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.
The Hendrick engine shop had four failures at Michigan. The 24 and the 14 reportedly both had valve spring failures. The worst was the 48, whose engine went south while leading with only six laps remaining. Jimmie Johnson drove the car up to the hauler and walked back to his motorcoach with his helmet on, not talking to reporters.
I don’t blame him, especially when you realize how close he got before the motor let go.
High, Sustained RPM
Michigan is one of the tracks where the speed at which the motor rotates stays constant throughout an entire lap. Watching the numbers from the television, most motors changed from only 7800 to 8500 rpm (revolutions per minute) throughout a lap.
Number of laps, or even miles are not the best way to gauge engine use because there is a huge difference between running at 8000 rpm and running at 3000 rpm. What’s important is how many times a part is called upon to do it’s job.
The valves (one intake and one exhaust) are raised and lowered by the rotations of the camshaft (as shown above). The camshaft is driven by the crankshaft. When we say an engine is running at 9000 rpm, we mean that the crankshaft makes nine thousand rotations every minute – or 150 rotations every second.
Here’s the critical part: The camshaft makes one rotation for every two rotations of the crankshaft in a four-stroke engine. At 9000 rpm, the camshaft is running at 4500 rpm, which translates to 75 openings and closing of the intake (or exhaust) valve every second. This means that the valve spring compresses and expands 75 times each second.
This is a linear phenomenon. If the engine runs half as fast, each of these things happens half as many (37.5) times each second. The faster the motor runs, the more movement, the more rubbing of parts and the more opportunity for pieces to break.
Watch the numbers this week at Bristol – you’ll see a much larger difference in speeds as the drivers slow down through the corners and accelerate through the straightaways. Even more importantly, watch the changes in engine speed coming up next week at Atlanta, where you’re going to see similar high, sustained speeds. The same issues will be in play for Charlotte and Texas. This may just have been a case of a box of sub-optimal valve springs, or the engine shop may have been trying a more aggressive setup in preparation for similar track in the Chase. I’m not worried – they’ll get it figured out (if they haven’t already).
By the Numbers
Let’s do a quick calculation. The race time was 2 hours, 46 minutes and 44 seconds to run 201 laps. There were 35 laps of caution, so (35/201=)17.4% of the race was run under caution and 82.6% of the race was run under green.
2 hours, 46 minutes and 44 seconds is 10,004 seconds. 82.6% of that is 8,263 seconds that were run under green. If we take an average of 8000 rpm, which is 66.6 revolutions of the camshaft every second, the average valve and valve spring went through half a million up-and-down cycles.
Jimmie Johnson ran a top happy hour lap of 36.323 seconds. Assuming an average of 8000 rpm, each lap at that speed adds another 2,421 cycles of the valve spring. Six laps means he was short 14,526 out of over a half-million cycles. Think about sixteen valves and valve springs that make well over a million (including practices) successful executions and come up short by a few tens of thousands.
No wonder Johnson didn’t want to talk to the press.
Just out of curiosity, I pulled up some data from racing-reference.info on different drivers’ rookie years in the Cup series. The data are from each driver’s first full year as a Cup driver. I picked out some drivers who have gone on to become series champions, some that will likely go on to become champions, and some who are struggling. I was wondering how predictive first year stats are of future performance.
The first graph shows how good drivers were at finishing races. The blue bars are the percent of races in which the car was running at the end of the race, and the red bars are the percent of races in which the driver finished on the lead lap.
The second graph and third graph analyze finishing position. The second graph summarizes wins (blue), top fives (red), top tens (green) and poles (purple). All are expressed as a percentage because not all drivers ran 36 races in their first year. The data are a lot more scattered here than they were in the first graph. It’s striking that Stewart, Johnson and Edwards each finished in the top 10 in over (or almost over 50% of the races).
Finally, the third graph compares how each driver finished compared to other drivers. The blue bar is where the driver finished in the drivers points at the end of the season. (Lower is better, of course.) The red bar is the average finishing rank over all races that season. Again, Johnson, Stewart and Edwards stand out in contrast to the other drivers.
Every week we hear at least one driver say that they are bringing back “the same car we raced at…”. This is a little misleading because — unlike Indy or ALMS racing — each shop builds multiple cars, each specialized for a specific track.
Let’s start by examining the anatomy of the stock car. I think of the car in three major components: The chassis, the body and the bolt-on parts.
The skeleton of the car is the chassis, a purpose-driven structure welded together from very strong round and square steel tubing. Shown at right, the structure consists of a front clip (to the left), a rear clip (where the fuel cell sits) and the roll cage (located in the center).
The plans were provided to teams via an AutoCAD file – which should give you some idea of how precise NASCAR expects the teams to be in implementing the chassis plan. Since the design was developed to optimize safety, teams aren’t allowed to modify the chassis at all.
How faithful teams were to the original blueprint is determined using coordinate-measuring machines (CMM). CMMs consist of a probe (which may be mechanical, optical or other) and a reading device that transmits data back to a computer that processes and stores the information. Mechanical CMM devices include the Romer and Faro arms, which are brand names of popular CMMs. These devices really do look like arms, with joints that mimic the elbow, wrist and fingers. Those joints allow motion along all three axes (up/down, left/right and back/forth), plus the ability to rotate about each of these axes. (Check out this interview with the inventor, Homer Eaton.) To measure something, the arm is touched to the car in specific spots. The probe transmits its three-dimensional coordinates to the computer. The pictures below shows a Faro arm.
NASCAR uses a Romer arm to certify the chassis (testing over 100 distinct points), and for measuring the body (as I’ll explain in a moment). One of the challenges using mechanical CMMs is that they have to be accurate over a very large volume. The NASCAR system measures over a 13′ x 20′ area defined by a set-up plate. To improve the measuring accuracy, 5/8″ diameter touchpoints are mounted in the plate every three feet. The placement of the touchpoints is verified during surface plate installation using laser triangulation. Before measuring the car, the CMM is touched to any three of the points to ensure that the probe uses the same origin every time and measurements are consistent from car to car.
Triangulation is also the basis for the CMM. The distance from the origin to the arm’s pointer is the unknown length of one leg in a triangle. If you know the length of one side and two angles of your triangle (which you do using your reference points on the plate), you can calculate the lengths of all sides and all angles.
After verifying the chassis, NASCAR attaches RFID (Radio Frequency IDentification) tags to strategic points. Those tags are scanned at the track to make sure that the chassis hasn’t been changed. For example, if a car was in an accident, these measurements tell the team whether the chassis has been even slightly bent or twisted. Very small changes can compromise safety, so accuracy is very important.
The roof, hood and decklid (a.k.a. trunk) are supplied by the manufacturer. The remainder of the body is fabricated by scratch from flat sheets of steel. The steel that makes up the body is surprisingly thin – in the the range of 25-30 thousandths of an inch thick. Most people who see a stock car up close are surprised at just how flimsy the metal is. (Ask Kevin Harvick and Carl Edwards how easy it is to accidentally dent the hood of a car during a fight discussion.) The only parts on the body that aren’t metal are the front and rear fascia, which are made from a carbon-fiber/Kevlar composite.
NASCAR uses Romer arms to measure body position and sheet metal thicknesses, as shown at right. We’re talking accuracy to the thousandths of inches level. Teams can take cars over to the R&D shop anytime to have them checked with the ‘official’ equipment, although most have one or more Romer arm systems in their own fabrication shops. It’s not a small investment: A Romer system costs about $60,000. That’s not including installing a surface plate, which has to have no more than a few thousandths of an inch variation in height across a distance of 12 x 20 feet.
It is impractical to bring a Romer arm and surface plate to the track. At the track, NASCAR uses a template structure – similar to the one shown here (from the Super Chevy website) to check that each car conforms to the rulebook. The template grid is not the most sensitive measuring device. I have watched inspectors tap the template to “make” it fit more than once. The template makes it easy to see gross violations, but racing these days comes down to thousandths of an inch and that is why the cars have to be brought back to the R&D center for measurement.
The video below shows the template grid system and the body. After the templates are lifted off, the body rises to reveal the chassis underneath. (In reality, of course, the body doesn’t just lift off the car – it’s attached with rivets and welds.) I think this demonstration (from the Hendrick museum and video courtesy of Santa Fe Productions) illustrates well the difference between the chassis and the body.
The “parts” as I call them are all the pieces that are bolted to the car: suspension component, transmission, engine, windows, etc. Because they aren’t welded to the car, these pieces can be changed during the course of a practice or even a race.
What Does “Same Car” Mean?
When a driver or a crew chief talk about ‘bringing back the same car’, they are almost always talking about the chassis. When you give “a car” a name, you’re naming the chassis, not the bodywork and certainly not the A-arms or the engine. When a car comes back to the shop after a race, the engine is removed, most (if not all) of the bolt-on parts are removed and more often than not, the body is removed. The engine is stripped down and entirely re-built before being used again. All of the bolt-on parts are inspected for wear and possible damage. In theory, the body could be left on and all the parts re-used.
It is rare, however, for a team to be satisfied with how a car ran — even if the car won the race. Teams are always looking for advantages, so there may be different bolt-on parts used for the next race, or the crew chief may want to modify the body slightly (within the rules, of course) to make it more aerodynamic. When a team talks about “a car”, they’re almost always talking about the chassis — which is changed only when it has been damaged.
Can You Bring Back “The Same Car”?
In their recent appeal, the 48 team claimed that the car that had been deemed illegal was the ‘same car they had used” for all plate races in 2011. How is that possible if so much changes from race to race? I guarantee you that there wasn’t one speedway car sitting in a corner in the Hendrick shop under a cover waiting to be brought back out for the next plate race.
The key is laser scanning.
Mechanical arms are really nifty pieces of technology; however, they measure specific points. The more complex a curve (or the more subtle its departure from the specification), the more points you have to measure. Laser scanning takes accuracy one step further.
We can make measurements similar to those made with a Romer arm using a laser. We know exactly how fast light travels (300 million miles meters every second), so measuring how long it takes for a beam of light to travel to and from a surface lets us calculate the distance from where the beam is emitted to the object.
A slightly more complex setup is used for 3D scanning. A laser stripe is projected on the car. If the surface onto which the line is projected is flat, the line will appear straight. A curved surface distorts the line, with the distortion proportional to the amount of curvature. A sensor looks at the line and back-calculates what surface shape would cause the observed line to appear as it does. Most of the big teams have their own laser scanning system and scan every car before and after it goes on track. Subtle differences in curvature could mean a few hundredths of a second improvement per lap. Everyone knows that the days of finding a half second per lap are over. A few hundredths can make a huge difference.
I suspect that the 48 team was able to produce laser scans of each of their speedway cars for the last year and show how the C-posts on those cars compared to the C-posts on the car that was deemed illegal. I can’t say anything about the decisions that were made on the basis of those measurements, but the routine laser scanning of cars provides a pretty solid documentation of everything about a car.
Putting Bristol “Back”
Cars aren’t the only thing laser scanners measure. Laser scanning is also used (in a slightly different form) to scan tracks. NASCAR.com’s Raceview and iRacing provide amazingly accurate pictures of the tracks. Those graphics are due to 3D laser scanning that allows them to measure every dip and every oil spot on a track. The video below shows how iRacing does it.
Bruton Smith definitely has access to very detailed measurements of the pre-2007 Bristol from a variety of sources. Does that mean he can put it “back” the way it was? If he can, does that mean racing will go back to the way it was?
No. Definitely not.
Our ability to measure accurately far exceeds our ability to replicate accurately. There is a huge human element, whether it be making a car or re-surfacing a track. Sure – you can replicate the track dimensions pretty accurately — but how do you duplicate exactly a concrete surface that has been weathered by decades of weather and use? Bruton hasn’t announced exactly what he’s going to change, but we’ll analyze it when he does.