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.

 

Why was Michigan so hard on Motors?

 Chad Knaus, Engines, Hendrick Motorsports, Jeff Gordon, Jimmie Johnson, Michigan International Speedway, Tony Stewart  3 Responses »
Aug 232012
 

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.

Engine Diagram

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.

 

Infographic: Current Drivers’ Rookie Years

 Darrell Waltrip, David Ragan, Edwards Carl, Jeff Gordon, Jimmie Johnson, Joey Logano, Kyle Busch, Martin Truex Jr, Tony Stewart  1 Response »
Jun 202012
 

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.

 

 

Inforgraphic: Hendrick Motorsports – 200 Wins by Driver

 Brian Vickers, Darrell Waltrip, Geoff Bodine, Jeff Gordon, Jerry Nadeau, Jimmie Johnson, Joe Nemechek, Ken Schrader, Mark Martin, Rick Hendrick, Ricky Rudd, Tim Richmond, Uncategorized  3 Responses »
May 162012
 

Statistics Presented Without Comment

 

 

Source:  http://racing-reference.info/owner/Rick_Hendrick

Yaw Envy – Repost

 Aerodynamics, Edwards Carl, Jeff Gordon, Yaw  No Responses »
May 082008
 

This blog was originally published in May 2008 on the stockcarscience.com site.  I’m reposting it here as part of the migration of that site to buildingspeed.org.

Apparently, Jeff Gordon has a slight case of yaw envy. David Newton reports on ESPN.com that Gordon asked NASCAR to take a look at the No. 99 car of Carl Edwards because he thinks that yaw is the reason Carl’s been so competitive this season.

You may have learned that it takes three numbers to uniquely locate an object in space: For example, right now I’m in Los Angeles at the corner of Hope and 8th Streets and I’m on the 11th floor.

The limitation of this description is that it only identifies a point. I (like a car) have spatial extent. I could be lying down or standing up, and the three points I just specified don’t tell you anything about how I’m oriented, only where I’m located. We have to specify the angles the car makes with respect to three axes, which we call the x-axis, y-axis and z-axis. In vehicle dynamics, the x axis is along the length of the car, the y-azis is crosswise, pointing toward the driver’s right, and the z axis points downward, as I’ve drawn below. (Engineers take the z-axis to be positive in the downward direction.)

Yaw describes the rotation of the car about the z-axis. The yaw angle is the angle between a line pointing in the direction the car is moving and the car’s x-axis (which is the direction the car is pointed). In the simplest case (shown on the left side of the drawing below), the car is traveling straight and is pointed in exactly the same direction it is traveling, so it has no yaw. The car on the right is yawed, which means that the car is headed in a different direction than it is pointing.

A car by definition is yawed when it corners because it is pointing in a different direction than it is moving at every point along the turn. Yaw is important because air hits the car differently when the car is at an angle to the oncoming air compared to when it is hitting the air head on, as shown below. In effect, the car on the right has a head start on the turn because it is yawed before it enters the turn. Yaw puts the car in a position so that the air helps the car turn.

A number of people have noticed that some cars seem look yawed heading down the straightaway. They appear to have an inherent yaw built into them. Darlington has nice straightaways, which is why yaw has been in the news this week.

Let’s review some history. The old cars were asymmetric–literally kidney-bean shaped–as shown below. Compare how much of the left fender (on the right side of the picture) you can see relative to the right fender. Gary Nelson, the founding director of the NASCAR Research and Development Center said once that the cars were so misshaped that they looked like they had been in an accident before they even got on the track.

All of this body manipulation was for aerodynamic advantage; however, the research that goes into figuring out exactly how to optimize bodies, as well as the cost of cutting off and replacing bodies, was getting out of hand. This was one NASCAR’s major motivations in introducing the new car.

Compare the old car with the new car in the drawing showing yaw. There still is some built-in asymmetry in the new car: Note how the wing isn’t exactly centered between the two taillight decals, for example. The left rear quarter panel is much more tapered than the right rear quarter panel; however, the amount of asymmetry is pretty much fixed by the NASCAR body templates.

Of all the drivers, Jeff Gordon knows that you don’t mess with the new car’s body. He has complained that something is more amiss than it should be with the rear end gear on the No. 99, causing it to have yaw and thus giving it the same type of asymmetry the new car’s fixed body shape was meant to eliminate.

NASCAR cars have a solid rear axle. The rear end gear links the driveshaft to the rear wheels. There are three holes in the rear windshield: Two of those are for adjusting the springs on either side of the car. The third (the bottom one on the right) is for adjusting the trackbar. The trackbar shifts the rear end gear to the left or the right, as I’ve illustrated in the drawing below. I’ve exaggerated the shifts–if I drew them to scale, you wouldn’t be able to see them. The leftmost drawing is a car with no offset in the rear end gear. Note how the front and rear wheels are lined up. The rear wheels would follow right in the front wheels’ tracks. The middle drawing shows a car with the rear end gear shifted to the right and the rightmost picture shows that a car with such a shift will be yawed.

Kyle Busch referred to the way Edwards’ car moves as it looks “stupid going down the straightaway because it’s dog-tracking.” (ESPN). A running dog is usually a little sideways. The rear paws never follow in the front paw prints. It’s also sometimes called crabbing, and refers to the situation shown above: the rear wheels do not follow straight behind the front ones.

The situation with some cars is so extreme, that Gordon said:

“When cars can’t even get on the scales because they’re running sideways, it’s something they need to address.” (ESPN)

The scales used during inspection are four plates(two in front, two in the rear), that are in line with each other. Jeff is suggesting that the offset between the front and the rear wheels is so great that some cars have trouble getting onto the scales.

It’s ironic that Gordon is complaining about this, as Hendrick Motorsports was one of the first teams to experiment with introducing yaw using the suspension. One possible motivation for Gordon’s comments is that he is of the opinion that Roush Fenway Racing is headed down the same slippery slope as coil binding: The engineers are modifying the car in way that makes it much more difficult to drive.

Almost every team has tried to duplicate what Edwards has, but not every driver can handle it. “It makes the cars drive so terrible that it doesn’t really help us in any way that we really need it,” Gordon said. (ESPN)

There are rules about how much you can move the trackbar, so there are obviously other things being done to induce yaw in the car. One possibility: The wheelbase (the distance between the front and rear wheels) can be 110″ plus or minus 1/2″. If you make the wheelbase 109.5″ on the left side and 110.5″ on the right side, you’ve gained an inch of asymmetry. There are a number of other places where you can make little changes and, when all the little changes are considered, they add up to a significant effect.

I noted early on in the introduction of the new car that it was only a matter of time before the very clever people working at race shops would come up with ways to get around the new NASCAR-imposed limitations. One consequence of this type of offset is that the cars are drifting, much like they do on dirt tracks. It should be no surprise then, that someone like Edwards, who still does a lot of dirt track racing, is comfortable driving a car set up like this. That’s one rationale to account for why Edwards, who really struggled with the new car last year, is doing so well this year. As with coil binding, some teams have figured out how to get yaw and others are a little behind on the curve. Some drivers caught on to how to drive a coil-bound car a lot faster than others. The question that remains is whether there are other ways to get the car to turn better that would be more comfortable for the drivers who aren’t comfortable driving horizontally down the straightaways.