Take a look at the driver correlation matrix, based on their finishes after 20 races this year. In all these blogs, you can always click on the pictures to get a larger view.

What sticks out the most? For a quick review, see the little table here - that correlations above 0.50 and below are -.50 are really big. In my article I will focus on anything above .40 and below -.40, so we can look at some extra data points hiding under the surface.

What we find is that Jimmie Johnson and Kasey Kahne have the strongest relationship with each other, more so than any other pair of drivers. They generally perform similarly at each race, either both of them do poorly, or both of them do well.

On the flip side of the spectrum, Clint Bowyer and Joey Logano are the most negatively correlated with each other. When one does well, the other does badly, and vice versa.

What can all this tell us? It may suggest that certain teams are doing a better job than others in getting all their drivers on the same page. Maybe it tells us that certain drivers have a much more similar style than we realized, that they tend to perform well at the same tracks, and perform badly at the same tracks. We see this with Johnson and Kahne in a big way.

And it can tell us which drivers are the opposite of each other, doing well when the other guy does badly. Like we do with Bowyer and Logano. Maybe their styles of driving are not compatible with each other?

Most notably, higher up in the standings, we see former teammates Kurt Busch and Ryan Newman with a high negative -.43 correlation between each other. Maybe they are drivers with such different styles that they couldn't work well together on the same team. Look now how much better they are both doing since they split up as teammates.

Let's see how teammates this season are doing:

Ryan Newman and Tony Stewart have a correlation of 0. that's right, 0.00 - meaning their results are not related to each other. In fact, Tony is more correlated with the Hendrick guys (Gordon, Johnson, Martin) and even Juan Montoya than with Newman.

At Gibbs, Denny Hamlin is positively correlated with Kyle Busch, but negatively correlated with Joey Logano. At 0.08, Kyle Busch and Joey Logano are almost completely uncorrelated with each other.

Childress teammates Bowyer and Burton have a -0.12 correlation with each other, so despite being next to each other in points, they don't tend to perform next to each on the track. Could this be part of the reason they are struggling this year?

Roush's Biffle and Kenseth are somewhat correlated with each other (0.26), but Carl Edwards is less correlated with both of them, especially with Biffle (only 0.05 between Edwards and Biffle).

It will be interesting to see over the rest of the season how these relationships play out. Will people still perform just as similarly or just as differently in the next 16 races?

email any comments to 36races@gmail.com

## Friday, July 31, 2009

## Thursday, July 30, 2009

### 67 Percent Chance that one of the Top 12 drops out

Let's followup on yesterday's post, where I showed the probabilities of each driver qualifying for the chase.

We saw that each driver ranked between 5 and 12 had at least a 68% chance of making the chase.

However, there is ONLY A 33% CHANCE THAT THE CURRENT 12 WILL ALL QUALIFY. MOST LIKELY SOMEBODY WILL DROP OUT OF THE TOP 12.

We see this by multiplying the percentages of each driver ranked 5-12. You see this in the BOLD section of the image below.

Multiplying percentages converts individual probabilities to a GROUP probability, will ALL of these guys stay in? Only a 33% for that. The math is here if you are interested.

33% chance of nobody dropping out means a 67% chance that somebody WILL drop out. Despite individually strong qualifying chances, there's a much slimmer chance that ALL these drivers will hit their potential.

This is good news for guys like Kyle Busch and David Reutimann who are looking to break in, since chances go against everybody in front of them all doing well in the next 6 races. As long as Busch and Reutimann perform to the upper end of their own potential.

email any comments to 36races@gmail.com

We saw that each driver ranked between 5 and 12 had at least a 68% chance of making the chase.

However, there is ONLY A 33% CHANCE THAT THE CURRENT 12 WILL ALL QUALIFY. MOST LIKELY SOMEBODY WILL DROP OUT OF THE TOP 12.

We see this by multiplying the percentages of each driver ranked 5-12. You see this in the BOLD section of the image below.

Multiplying percentages converts individual probabilities to a GROUP probability, will ALL of these guys stay in? Only a 33% for that. The math is here if you are interested.

33% chance of nobody dropping out means a 67% chance that somebody WILL drop out. Despite individually strong qualifying chances, there's a much slimmer chance that ALL these drivers will hit their potential.

This is good news for guys like Kyle Busch and David Reutimann who are looking to break in, since chances go against everybody in front of them all doing well in the next 6 races. As long as Busch and Reutimann perform to the upper end of their own potential.

email any comments to 36races@gmail.com

## Wednesday, July 29, 2009

### Kyle Busch 23 Percent, Matt Kenseth 68 Percent: Chase Qualifying Probabilities for Every Driver

I ran some analysis. Let's take a look at the results.

20 races down, 6 more to go. If each driver runs the next 6 races in some combination of their previous 20, there are 38760 possibilities for how many points they can score. (A link here for those interested in seeing the math.) How many of those 38760 possibilities can get them to the magic 3120 points total? The 3120 number is 120 x 26. 120 is the PPR needed to get 12th place, as we've seen in many of our past posts (here, here, and here)

Assuming each driver doesn't score their very best or very worst 6 races, the 38760 possibilities are an excellent summary of what will most likely happen.

I ran the numbers for every driver, and compared what portion of the combinations were enough to get them into the Chase. The data is below. You can click on the image for a bigger picture.

For example, Kyle Busch has 9078 possible ways he could score more than 773 points in 6 races (based on his first 20), which is only 23% of all the possibilities. His best 6 races this year scored him 1046 points. His worst 6 races scored 414 points. But only 23% of his 6-race combinations this year were above the 773 points he needs to reach 3120.

What you see here is color coding based on groups. Tony Stewart is going to make the chase even if he gets last place in the next 6 races.

The next set of drivers, in light blue, are common-sense certainties, given their performance this year.

The drivers in yellow all have a very strong chance of qualifying, with chances between 68 and 97 percent. Notice these are spots 5 through 12, the same drivers currently qualified.

The drivers in light orange make up spots 13-16. They have a slight chance of getting in, based on their performance this year. Between Reutimann's 26% and Bowyer's 1%. Although it's tough - they have already shown the ability this year to get the finishes they need to crack the top 12. Not likely, but it is possible.

The drivers in pink are not mathematically eliminated yet, but they haven't shown the performance this year to make it. They'd have to come up with their best streak of the year right now.

And finally, the drivers in orange, are already mathematically eliminated. Since the most you can get is 195 points per race, the guys at Harvick's level and below, don't have any chance of getting in, no matter how well they drive.

email any comments to 36races@gmail.com

20 races down, 6 more to go. If each driver runs the next 6 races in some combination of their previous 20, there are 38760 possibilities for how many points they can score. (A link here for those interested in seeing the math.) How many of those 38760 possibilities can get them to the magic 3120 points total? The 3120 number is 120 x 26. 120 is the PPR needed to get 12th place, as we've seen in many of our past posts (here, here, and here)

Assuming each driver doesn't score their very best or very worst 6 races, the 38760 possibilities are an excellent summary of what will most likely happen.

I ran the numbers for every driver, and compared what portion of the combinations were enough to get them into the Chase. The data is below. You can click on the image for a bigger picture.

For example, Kyle Busch has 9078 possible ways he could score more than 773 points in 6 races (based on his first 20), which is only 23% of all the possibilities. His best 6 races this year scored him 1046 points. His worst 6 races scored 414 points. But only 23% of his 6-race combinations this year were above the 773 points he needs to reach 3120.

What you see here is color coding based on groups. Tony Stewart is going to make the chase even if he gets last place in the next 6 races.

The next set of drivers, in light blue, are common-sense certainties, given their performance this year.

The drivers in yellow all have a very strong chance of qualifying, with chances between 68 and 97 percent. Notice these are spots 5 through 12, the same drivers currently qualified.

The drivers in light orange make up spots 13-16. They have a slight chance of getting in, based on their performance this year. Between Reutimann's 26% and Bowyer's 1%. Although it's tough - they have already shown the ability this year to get the finishes they need to crack the top 12. Not likely, but it is possible.

The drivers in pink are not mathematically eliminated yet, but they haven't shown the performance this year to make it. They'd have to come up with their best streak of the year right now.

And finally, the drivers in orange, are already mathematically eliminated. Since the most you can get is 195 points per race, the guys at Harvick's level and below, don't have any chance of getting in, no matter how well they drive.

email any comments to 36races@gmail.com

## Monday, July 27, 2009

### Montoya's Team Math is wrong

If you saw the race on ESPN this week, they mentioned Montoya's team calculation that he needed to average a 14th place finish to make into the chase.

That sounds *VERY* similar to the post I made on March 11 of this year, suggesting that you need about 120 Points Per Race to make 12th place after 26 races. The post is here http://36races.blogspot.com/2009/03/ppr-and-getting-into-chase.html

The *mistake* however that Montoya's team is making, is comparing the 120 Points average to an average of 14th place finishes. Yes, we know that 14th place earns you 121 points, but....

The Average of Finishes DOES NOT EQUAL The Average of Points.

Montoya's team is making a big mistake, and we'll go through some examples why.

This is because of the non-linearity of the way points are awarded. Let's consider a few examples:

14th place is 121 points. So after 2 races if you got 14th and 14th, you'd have 242 points, and an average finish of 14.0

But what other ways can you have a 2-race average of 14.0? And how many points would that earn you?

Look at the table below:

Do you see the pattern here? If you average a 14.0 with mediocre finishes, you only get 242 points. But if you can average a 14.0 with one really good finish (like a win) then you can actually score a lot more than 242 points.

And look at this graph below, showing the total points after two races. Again you see the big advantage when one of your races is good - much better than two mediocre finishes:

The point here is that you don't just want to race for a 14th place, but for higher spots - since it will serve you better on your bad days, giving you more cushion.

From my previous posting on March 11 and my visualizations from May, we already know that you need to average 120 (or call it 121 in this case) points per race over the course of the season, so the more you win, the worse you can do in other races and still be okay. This year we have a perfect example: Montoya has an average finish better than Mark Martin's, but because Mark has scored 4 wins, he has more points than Montoya. Mark's DNFs have been balanced out by his wins. Montoya does not have this luxury, because with ZERO top fives all year, he's relied on a bunch of finishes between 6-15. He hasn't the same cushion to save a bad day as the other Chase drivers.

Maybe it's because their math is all wrong, and they are focused too much on Top 15s instead of the Top 5s you need to really make a move up in points.

Finally, consider this perspective. What possible sets of two finishes would earn a minimum of 242 points.

Notice again, that when you have a really good finish in there, you can balance it with a bad finish, have a lower average finish than 14.0, but still have more than 121 points per race. Look at what happens if you finish 31st to 35th in the first race. If you win the next race, your average finish is in the 16-18 area, but you always earned more than 242 points.

The final point to all of this is that YOU ARE NOT TRYING TO RACE FOR POSITIONS, BUT YOU NEED TO RACE FOR POINTS INSTEAD!

And the best way to race for points, is to go out there and RACE FOR WINS.

email any comments to 36races@gmail.com

That sounds *VERY* similar to the post I made on March 11 of this year, suggesting that you need about 120 Points Per Race to make 12th place after 26 races. The post is here http://36races.blogspot.com/2009/03/ppr-and-getting-into-chase.html

The *mistake* however that Montoya's team is making, is comparing the 120 Points average to an average of 14th place finishes. Yes, we know that 14th place earns you 121 points, but....

The Average of Finishes DOES NOT EQUAL The Average of Points.

Montoya's team is making a big mistake, and we'll go through some examples why.

This is because of the non-linearity of the way points are awarded. Let's consider a few examples:

14th place is 121 points. So after 2 races if you got 14th and 14th, you'd have 242 points, and an average finish of 14.0

But what other ways can you have a 2-race average of 14.0? And how many points would that earn you?

Look at the table below:

Do you see the pattern here? If you average a 14.0 with mediocre finishes, you only get 242 points. But if you can average a 14.0 with one really good finish (like a win) then you can actually score a lot more than 242 points.

And look at this graph below, showing the total points after two races. Again you see the big advantage when one of your races is good - much better than two mediocre finishes:

The point here is that you don't just want to race for a 14th place, but for higher spots - since it will serve you better on your bad days, giving you more cushion.

From my previous posting on March 11 and my visualizations from May, we already know that you need to average 120 (or call it 121 in this case) points per race over the course of the season, so the more you win, the worse you can do in other races and still be okay. This year we have a perfect example: Montoya has an average finish better than Mark Martin's, but because Mark has scored 4 wins, he has more points than Montoya. Mark's DNFs have been balanced out by his wins. Montoya does not have this luxury, because with ZERO top fives all year, he's relied on a bunch of finishes between 6-15. He hasn't the same cushion to save a bad day as the other Chase drivers.

Maybe it's because their math is all wrong, and they are focused too much on Top 15s instead of the Top 5s you need to really make a move up in points.

Finally, consider this perspective. What possible sets of two finishes would earn a minimum of 242 points.

Notice again, that when you have a really good finish in there, you can balance it with a bad finish, have a lower average finish than 14.0, but still have more than 121 points per race. Look at what happens if you finish 31st to 35th in the first race. If you win the next race, your average finish is in the 16-18 area, but you always earned more than 242 points.

The final point to all of this is that YOU ARE NOT TRYING TO RACE FOR POSITIONS, BUT YOU NEED TO RACE FOR POINTS INSTEAD!

And the best way to race for points, is to go out there and RACE FOR WINS.

email any comments to 36races@gmail.com

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