and I can tell you first hand that being out there trying to cover a race in a monsoon was not even close to fun.  I spent ten hours in a damp firesuit with wet feet.  My notes got so wet I couldn’t make half of them out.  Do you really want to sit for three hours in the rain — even a light rain — trying to watch a race that you may or may not even be able to see because of the moisture?

5.  Safety.  Rain often is accompanied by thunder and lightening.  Lightening is dangerous, as I wrote about after a fan was killed and several more were injured at Pocono in 2012.  You’ve got tens to hundreds of thousands of fans, often seated at high points and surrounded by metal.  That’s a disaster waiting to happen.  Pit crews face additional hazards, including slipping (them and/or the car).

6.  The Drivers.  There is something to be said for experience.  Novice drivers make a lot more mistakes, even if they are being as careful as they can be.  I know… NASCAR drivers are the best in the world… but very few NASCAR drivers have  experience racing in the rain.  There are going to be accidents.  Since the tires are responsible for making any directional changes, wet tires are going to make it harder for the driver to make sudden changes in speed and/or direction, which means they will have a harder time avoiding accidents.

7.  The Racing.  In passenger cars, hydroplaning can happen at speeds as low as 35 mph.  The higher the speed, the more likely you are to have hydroplaning, so racing in the rain means lower speeds.  In the Montreal race, the average speed went from 90 mph to 75 mph when the rain tires went on.  Racing on an oval in the rain would probably look like a funeral procession when they cars aren’t busy crashing into each other.  Remember that the series that race in the rain race a lot more road courses and have a lot more downforce.  The increased downforce allows them to keep the speeds a little higher than you could with low-downforce stock cars.

Stock cars weren’t designed for racing in the rain.  Could they be?  Sure – the technical challenges can be overcome given enough time and money.  Goodyear would probably have to invest some money in research and testing to come up with a tire optimized for wet stockcars.  Motors, blowers, wipers, etc. could be designed and tested.  But you’re still left with the question of whether a race in the rain can be just as good as a race without rain.  I think not.  Add in the safety concerns, and it seems like the smartest thing to do when it rains at a NASCAR race is still to stay indoors.


Jun 132013

NASCAR fans are used to having our drivers walk away from spectacular crashes.  Unfortunately, we are reminded all too often — like last night — that racing, regardless of all the technical improvements we’ve made, remains a dangerous sport.  As you move from the top-level Indy and NASCAR series, the number of driver deaths increases.  Some of the higher risk level is because of the funding – racers running on much smaller budgets tend to want to put their money into making the car go faster rather than buying more/higher-quality safety equipment.  Sanctioning body requirements are also not as rigid

Sprint Cars (like the one shown at right) are tiny, very powerful racecars.  The 410-series uses a 410-cubic-inch V-8 engine that generates 800-900 hp.  For comparison, NASCAR Sprint Cup engines are 358 cubic inches and generate around 900 hp; however Sprint Cars are about half the weight of a NASCAR car.

You’ll often hear people talk about power-to-weight ratio.  For a NASCAR Sprint Cup car, the power-to-weight ratio is 900 hp/3480 lbs = 0.26 hp/lb.  (I know, those aren’t standard units, but they’re more accessible than W/kg.)   Taking a weight of 1575 lb (including driver) for a Sprint Car (I’m finding all kinds of numbers on the web for required weight), the power-to-weight ratio for a Sprint Car is 850 hp/1575 lb is 0.54 hp/lb.  Just for reference, Wikipedia lists the power-to-weight ratio for a Funny Car Drag Racer at about 3.3 hp/lb.  A street Corvette Z06 is about 0.16 hp/lb.

That’s an awful lot of power for a very light car and Sprint Cars need aerodynamic help to stay planted on the ground.  That’s the purpose of the giant wings on the top and front.  The wing at top is about 5 foot x 5 foot and the wing  over the front wheels is about 2 foot x 3 foot.  Those giant areas give air molecules plenty of places to hit and push the car into the ground, thus generating a lot of downforce.

SprintCarChassisSprint cars are smaller (they have a 84″ wheelbase, while the NASCAR Sprint Cup cars have a 110″ wheel base), but they have the same type of tube frame construction as stock cars.  They also have a relatively high center of gravity, which makes them much more prone to tip over than other types of cars.  For the gearheads among you, Circle Track does an absolutely great job with tech details.   NOTE:  Although the wing does raise the Center of Gravity, the issue is not just with the wing:  wingless Sprint cars have the same issue with a high CG.

Sprint Cars reach a maximum of about 140 mph, which is a combination of the very powerful engine, the light weight, and the huge amount of drag that the wings create.  Using the max speed of 140 mph, a Sprint Car has the same kinetic energy (aka energy of motion) as contained in a third of a pound of TNT.  Energy is critical because (as you no doubt have had pounded into your head), energy cannot be created or destroyed – it can only change forms.

There are two critical factors in crashes:  How much energy you’re carrying when you crash (your kinetic energy) and how that energy is transformed into other kinds of energy.  For example, when a car pulls into the pits on a green-flag pit stop, its kinetic energy is slowly transformed into other forms of energy:  heat (brakes, the tires if you skid them), light (brake rotors glowing), and even sound (squealing).  It’s a slow, controlled transformation of energy from kinetic to other forms.

When you crash, energy is transformed into different forms.  Energy may be transformed into spinning or skidding motions of the car, the noise of tires squealing — or sheet metal crushing.  The one place you do not want to dissipate energy is through your driver.

The amount of energy is important, but so is the time over which the energy transformation happens.  The force you experience when you change speed is proportional to the change in speed divided by the time it takes for you to change speed.  I like to say that it’s not how fast you go… it’s how fast you stop.


The airbag in your car works on the principle of slowing down how fast your head comes to a stop.  If you extend the time it takes for your head to stop from a tenth of a second to a second, you experience ten times less force.  This is the principle behind how SAFER barriers work:  They flex when hit slowing down the car in a much gentler way than a concrete wall.

It took four deaths between 2000 and 2001 for NASCAR to put their considerable brain power to making revolutionary changes in safety.  The folks at the NASCAR R&D Center are concerned about racers at all levels of stock car racing, from the Sprint Cup down to the local tracks.  Some of their research – like the development of strong tube-frame chassis and solid construction methods – are transferable to open-wheel racing; however, there are some unique challenges to improving safety for this type of racing.  There are also people like Randy LaJoie, who work with racers in many of the lower series and are just as concerned about short track racers as they are NASCAR drivers at the top level.

Sprint Cars race at a lot of tracks that do not have SAFER barriers.  Installing SAFER barriers is very expensive and many smaller tracks are struggling to stay open during the economic challenges of the current era.  Maybe this is a place for someone to design a lower-cost SAFER barrier that doesn’t need to meet the requirements of a Daytona or Indy.  Sprint Cars race at many highly banked tracks — when you combine an incline with a car having a high center of gravity, you get cars flipping over.  Lowering the CG of the car would go a long way to keeping them on the ground.  An additional complication is that there are a slew of sanctioning bodies for Sprint Car racing, which complicates any type of unified action.  It was easy for NASCAR to put their considerable economic heft behind an edict that all tracks they race at must have SAFER barriers.  It will be much harder for a similar effort at smaller tracks and multiple sanctioning bodies.

Perhaps the tragic loss of Jason Leffler will be the catalytic incident that spurs a safety initiative for Sprint Car racing similar to the one NASCAR initiated in 2001.  I can think of no greater tribute to a driver than that his very untimely death ends up saving more lives.  Thirty-seven is just too, too young to go.

NOTE added:  As I noted above, the win provides a LOT of aerodynamic downforce and drag.  This does help the car be more stable; however, it does not address the problem that, in high banked turns, a high center of gravity make a car more probable to tip over.


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