A Tale of Two Motorsports: A Graphical

PRACTICE, QUALIFYING, AND PAST SUCCESS IN NASCAR AND F1 1 A Tale of Two Motorsports: A Graphical-­‐Statistical Analysis of How Practice, Qualifying, and Past Success Relate to Finish Position in NASCAR and Formula One Racing* Kathleen M. Silva and Francisco J. Silva Department of Psychology, University of Redlands, Redlands, California 92373-­0999 USA ABSTRACT We analyzed data from the 2009 National Association for Stock Car Auto Racing (NASCAR) and Formula One (F1) racing seasons to examine the relationships between drivers’ finish positions and their performances during the final practice, qualifying, and past races. NASCAR drivers’ performances in practice, qualifying, and past races were usually positively correlated with their finish positions. In F1 racing, only drivers’ performances during qualifying and, to a lesser extent, in past races were positively correlated with their finish positions. In contrast, there was rarely a significant correlation between the finish positions of the best NASCAR drivers and their performances in practice, qualifying, or previous races. We discuss the results in the context of the demands and characteristics of NASCAR and F1 racing. Keywords: correlation, Formula One, motorsports, NASCAR, practice, qualifying, regression, Sprint Cup In terms of their environments or physical features (e.g., cars, racetracks), National Association
for Stock Car Auto Racing (NASCAR) and Formula One (F1) racing are very different forms of
automotive racing (Blount, 2009; Collantine, 2006; Hook, 2010; “NASCAR’s Jeff Gordon on
Formula One racing,” 2004). For example, the premier NASCAR series, currently known as the
Sprint Cup Series, consisted of 36 races in 2009.1 Of these races, all were run at tracks in the
United States and all but two of the races were on run on speedways shaped like ovals or
distorted ovals (e.g., rounded triangles or D’s). In contrast, the F1 Grand Prix series consisted of
17 races in 2009, each of which was run in a different country and all of which consisted of
irregularly shaped circuits and road courses. Table 1 presents a summary of some key physical
differences between NASCAR and F1 racing.
*
© 2010 Kathleen M. Silva and Francisco J. Silva. All right reserved.
Cite as: Silva, K. M., & Silva, F. J. (2010). A tale of two motorsports: A graphical-statistical analysis of how
practice, qualifying, and past success relate to finish position in NASCAR and Formula One racing. Retrieved from
http://newton.uor.edu/FacultyFolder/Silva/NASCARvF1.pdf
Address correspondence to K. Silva or F. Silva, Department of Psychology, University of Redlands, Redlands,
California 92373-0999 USA (email: [email protected] or [email protected]).
1
Throughout the manuscript, any reference to NASCAR will mean, more specifically, a reference to NASCAR’s
Sprint Cup Series and never to its other series (e.g., Nationwide Series, Camping World Truck Series, K&N Pro
Series). Although Sprint Cup Series is more accurate, the name of NASCAR’s premier racing series changes as a
function of corporate sponsorship. The Sprint Cup Series was previously known as the Nextel Cup Series and,
before that, the Winston Cup Series. Thus, although less precise than Sprint Cup Series, it is commonplace to refer
to this racing series simply as NASCAR (e.g., NASCAR on Fox and NASCAR TNT Summer Series, both of which
refer to television programs that cover of Sprint Cup races).
PRACTICE, QUALIFYING, AND PAST SUCCESS IN NASCAR AND F1 2 Table 1
Physical Variables: Similarities and Differences Between NASCAR and F1 Racing in 2009
Characteristic
Number of Drivers
NASCAR
43
Motorsport
F1
20
Number of Crew Members
During Pit Stops
7
20
Number of Races
36
17
Design of Cars
front-engine, “stock" car,
heavy (1500 kg)
mid-engine, open-wheel, light (600
kg)
Technological
Sophistication of Cars
basic; relatively simple
engineering
sophisticated; advanced
engineering
Racing Tracks and Circuits
oval-shaped speedways
circuits and road courses
Width of Tracks and
Circuits
relatively wide, side-by-side
racing is common
relatively narrow, side-by-side
racing is rare
Length of Tracks and
Circuits
relatively short (0.85 km to
4.18 km)
relatively long (3.34 km to 7.00 km)
Location of Races
23 locations in USA
17 countries in Asia, Australia,
Europe, South America
Turning
all left turns 34 of 36 races
left and right turning
Overtaking and Lead
Changes
relatively common
relatively rare
Qualifying
1 session consisting of 1 or 2
laps
3 sessions consisting of several
(e.g., 7, 12) laps in each
Final Practice
occurs after qualifying
occurs before qualifying
Ability to race in wet
weather
cannot race in rain under any
circumstances
can race in rain with tires designed
for this purpose
Time Limit
none
2 hours
Despite these differences, there are noteworthy similarities between the two motorsports.
For example, both NASCAR and F1 award points commensurate with when a driver finishes a
race to determine who is the best driver, overall, at the end of the racing season. Also, both
NASCAR and F1 set a driver’s starting position for a race based on his2 time during qualifying.
The drivers’ qualifying times are ranked such that there is normally a perfect and positive
2
All drivers during all of the races analyzed in the present article were men.
PRACTICE, QUALIFYING, AND PAST SUCCESS IN NASCAR AND F1 3 correlation between a driver’s rank during qualifying and his starting position (e.g., fastest in
qualifying = 1st or pole position to start a race; slowest in qualifying = last position on the
starting grid).3 Finally, both NASCAR and F1 racing allow drivers to practice their driving, and
teams to set up their cars for the conditions of the speedway or circuit. But, even here, the two
motorsports differ: NASCAR’s final practice session normally occurs the day after qualifying;
F1 racing’s final practice occurs before qualifying.
In this article, we examine whether there are similarities and differences between
NASCAR and F1 racing in terms of performance features – i.e., those factors tied to the drivers’
and their teams’ performance rather than the physical features of the two motorsports (e.g. see
Table 1). We examined these performance features by answering six questions. (1) What is the
relationship between a driver’s performance during the final practice before a race and his finish
position? (2) What is the relationship between a driver’s performance during qualifying (and
thus his position at the start of a race) and his finish position? (3) What is the relationship
between a driver’s points-standing before a race (i.e., a measure of his overall success) and his
finish position? (4) How do the relationships in (1) through (3) change across races? (5) What is
a more reliable predictor of a driver’s finish position: His performance during practice, his
performance during qualifying, his overall success prior to a race, or a combination of these
variables? (6) What factors are related to the degree that a driver’s finish position is predictable
from his performance in practice, qualifying, and his success up to that point in the season? To
answer these questions, we analyzed the results of the 2009 NASCAR and F1 racing seasons
using a combination of visual inspection of graphed data (see, e.g., Kazdin, 1982) and inferential
statistics (primarily correlation and regression).
Published research that investigated NASCAR drivers’ performance is rare. Most of the
studies that do exist take the form of working papers available through the authors’ personal
archives. However, two exploratory studies of whether reliable predictors exist for the outcomes
of NASCAR races hint at answers to some of the preceding six questions. One project examined
the results from 14 races from the 2003 NASCAR season to see whether the outcome of a race
was predicted from a variety of performance variables, such as how drivers performed in the
practice session closest to the start of the race, the drivers’ performance during qualifying, the
drivers’ overall success leading up to a race, the number of laps a driver completed in all races
during the previous season, how often a driver did not finish a race, the drivers’ finish positions
at the same race the year before, and the drivers’ finish positions in the preceding race. The
results showed that drivers’ performance during practice and qualifying, as well as their overall
success leading up to a particular race and the number of laps they completed during the previous
season, were correlated with their finish position (Pfitzner & Rishel, 2005). A similar project
that used the results of 38 races in the 2002 NASCAR season found that the drivers’
3
Although there is normally a perfect and positive correlation between the rank of a driver’s qualifying time and his
starting position, there are occasions when this is not the case. For example, a driver may produce the fastest time
during qualifying (and thus be ranked first following qualifying) and yet start a race at the rear of the field for any of
several reasons (e.g., changing an engine after qualifying; having his qualifying time disallowed because of a rules
violation). These sorts of events, though, are uncommon. Also, in NASCAR, qualifying is sometimes cancelled
because of rain. When this happens, the starting positions for a race are determined by so-called “car owner points,”
which are usually but not always the same as a driver’s points-standing. Nevertheless, for most intents and purposes
(including those of the present article), there is a perfect and positive correlation between a driver’s rank following
qualifying and his starting position. During the 2009 NASCAR season, qualifying was cancelled at the following
races: Martinsville, Pocono, New Hampshire, *Daytona, *Pocono.
PRACTICE, QUALIFYING, AND PAST SUCCESS IN NASCAR AND F1 4 performances during qualifying (and thus their starting positions) and their number of years of
NASCAR driving experience were important predictors of their finish positions (Allender,
2008). Published studies that investigated the performance of F1 drivers are non-existent.
The present study attempts to fill a void by providing the first comprehensive,
quantitative, and comparative analysis of the performance of NASCAR and F1 drivers across an
entire racing season. Our ultimate goal is to create a table (comparable to Table 1), based on the
answers to the six questions posed above, which highlights the similarities and differences
between NASCAR and F1 drivers in relation to key performance variables of these motorsports.
Method The data that we analyzed were downloaded from the official websites of NASCAR and F1
racing: nascar.com and formulaone.com. For each points-awarding race in 2009,4 we obtained
each driver’s rank during the final practice session before a race, each driver’s rank in qualifying
(and, thus, his starting position), each driver’s points-standings (i.e., his ranking based on the
number of points he accrued before the start of a race, which is a measure of his overall success
up to that race), and each driver’s finish position.5 For short, we refer to these variables as
Practice, Qualifying, Points, and Finish.
In NASCAR, the final practice session normally occurs after qualifying. In F1 racing,
the final practice session normally occurs before qualifying. Thus, for NASCAR, the final
practice is the last time a driver is on the speedway before the start of the race; for F1 racing,
qualifying is the last time a driver spends any substantial amount of time on the racing circuit
before the start of a grand prix.6
The primary results were obtained by calculating Spearman rank correlation coefficients
(known as Spearman’s rs) between Practice and Finish, Qualifying and Finish, and Points and
Finish for each NASCAR and F1 race. We chose to calculate Spearman’s rs instead of Pearson’s
product moment correlation coefficients or r for three main reasons. One, we calculated a total
of 159 correlation coefficients (36 for NASCAR + 17 for F1 x 3 relationships, explained below).
Rather than worry about whether the characteristics of any set if data violated one or more
assumptions necessary to calculate Pearson’s r, we opted for the assumption-free Spearman’s rs.
4
All of the 36 NASCAR and 17 F1 races analyzed in the present article award drivers points commensurate with
their performance in a race. These points are awarded exclusively on the basis of a driver’s finish position in F1
racing and primarily on the basis of a driver’s finish position in NASCAR. Other factors that contribute to a
NASCAR driver’s points include leading the most laps in a race and leading a lap during a race. Races that did not
contribute to the drivers’ points total (e.g., all-star race) were excluded from the analyses.
5
The one exception was the first race for each of the NASCAR and F1 seasons. Because all drivers start the first
race of the season with 0 points, we used the drivers’ final points-standing from the previous season. For 2009
rookie drivers who did not race in 2008, we assigned a value of 0 points to their points-total before the first race of
the 2009 season and ranked them accordingly.
6
In NASCAR, there are two notable exceptions to this schedule. Because NASCAR cars cannot race in wet
weather (drizzle, showers, rain), final practice is sometimes cancelled because of precipitation. In these
circumstances, the final practice occurs before qualifying. Also, 3 of the 36 NASCAR races held in 2009 were socalled impound races. At both Talladega races and the second Daytona race, NASCAR officials impound cars
following qualifying. This means that drivers cannot drive their cars and teams cannot work on their cars between
the end of qualifying and the start of a race. At impound races, the final practice also occurs before qualifying.
PRACTICE, QUALIFYING, AND PAST SUCCESS IN NASCAR AND F1 5 Two, the number of data points used in some analyses was relatively small (n = 20). Pearson
correlation coefficients can be misleading when sample sizes are small (Aliaga & Gunderson,
2006). Third, the ranked Practice, Qualifying, and Finish data seemed ideally suited to a
Spearman analysis, which converts data to ranks before rs is calculated. We used α < .05 to
determine the statistical significance of all two-tailed analyses.
To determine how combinations of Practice, Qualifying, and Points correlated with
Finish, we tested the following four models:
(1) Finish = α + β1Practice + β2Qualifying
(2) Finish = α + β1Practice + β2Points
(3) Finish = α + β1Qualifying + β2Points
(4) Finish = α + β1Practice + β2Qualifying + β3Points
For each analysis, we were interested only in (a) the multiple correlation coefficient or R,
which expresses the correlation between Finish and a combination of the predictor variables
(Practice, Qualifying, Points) in the equation, and (b) the accompanying F statistic and p value,
which provide information about the degree that the combination of variables in the model is
significantly correlated with Finish.
Given the number of races for which we tested the models listed above,7 “by the book”
evaluations of each model for each race – which normally consists of specifying the model,
identifying multicollinearity, disentangling partial correlations, removing nonsignificant
variables, specifying a new model, evaluating it, and so on (Keith, 2006; Younger, 1985) – were
not reasonable. Instead, we relied on visual inspection of graphed data to form generalizations
about the four models and their relation to NASCAR and F1 racing. We will explain more
completely in the Results section how we evaluated the models by graphical inspection, and how
we used chi-square tests of independence to provide corroborating support for our evaluations.
Results Correlations: NASCAR Figure 1 shows how Finish was correlated with Practice, Qualifying and Points across the 2009
NASCAR season. Values in the grey area are not statistically significant; values in the white
area are statistically significant. An asterisk before the location of the race means it was the
second time during the season that a race was held at that location. For all but one race, the data
from 43 drivers were used to calculate each rs. Appendix A shows Spearman’s rs values and
their associated two-tailed p values used to construct Figure 1.
An analysis of NASCAR drivers’ ranking in final practice and their finish positions
throughout the 2009 season revealed statistically meaningful correlations between their practice
7
Data from 36 NASCAR and 17 F1 races were analyzed. However, as explained in the Results section, we also
analyzed the data of the top 20 points-leaders leading up to each NASCAR race. Thus, two sets of data were
analyzed for each NASCAR race: one set that included every driver in the race (n = 43) and one set that included
only the top 20 points-leaders before the race (n = 20). In total, 89 sets of data were analyzed: 36 NASCAR races,
17 F1 grands prix, and 36 NASCAR races for the top 20 points-leaders.
PRACTICE, QUALIFYING, AND PAST SUCCESS IN NASCAR AND F1 6 performance and their finish positions in 29 of the 36 (81%) races. The better someone
performed in practice, the better his finish position. For 27 of the 36 (75%) races, the drivers’
performances in the final practice and in qualifying were significantly correlated with their finish
positions in a race. For most races, the correlations between Practice and Finish and between
Qualifying and Finish were similar. However, there were some notable exceptions. At Bristol
and Kansas, the correlations between Practice and Finish were statistically significant, but the
correlations between Qualifying and Finish were not. The reverse was true in the second races
held at Daytona and Atlanta. During these races, the correlations between Practice and Finish
were not statistically significant, but those between Qualifying and Finish were significant.
Finally, Talladega is notable for the fact that it was the only speedway that hosted two races for
which the correlations between Practice and Finish and between Qualifying and Finish were not
statistically significant in either race.
Figure 1. A graph of the correlations (rs) between Practice and Finish, Qualifying and Finish, and Points and Finish for each
race in the 2009 NASCAR season. An asterisk before the name of a race means it was the second time during the season that a
race was held at that location. Forty-three drivers started all races except for the first race at Pocono, where 42 drivers started the
race. Thus, df = 41 for most races and df = 40 for one race. In general, the values in the grey area are not statistically significant
and the values in the white area are statistically significant. However, because of limitations in the graphing software, the plot
symbols of some marginally significant/insignificant values are not entirely within the grey or white areas. To see precisely
which Spearman’s rank correlation coefficients were statistically significant, see Appendix A.
Figure 1 also shows that there were statistically significant correlations between the
drivers’ finish positions and their points-standings before a race in 31 of the 36 races (86%).
Drivers ranked higher in the standings tended to finish a race before drivers ranked lower in the
standings. Although this relationship was not evident during the first three races of the season, it
occurred reliably thereafter except at both races held at Talladega. Moreover, if we compare the
correlations between Finish and each of Practice, Qualifying, and Points, we see that the
PRACTICE, QUALIFYING, AND PAST SUCCESS IN NASCAR AND F1 7 correlations between Points and Finish are generally greater than those between Practice and
Finish and those between Qualifying and Finish.
To get a visualization of the raw data used to calculate the correlations shown in Figure 1,
Figure 2 shows scatter plots of the strongest and weakest associations in Figure 1. The top graph
illustrates the strong linear relationship between Points and Finish, which occurred in the second
race held at Richmond. The bottom graph illustrates the almost-zero correlation between
Practice and Finish from the first race held at Talladega.
Figure 2. Scatter plots showing the strongest (top graph) and weakest (bottom graph) associations among the correlations in
Figure 1. The top graph illustrates the relationship between Points and Finish for the second race held at Richmond [rs(41) =
.809]. The bottom graph illustrates the relationship between Practice and Finish for the first race held at Talladega [rs(41) = .013]. Note: Although 45 drivers participated in the final practice at Talladega (which occurs before qualifying at this race), only
43 drivers qualified for the race.
Correlations: F1 Figure 3 shows how Finish was correlated with Practice, Qualifying, and Points across the 2009
F1 racing season. Values in the grey area are not statistically significant; values in the white area
are statistically significant. For most grands prix, the data from 20 drivers were used to calculate
PRACTICE, QUALIFYING, AND PAST SUCCESS IN NASCAR AND F1 8 each rs. Appendix B shows Spearman’s rs values and their associated two-tailed p values used to
construct Figure 3.
Figure 3. A graph of the correlations (rs) between Practice and Finish, Qualifying and Finish, and Points and Finish for each
grand prix in the 2009 F1 season. Twenty drivers started each grand prix except Hungary (18 drivers) and Japan (19 drivers),
thus df = 18 for all grands prix except Hungary (df = 16) and Japan (df = 17). Details are the same as for Figure 1. To see
precisely which Spearman’s rank correlation coefficients were statistically significant, see Appendix B.
In general, and in contrast to the NASCAR drivers, only the correlations between F1
drivers’ qualifying positions and their finish positions and between the F1 drivers’ pointsstanding and their finish positions were statistically significant. Statistically significant
correlations between Practice and Finish were rare, occurring in only 7 of the 17 races (41%).
Statistically significant correlations between Qualifying and Finish were observed in 14 of the 17
(82%) races, and between Points and Finish in 10 of the 17 races (59%). Also, unlike the
NASCAR drivers, the correlations between Practice and Finish and between Qualifying and
Finish were often dissimilar. Finally, with the exception of an upward trend in the correlations
between Practice and Finish that started with the grand prix held in China and ended with the
grand prix held in Great Britain, there were no strong trends in the correlations between Finish
and each of Practice, Qualifying, and Points across the racing season.
To get a visualization of the raw data used to calculate the correlations shown in Figure 3,
Figure 4 shows scatter plots of the strongest and weakest associations in Figure 3. The top graph
illustrates the strong relationship between Qualifying and Finish from the Japanese Grand Prix.
The bottom graph illustrates the near-zero correlation between Qualifying and Finish from the
Brazilian Grand Prix.
PRACTICE, QUALIFYING, AND PAST SUCCESS IN NASCAR AND F1 9 Figure 4. Scatter plots showing the strongest (top graph) and weakest (bottom graph) associations among the correlations in
Figure 3. The top graph illustrates the relationship between Qualifying and Finish for the grand prix held in Japan [rs(17) =
.849]. The bottom graph illustrates the relationship between Qualifying and Finish for the grand prix held in Brazil [rs(18) = .007].
Correlations: NASCAR’s Top 20 Points-­Leaders Because correlation coefficients are affected by sample size, the differences in the results shown
in Figures 1 and 3 may have occurred because Spearman’s rank correlation coefficients were
calculated across different numbers of drivers (43 NASCAR drivers vs. 20 F1 drivers). If we
calculated correlation coefficients for only 20 NASCAR drivers, the results of the analyses of the
NASCAR and F1 drivers may have been more alike. To evaluate this possibility, we calculated
PRACTICE, QUALIFYING, AND PAST SUCCESS IN NASCAR AND F1 10 Spearman’s rank correlation coefficients between Practice and Finish, Qualifying and Finish,
and Points and Finish for the top 20 points-leading drivers before each NASCAR race.8
Figure 5 shows how Finish was correlated with Practice, Qualifying, and Points across
the 2009 NASCAR season for the top 20 points-leaders before each race. Most striking is that
there were few statistically significant correlations between Finish and each of Practice,
Qualifying, and Points. This contrasts with the F1 drivers’ data for which there were statistically
Figure 5. A graph of the correlations (rs) between Practice and Finish, Qualifying and Finish, and Points and Finish for the top
20 points-leaders before each race in the 2009 NASCAR season. For all races, df = 18. Details are the same as for Figure 1. To
see precisely which Spearman’s rank correlation coefficients were statistically significant, see Appendix C.
significant correlations between Practice and Finish, between Qualifying and Finish, and
between Points and Finish in 41%, 82%, 59% of the grands prix, respectively. For the top 20
points-leaders in NASCAR, statistically significant correlations between Practice and Finish,
Qualifying and Finish, and Points and Finish occurred in only 8 of 36 (22%), 10 of 36 (28%), 7
8
It could be argued that taking a random sample of NASCAR drivers, rather than taking a sample of the best
NASCAR drivers, is the best way to assess whether the differences between the results of the NASCAR and F1
drivers were because of the difference in the sample sizes. Although this may be true, we chose to use the Top 20
NASCAR drivers instead of a random sample of them because using the best NASCAR drivers may actually be a
better way to assess the role of sample sizes in the observed differences between the 43 NASCAR drivers and the 20
F1 drivers. Why? Because the 20 F1 drivers are not a random sample of F1 drivers; they are the best F1 drivers. A
comparable sample of NASCAR drivers consists of the 20 best NASCAR drivers, not a random sample of them.
PRACTICE, QUALIFYING, AND PAST SUCCESS IN NASCAR AND F1 11 of 36 (19%) races, respectively. Appendix C shows Spearman’s rs values and their associated
two-tailed p values used to construct Figure 5.
To get a visualization of the raw data used to calculate the correlations shown in Figure 5,
Figure 6 shows scatter plots of the strongest and weakest associations in Figure 5. The top graph
illustrates the strong relationship between Qualifying and Finish, which occurred in the second
race held at Richmond. The bottom graph illustrates the almost-zero correlation between Points
and Finish from the first race held at Charlotte.
Figure 6. Scatter plots showing the strongest (top graph) and weakest (bottom graph) associations among the correlations in
Figure 5. The top graph illustrates the relationship between Qualifying and Finish for the second race held at Richmond [rs(18) =
.699]. The bottom graph illustrates the relationship between Points and Finish for the first race held at Charlotte [rs(18) = .001].
Regression: NASCAR Figure 7 shows the values of the multiple correlation coefficient for each of the four models
listed in the Method section plotted across the races of the 2009 NASCAR season. For the
models with the combinations Practice and Qualifying, Practice and Points, and Qualifying and
Points, the R values plotted in the white area are statistically significant and those in the grey
area are not. For the model with the combination Practice, Qualifying, and Points, only values
PRACTICE, QUALIFYING, AND PAST SUCCESS IN NASCAR AND F1 12 above the dashed horizontal line are statistically significant. Appendix D shows the R values and
the associated F statistics and p values used to construct Figure 7.
Figure 7. A graph of the multiple correlation coefficient (R) for each race in the 2009 NASCAR season. The R values plotted in
the white area are statistically significant and those in the grey area are not, except for the model with the combination Practice,
Qualifying, and Points. For this model, only values above the dashed horizontal line are statistically significant. However,
because of limitations in the graphing software, the plot symbols of some marginally significant/insignificant values are not
entirely within the grey or white areas. To see precisely which R values were statistically significant, see Appendix D. The
degrees of freedom for the models with two predictor variables were (2, 40) for all races except for the second Pocono race (df =
2, 39). For the model with three predictor variables, the degrees of freedom were (3, 39) for all races except for the second
Pocono race (df = 3, 38).
There are five noteworthy features in the graph. One, most R values were statistically
significant. Two, the R values were similar across races. Three, the two races at Talladega
produced the lowest R values. Four, the R values for the model with only Practice and
Qualifying were often smaller than the R values of the other three models. Five, there was
considerable overlap among the R values for the models with Practice and Points, Qualifying
and Points, and Practice, Qualifying, and Points. Given that there is a lot of overlap among
these three models and that the common variable to all three models is Points, we can conclude
that a model with Points as the only predictor variable is as good as any model with it plus
Practice and/or Qualifying. In other words, the best predictor of a driver’s finish is his success
up to that point in the racing season, and additional information about how he performed in
practice and qualifying does little to help predict his finish position in most races.
PRACTICE, QUALIFYING, AND PAST SUCCESS IN NASCAR AND F1 13 Regression: F1 Figure 8 shows the R values for each of the four models listed in the Method section plotted
across the grands prix of the 2009 F1 season. Appendix E shows the R values and the associated
F statistics and p values used to construct Figure 8. Similar to the NASCAR drivers, there was
relatively little change in the R values across grands prix. In contrast to the NASCAR drivers’
data, the model with Practice and Points generated lower R values than the other models. Also,
there was considerable overlap between the model with Practice, Qualifying, and Points and the
models with Practice and Qualifying and with Qualifying and Points. Given that there was a lot
of overlap among these three models and that the common variable to all three models is
Qualifying, we can conclude that a model with Qualifying as the only predictor variable is as
good as any model with it plus Practice and/or Points. In other words, the best predictor of a
driver’s finish is his performance during qualifying, and additional information about his success
in the season and how he performed in practice does little to help predict his finish position in
most grands prix.
Figure 8. A graph of the multiple correlation coefficient (R) for each grand prix in the 2009 F1 racing season. The R values
plotted in the white area are statistically significant and those in the grey area are not, except for the model with the combination
Practice, Qualifying, and Points. For this model, only values above the dashed horizontal line are statistically significant.
However, because of limitations in the graphing software, the plot symbols of some marginally significant/insignificant values
are not entirely within the grey or white areas. To see precisely which R values were statistically significant, see Appendix E.
The degrees of freedom for the models with two predictor variables were (2, 17) for all grands prix except Hungary (df = 2, 15)
and Japan (df = 2, 16). For the model with three predictor variables, the degrees of freedom were (3, 16) for all grands prix
except Hungary (df = 3, 14) and Japan (df = 3, 15).
PRACTICE, QUALIFYING, AND PAST SUCCESS IN NASCAR AND F1 14 Regression: NASCAR’s Top 20 Points-­Leaders Figure 9 shows the R values for each of the four models listed in the Method section plotted
across the 2009 NASCAR season for the top 20 points-leaders before each race. Appendix F
shows the R values and the associated F statistics and p values used to construct Figure 9.
Except for two clusters late in the season (*Michigan, *Bristol, *Atlanta in one cluster and
*Talladega, *Texas, *Phoenix in the other cluster) where the R values were near or below .20,
there was no trend in the R values across races. Also, in contrast to the data of the F1 drivers and
the 43 drivers who comprise the broader NASCAR field, few of the R values from any of the
four models reached statistical significance for the top 20 NASCAR points-leaders. Also in
contrast to the data of the F1 drivers and the broader NASCAR field, there was no consistent
overlap between any of the models across races. Given that none of the four models resulted in
R values that were consistently statistically significant and that there was no consistent overlap
between any of the models, we can conclude that no combinations of Practice, Qualifying,
and/or Points can predict Finish for the top 20 points-leaders in most races.
Figure 9. A graph of the multiple correlation coefficient (R) for the top 20 points-leaders before each race in the 2009 NASCAR
season. The R values plotted in the white area are statistically significant and those in the grey area are not, except for the model
with the combination Practice, Qualifying, and Points. For this model, only values above the dashed horizontal line are
statistically significant. However, because of limitations in the graphing software, the plot symbols of some marginally
significant/insignificant values are not entirely within the grey or white areas. To see precisely which R values were statistically
significant, see Appendix F. The degrees of freedom for the models with two predictor variables were (2, 17) for all races. For
the model with three predictor variables, the degrees of freedom were (3, 16) for all races.
PRACTICE, QUALIFYING, AND PAST SUCCESS IN NASCAR AND F1 15 Contingency Table Analyses For many reasons, regression can be a complicated procedure (see Keith, 2006; Younger, 1985).
Our brute-force approach that relied on visual analysis of the graphed R values is one way to
simplify the testing of regression models. Another approach to evaluating the relative
importance of Practice, Qualifying, and Points to predicting Finish is to use a chi-square test of
independence. This approach involves ranking the magnitude of the correlations in each of the
pairs of variables “Practice and Finish,” “Qualifying and Finish,” and “Points and Finish” for
each race, and then tallying how often the largest correlation was associated with each pair of
variables, how often the median correlation was associated with each pair of variables, and how
often the smallest correlation was associated with each pair of variables. This produces a 3 x 3
contingency table with three rows for the pairs of variables (“Practice and Finish,” “Qualifying
and Finish,” and “Points and Finish”) and three columns for the rank of a correlation (largest,
median, smallest).
The results of the contingency table analyses are shown in Table 2. For the 43 drivers
who normally start a NASCAR race (top panel), the largest correlations occurred most often
between “Points and Finish” (28 of the 36 races). The correlations between “Practice and
Finish” and between “Qualifying and Finish” were the median and smallest correlations in 15 to
17 of the 36 races. A chi-square test of independence confirmed that the pairs of variables and
the correlation-ranks were not independent [χ2(4) = 48.50, p < .001] and that the largest
correlations occurred most often in “Points and Finish” [χ2(2) = 32.17, p < .001].
Table 2
Three Panels Showing 3 x 3 Contingency Tables
Drivers
Variable Correlated With Finish
Rank of rs
NASCAR
Practice
Qualifying
Points
1st
5
3
28
2nd
16
17
3
3rd
15
16
5
F1
Practice
Qualifying
Points
4
11
2
3
4
10
10
2
5
NASCAR (Top 20)
Practice
Qualifying
Points
12
13
11
7
15
14
17
7
12
For the F1 drivers (middle panel), the largest correlations occurred most often between
“Qualifying and Finish” (11 of the 17 grands prix). The correlations between “Practice and
Finish” and between “Points and Finish” were the median and smallest correlations in 10 of the
17 races. A chi-square test of independence confirmed that the pairs of variables and the
correlation-ranks were not independent [χ2(4) = 18.71, p < .001] and that the largest correlations
occurred most often in “Qualifying and Finish” [χ2(2) = 7.88, p = .01].
PRACTICE, QUALIFYING, AND PAST SUCCESS IN NASCAR AND F1 16 For the top 20 points-leaders before each NASCAR race (bottom panel), the results
showed that, in contrast to the broader NASCAR field and the F1 drivers, there was no
relationship between categories and the correlation-ranks [χ2(4) = 7.33, p = .12].
Thus, the 3 x 3 contingency table analyses corroborated our visual analyses of the
graphed R values from the four models listed in the Method section. For the 43 NASCAR
drivers who started a race, the best predictor of a driver’s finish was his overall success up to that
point in the racing season (i.e., his points-standing). For the F1 drivers, the best predictor of a
driver’s finish was his performance during qualifying. For the top 20 points-leaders in
NASCAR, none of the variables (Practice, Qualifying, Points) were useful predictors of a
driver’s finish position.
How Lead Changes and Cautions Relate to Predictability of Finish The analyses above quantified the correlation between Finish and each of Practice,
Qualifying, and Points. Because correlation and prediction are closely related (the latter
dependent on the former), we could say that the values of Spearman’s rs measured the degree
that a driver’s finish position was predictable from his performance during practice, his
performance during qualifying, and his overall success leading up a race. What we attempt to
address next is, what factors are related to the predictability of Finish from Practice, Qualifying,
and Points? We focused on two factors that occur during a race: lead changes and cautions. To
answer the question, we correlated the values of Spearman’s rs from the analyses above with
how often lead changes and cautions occurred in a race. In this context, we refer to the values of
Spearman’s rs as Predictability of Finish.
Because many races had the same number of lead changes or cautions, we calculated the
relationship between Predictability of Finish and each of Lead Changes and Cautions using
Pearson’s product moment correlation coefficient (r). This measure of the association between
variables works better than Spearman’s rs when many values in the data are the same.
Spearman’s rs, but not Pearson’s r, requires that all raw data be converted to ranks, something
that can be problematic if there are many values in the data that are the same.
NASCAR. The mean number of lead changes in a 2009 NASCAR race was 20 (SD =
11.46) and the mean number of cautions was 8.47 (SD = 3.40). Table 3 shows the correlations
between Lead Changes and Predictability of Finish from each of the variables Practice,
Qualifying, and Points, as well as between Cautions and Predictability of Finish from Practice,
Qualifying, and Points.
The results showed that there were statistically significant inverse (negative) correlations
between Lead Changes and Predictability of Finish from Practice, Qualifying, and Points. More
intuitively, these results show that the more lead changes that occurred during a race, the more
difficult it was to predict a driver’s finish position from his performance during practice, his
performance during qualifying, or his points-standing. In short, an increase in lead changes
meant a decrease in the Predictability of Finish from Practice, Qualifying, and Points. There
were no statistically significant relationships between Cautions and Predictability of Finish from
Practice, Qualifying, or Points.9
9
The correlation between the number of cautions and the number of lead changes was not statistically significant (r
= .03, p < .88).
PRACTICE, QUALIFYING, AND PAST SUCCESS IN NASCAR AND F1 17 Table 3
Correlations (r) Between Lead Changes and Predictability of Finish
and Cautions and Predictability of Finish
Drivers
Variable
Predictability of Finish from
Practice
Qualifying
Points
NASCAR
Lead Changes
Cautions
-0.636*
-0.218
-0.356*
-0.110
-0.553*
-0.061
F1
Lead Changes
Cautions
-0.129
n/a
0.277
n/a
-0.261
n/a
NASCAR (Top 20)
Lead Changes
Cautions
-0.433*
0.091
-0.313
0.119
-0.412*
0.108
Note. For both groups of NASCAR drivers, n = 36; for F1 drivers, n = 17.
* p < .05.
F1. The mean number of lead changes in an F1 grand prix was 4.53 (SD = 2.45),
significantly fewer than the 20 that typically occurred in a NASCAR race [t(51) = 5.48, p <
.001]. In contrast to NASCAR races, there were no statistically significant correlations between
Lead Changes and Predictability of Finish from Practice, Qualifying, or Points in F1 racing.
(Information about the number of cautions in F1 grands prix was not available from
formulaone.com, and thus no analyses involving Cautions were possible.)10
NASCAR Top 20 Points-­Leaders. The results for the top 20 points-leaders before each
NASCAR race were similar to the results of the broader 43-driver field. However, there was one
exception: The correlation between Lead Changes and Predictability of Finish from Qualifying
approached but did not reach statistical significance (p = .06). Thus, for the top 20 pointsleaders, an increase in lead changes meant a decrease in the Predictability of Finish from
Practice and Points.
Discussion We used the results of the 2009 NASCAR and F1 seasons to answer six questions related to
drivers’ performances in these two motorsports, which differ considerably in terms of their
physical features. In what follows, we restate the questions and discuss the answers to each.
What is the relationship between a driver’s performance during the final practice before a race and his finish position? 10
Also, yellow- and red-flag cautions in F1 racing are different from those in NASCAR. In NASCAR, all yellowand red-flag cautions apply to the entire speedway. In F1 racing, a red-flag caution also applies to the entire race
circuit, but a yellow-flag caution may apply to only a particular section of the circuit (termed a “local caution”) or it
may apply to the whole course (termed a “full-course caution”).
PRACTICE, QUALIFYING, AND PAST SUCCESS IN NASCAR AND F1 18 For the 43 drivers who comprise the starting field of a NASCAR race there was a
statistically significant relationship between their performances during the final practice and their
finish positions in most races (see also Pfitzner & Rishel, 2005). For these statistically
significant correlations, the rs values were generally between .4 and .6. This was not the case for
the 20 drivers who comprise the starting field of an F1 grand prix. For these drivers, there was
no reliable relationship between their performances during final practice and their finish
positions; the rs values for most grands prix were between .2 and .4.
If we limit our analysis to the top 20 drivers in the NASCAR points-standings, there was
no reliable relationship between a driver’s performance in final practice and his finish position.
Moreover, in contrast to the F1 drivers, there was more variability in the rs values from race to
race. In sum, a NASCAR driver’s performance during final practice is related to his finish
position if the entire 43-driver field is entered into the analysis; the better a driver performed in
practice, the better he performed in the race. This relationship was not evident for F1 drivers or
for the top 20 points-leaders in NASCAR.
One possible reason for the difference between the standard 43-driver NASCAR field and
the F1 drivers relates to when the final practice session occurs. In NASCAR, the final practice
session normally occurs after qualifying. In F1 racing, the final practice session occurs before
qualifying. These two motorsports thus differ in terms of how contiguous the final practice
session is with the start of the race. In NASCAR, the purpose of the final practice is to set up the
car for the conditions expected during a race. In F1 racing, the purpose is to set up a car for
optimal performance during qualifying conditions, which may not necessarily be the conditions
during the race. These differences between the two motorsports reflect what is known about
contingencies of reinforcement and the allocation of behavior: People and other animals
generally respond to satisfy the requirements of the more immediate consequence (Pear, 2001).
Alternatively, the similarity of the results for the top 20 NASCAR points-leaders and the
F1 drivers suggests that performance in final practice, regardless of when it occurs, may not
relate much to the race-day performance of elite drivers. Perhaps it is that the best NASCAR
drivers and their teams are excellent at adapting during a race, that their improvisational skills
are better than those of the 23 drivers who comprise the rest of the starting field. In relation to
their finish position, how a top 20 points-leading NASCAR driver and his team adapt during a
race may be more important than what they do during practice. Or, perhaps what they do during
practice is not so much about producing the fastest laps during practice (a short-term payoff) but
about testing configurations and strategies that may help them produce consistently fast laps
across a variety of race conditions (a long-term payoff). As a result, there were few statistically
significant correlations between these drivers’ performance during final practice and their finish
positions. Whether this explanation or the difference in the timing of the final practice sessions
(or both) best explains the differences among the broader NASCAR field, the best NASCAR
driver, and the F1 drivers, we cannot say.
What is the relationship between a driver’s performance during qualifying (and thus his position at the start of a race) and his finish position? A driver’s starting position is normally determined by his performance during qualifying. The
better a driver performs in qualifying, the closer to the front of the field he will start a race. For
the 43 drivers who comprise the starting field of a NASCAR race, there was a statistically
significant relationship between their performances in qualifying and their finish positions in
PRACTICE, QUALIFYING, AND PAST SUCCESS IN NASCAR AND F1 19 most races (see also Allender, 2008; Pfitzner & Rishel, 2005). For these statistically significant
correlations, the rs values were generally between .4 and .6. Similar results were noted for the F1
drivers, except that the typical rs values were greater (between .6 and .8). This was not the case
for the top 20 drivers in the NASCAR points-standings. For these drivers, there was no reliable
relationship between a driver’s performance in qualifying and his finish position. Why this
relationship was absent for these drivers is unclear. Perhaps here, too, how a top 20 pointsleading driver and his team adapt during a race may be more important to their finish positions
than where these drivers start a race. Alternatively, for the best drivers in NASCAR, perhaps it
is that individual drivers and their teams are better suited to particular speedways or race
conditions (Grace, Reeves, & Fitzgerald, 2003), and it is this fit between driver and environment
that is more related to a driver’s finish position than his performance in qualifying.
If the difference in the importance of qualifying between NASCAR and F1 racing reflects
differences in the demands of these two motorsports, then we might expect the importance of
qualifying to be more similar in the two types of racing when the demands of each motorsport
are more similar. Such is the case at NASCAR’s Sonoma and Watkins Glen races, both of
which are run at road courses similar to the circuits used in F1 racing. The results, though, were
inconsistent with this expectation. For the top 20 points-leading NASCAR drivers, the
correlations between their qualifying performances and their finish positions were not
statistically significant at either Sonoma or Watkins Glen.
What is the relationship between the number of points a driver has accrued in a season (i.e., his overall success) and his finish position? For the 43-driver NASCAR field, the more points a driver had accrued before a race, the better
his finish position (see also Pfitzner & Rishel, 2005). This relationship got stronger as the season
progressed with the correlation between Points and Finish approaching rs = .8 for several races
in the last quarter of the season. In contrast, the relationship between Points and Finish was not
as reliable for F1 drivers, and there was rarely a statistically significant correlation between these
variables for the top 20 points-leaders in NASCAR.
In relation to NASCAR racing, the different results for the 43-driver field versus the top
20 points-leaders suggests again some sort of fundamental differences between the best drivers
and the rest of the field. We speculated above that one of these differences might be the drivers’
and their teams’ abilities to make adjustments throughout the race, perhaps similar to a team who
makes adjustments at halftime or alters their behavior as a function of variations that occur
during a game (e.g., the other team’s strategy, injuries, weather conditions). That the results of
the top 20 points-leading drivers in NASCAR were similar to those of the F1 drivers – all of
whom could be considered elite in the sense that the starting field consists of only 20 drivers –
adds some support to this speculation.
How do the three relationships above (i.e., between Practice and Finish, Qualifying and Finish, and Points and Finish) change across races? In general, there were no trends across the racing seasons in the correlations between drivers’
finish positions and their performances in final practice and qualifying, as well as how successful
they were in previous races. This was true for NASCAR and F1 racing. The one exception was
PRACTICE, QUALIFYING, AND PAST SUCCESS IN NASCAR AND F1 20 that the correlations between NASCAR drivers’ finish positions and their points-standing before
a race became somewhat larger as the NASCAR season progressed.
It was interesting to note that the weakest correlations in NASCAR occurred during the
two races at Talladega. During both of these races, NASCAR requires that all cars use restrictor
plates that limit the amount of horsepower the engines can produce. The net effect of using a
restrictor plate is a reduction in the maximum speed that a car can attain, which then results in a
clustering of the cars as they travel around the speedway. Drivers have lamented and columnists
have written about the unpredictability of Talladega races (Caraviello, 2009; McGee, 2009;
Snider, 2009), which may be partly the result of a situation where a driver’s particular skills are
less important. That is, somewhat independent of what a driver does, his car will not go much
faster or slower than any other car. Although races at Daytona also require the use of restrictor
plates, only the first Daytona race was unpredictable. This result may have as much to do with
the use of restrictor plates as it does with Daytona being the first race of the season and its
atypical qualifying sessions (known in 2009 as the Gatorade Duels).
In F1 racing, the presence of wet weather allows us to evaluate the influence of an
uncommon environmental condition on the drivers’ finish positions. If rain is disruptive, we
should observe noticeably lower correlations between Practice and Finish and between
Qualifying and Finish, and perhaps even Points and Finish. The opportunity to evaluate the
influence of rain occurred during the grands prix held in Malaysia and China. At the Malaysian
Grand Prix, the practice and qualifying sessions were conducted in dry weather, but the grand
prix took place in heavy rain. Despite the different conditions in practice and qualifying versus
the grand prix, the correlations between the drivers’ finish positions and their performances in
practice, qualifying, and the previous grand prix were all statistically significant. The results
were different for the grand prix in China, where it also rained during the grand prix but not
during practice or qualifying. At this grand prix, only the correlation between Qualifying and
Finish was statistically significant. Although different from the result in Malaysia, the results
from the Chinese Grand Prix are consistent with the other grands prix in the 2009 season. It
seems that, overall, the relationship between F1 drivers’ performance in practice, qualifying, and
previous races and their finish positions is about the same regardless of whether there were very
different conditions in the practice and qualifying sessions versus the grand prix.
For any particular race, a driver’s performance in practice, qualifying, or previous races,
may be better predictors of his finish position. For example, some racing analysts argue that
qualifying is key at NASCAR’s Dover races because qualifying well gives a driver both a good
starting position and a good pit selection (McReynolds, 2007). This analysis was not supported
by the results from the two Dover races in 2009. For the first race at Dover, the correlations
between Finish and each of Practice, Qualifying, and Points were rs = .58, .49, and .49,
respectively. Practice was a better predictor of Finish than either Qualifying or Points. For the
second race at Dover, the correlations between Finish and each of Practice, Qualifying, and
Points were rs = .49, .59, and .74, respectively. For this race, Points was a better predictor than
either Practice or Qualifying. If we restrict our analysis to the top 20 points-leaders, the only
statistically significant correlation occurred between Points and Finish (rs = .56) in the second
race at Dover.
Similarly, some NASCAR drivers contend that the final practice before a race is critically
important to success (“NASCAR Sprint Cup Series: News and Notes – Lowe’s Motor
Speedway,” 2009). But here, too, the results from 2009 only partially support this contention.
Although Practice was significantly correlated with Finish in many races, the regression
PRACTICE, QUALIFYING, AND PAST SUCCESS IN NASCAR AND F1 21 analyses and contingency table analyses showed that Practice was not as important as Points for
predicting a NASCAR driver’s success. Among the top 20 points-leaders in NASCAR, the
prevailing result was the unpredictability of the drivers’ finishing positions.
What is a more reliable predictor of a driver’s finish position: His performance during practice, his performance during qualifying, his overall success prior to a race, or a combination of these variables? Overall, two different analyses – the visual inspection of the R values from the four regression
models evaluated and the contingency table analyses – showed that the best predictor of a
NASCAR driver’s finish position was his points-standing. For F1 drivers, the best predictor of
their finish position was their performance during qualifying and thus their position at the start of
a grand prix. For the top 20 points-leaders in NASCAR, there was no reliable predictor across
races held in 2009.
One reason for this difference between NASCAR and F1 racing is probably related to
differences in overtaking (i.e., passing another driver) in these two motorsports. Overtaking in
NASCAR is a common occurrence; overtaking in F1 racing is rare. For this reason, lead changes
in NASCAR are more prevalent than lead changes in F1 racing. The relative difficulty of
overtaking in F1 means that a driver’s starting position is likely to have an important influence
on a driver’s finish position (“Hungarian Grand Prix,” 2009). Given the importance of starting
position in F1 racing, it should not surprise us that the most reliable correlation was between a
driver’s performance in qualifying and his finish position. The lack of reliable predictors for the
finish positions of NASCAR’s top 20 points-leaders going into a race is puzzling in light of the
reliable predictors noted for the broader 43-driver field that starts most NASCAR races and the
20-driver field that starts most F1 grands prix. We speculated above that predicting the outcome
of a NASCAR race based on the top 20 points-leaders’ performance in practice, qualifying, or
past races is difficult because what these elite drivers and their teams do during a race may be
what distinguishes the best drivers and teams at any given race. What might tip the scale
towards a better finish position for a top 20 points-leading NASCAR driver and his team during
a race? Any number of variables may be involved: faster pit stops, better mechanical
adjustments to the car, more effective pit strategies (e.g., changing two vs. four tires), more
effective communication between a driver and his crew chief, the superiority of a driver’s
physical fitness in a demanding race, the superiority of a driver’s ability to concentrate in
different circumstances, a better fit between the demands of race and a driver’s skills, a greater
willingness on the part of a driver to incur risks to produce faster laps times or overtake other
cars, and the like.
What factors are related to the predictability of a driver’s finish position from his performance in practice, qualifying, and his success up to that point in the season? For the 43 drivers who normally start a NASCAR race, the results showed that an increase in
lead changes, but not cautions, was correlated with an increase in the difficulty of predicting a
driver’s finish position from his performance during practice, qualifying, and previous races.
This result was similar for the top 20 points-leaders in NASCAR. However, for F1 drivers, there
was no relationship between lead changes and the predictability of the finish positions from
PRACTICE, QUALIFYING, AND PAST SUCCESS IN NASCAR AND F1 22 drivers’ performances during practice, qualifying, or how they had performed up to that point in
the racing season.
Intuitively, this result makes sense. By definition, an increase in lead changes means that
drivers in the lead are having a difficult time maintaining their position. As variability (of
position) increases, predictability (of finish) decreases. This effect was absent in F1 racing
because there are many fewer lead changes than in NASCAR.
That cautions were unrelated to the predictability of finish position from practice,
qualifying, or past success is puzzling. Cautions lead to restarts in which all of the cars are lined
up close together. One might think that restarts would cause lead changes because the gaps
(distances) between cars are minimized during a restart. Given that there are as many restarts as
there are cautions, one might expect a correlation between the number of cautions and the
number of lead changes, and yet no such relationship occurred in the 2009 NASCAR season.
Conclusions We began this paper with a summary of some key physical differences between NASCAR and
F1 racing (see Table 1). We can now create a new table of performance differences based on the
results of the analyses of the 2009 races. As shown in Table 4, the most significant difference
between these two forms of racing is that the finish positions in NASCAR are related to more
variables than the finish positions in F1 racing. NASCAR drivers’ performances in practice,
qualifying, and past races were usually positively correlated with their finish positions. In F1
racing, only drivers’ performances during qualifying and, to a lesser extent, in past races were
positively correlated with their finish positions. Surprising (at least to us), there was rarely a
significant correlation between the finish positions of the best NASCAR drivers and their
performances in practice, qualifying, or previous races. Predicting these drivers’ finish positions
from any combination of their performances in practice, qualifying, or previous races was
usually unsuccessful. It seems that in NASCAR, the best drivers predictably win a race, but who
among these drivers will win is not predictable from how they performed in practice, qualifying,
or in previous races. It remains for future research to identify and study variables associated
with these elite drivers’ finish positions and to identify what makes their performances different
from those of drivers in F1 racing.
PRACTICE, QUALIFYING, AND PAST SUCCESS IN NASCAR AND F1 23 Table 4
Performance Variables: Similarities and Differences Between NASCAR and F1 in 2009
Characteristic
Drivers
NASCAR
F1
NASCAR (Top 20)
Finish position generally
correlated with practice
performance
Yes, 81% of races
No, 41% of grands prix
No, 22% of races
Finish position generally
correlated with qualifying
performance/starting position
Yes, 75% of races
Yes, 82% of grands prix
No, 28% of races
Finish position generally
correlated with overall
success in season
Yes, 86% of races
Somewhat, 59% of grands
prix
No, 19% of races
Best overall predictor(s) of
finish position
Points-standing before a
race
Qualifying performance
(starting position)
None of the performance
variables studied
Relationship between lead
changes and predictability of
finish position
↑ lead changes, ↓
predictability
None based on performance
variables studied
↑ lead changes, ↓
predictability based on
practice performance and
overall success in season
Relationship between
cautions and predictability of
finish position
None based on
performance variables
studied
(Data not available)
None based on
performance variables
studied
Changes in correlations
across season
Slight increase in
correlation between Finish
and Points
Transitory increase in
correlation between Finish
and Practice
None based on
performance variables
studied
References Aliaga, M., & Gunderson, B. (2006). Interactive statistics (3rd ed.). Upper Saddle River, NJ: Prentice Hall.
Allender, M. (2008). Predicting the outcome of NASCAR races: The role of driver experience. Journal of
Business & Economic Research, 6, 79-84.
Blount, T. (2009. March 31). F1, Cup made for wildly different day. ESPN.com. Retrieved from
cvchttp://sports.espn.go.com/rpm/nascar/cup/columns/story?columnist=blount_terry&id=4029638
Caraviello, D. (2009, November 4). Like an unwelcome journey into NASCAR’s difficult past. NASCAR.com.
Retrieved from
http://www.nascar.com/2009/news/opinion/11/04/inside.line.dcaraviello.talladega.past/index.html
Collantine, K. (2006, July 22). F1 vs NASCAR [Web log post]. Retrieved from
http://www.f1fanatic.co.uk/2006/07/22/f1-vs-nascar
Graves, T., Reese, C. S., & Fitzgerald, M. (2003). Hierarchical models for permutations: Analysis of auto racing
results. Journal of the American Statistical Association, 98, 282-291.
Hook, N. (2010, June 12). NASCAR vs. Formula One. Examiner.com. Retrieved from
http://www.examiner.com/x-4026-Minneapolis-Autos-Examiner~y2009m6d12-NASCAR-vs-Formula-One
Hungarian Grand Prix – Team and Driver Preview Quotes (2009, July 21). Formula1.com. Retrieved from
http://www.formula1.com/news/headlines/2009/7/9631.html
Kazdin, A. E. (1982). Single-case research designs: Methods for clinical and applied settings. New York: Oxford
University Press.
Keith, T. Z. (2006). Multiple regression and beyond. Boston, MA: Allyn and Bacon.
PRACTICE, QUALIFYING, AND PAST SUCCESS IN NASCAR AND F1 24 McGee, R. (2009, October 30). A Talladega twist of fate. ESPN.com. Retrieved from
http://insider.espn.go.com/espn/blog/index?entryID=4608684&name=mcgee_ryan&action=login&appRedi
rect=http%3a%2f%2finsider.espn.go.com%2fespn%2fblog%2findex%3fentryID%3d4608684%26name%3
dmcgee_ryan
McReynolds, L. (2007, September 21). Mac Track: Past can’t predict future success. msn.foxsports.com. Retrieved
from http://foxsports.foxnews.com/nascar/story/7243656/Mac-Track:-Past-can't-predict-future-success
NASCAR’s Jeff Gordon on Formula One Racing (2004, June 17). Formula1.com. Retrieved from
http://www.formula1.com/news/features/2004/6/1745.html
NASCAR Sprint Cup Series: News and Notes – Lowe’s Motor Speedway (2009, October 14). Retrieved from
http://www.autoracingdaily.com/news/nascar-sprint-cup-series/nascar-sprint-cup-series-news-notes-lowesmotor-speedway1
Pear, J. J. (2001). The science of learning. Philadelphia, PA: Psychology Press.
Pfitzner, B., & Rishel, T. (2005). Do reliable predictors exist for the outcomes of NASCAR races? The Sport
Journal, 8(2). Retrieved from http://www.thesportjournal.org/article/do-reliable-predictors-existoutcomes-nascar-races
Snider, M. (2009, October 30). Chasers have a lot on their plate as Talladega calls. NASCAR.com. Retrieved from
http://www.nascar.com/2009/news/features/10/30/chase.tiering.talladega/index.html
Younger, M. S. (1985). A first course in linear regression (2nd ed.). Boston, MA: Duxbury Press.
PRACTICE, QUALIFYING, AND PAST SUCCESS IN NASCAR AND F1 25 Appendix A Spearman rs (and their p values) used to construct Figure 1
Race
Variables
Finish and Practice
Spearman's rs
Daytona
Fontana
Las Vegas
Atlanta
Bristol
Martinsville
Texas
Phoenix
Talladega
Richmond
Darlington
Charlotte
Dover
Pocono
Michigan
Sonoma
New Hampshire
*Daytona
Chicago
Indianapolis
*Pocono
Watkins Glen
*Michigan
*Bristol
*Atlanta
*Richmond
*New Hampshire
*Dover
Kansas
*Fontana
*Charlotte
*Martinsville
*Talladega
*Texas
*Phoenix
Homestead
0.119
0.557
0.328
0.499
0.469
0.560
0.402
0.627
-0.013
0.402
0.164
0.613
0.580
0.498
0.640
0.426
0.450
0.236
0.614
0.588
0.711
0.516
0.349
0.431
0.105
0.460
0.596
0.485
0.471
0.443
0.510
0.443
0.127
0.168
0.614
0.589
p
0.447
0.000
0.031
0.000
0.001
0.000
0.007
0.000
0.931
0.007
0.292
0.000
0.000
0.000
0.000
0.004
0.002
0.126
0.000
0.000
0.000
0.000
0.021
0.003
0.504
0.001
0.000
0.000
0.001
0.002
0.000
0.020
0.414
0.280
0.000
0.000
Finish and Qualifying
Spearman's rs
-0.085
0.489
0.270
0.392
0.187
0.645
0.549
0.529
0.084
0.320
0.280
0.460
0.493
0.688
0.450
0.476
0.607
0.557
0.456
0.549
0.783
0.514
0.322
0.300
0.398
0.591
0.460
0.592
0.191
0.397
0.568
0.467
0.215
0.259
0.594
0.353
p
0.587
0.000
0.080
0.009
0.231
0.000
0.000
0.000
0.590
0.036
0.069
0.001
0.000
0.000
0.002
0.001
0.000
0.000
0.002
0.000
0.000
0.000
0.034
0.050
0.008
0.000
0.001
0.000
0.220
0.008
0.000
0.001
0.165
0.092
0.000
0.020
Note. The degrees of freedom for all races was 41, except for Pocono (df= 40)
The * denotes that drivers had raced at that track earlier in the season.
Finish and Points
Spearman's rs
0.263
0.299
0.131
0.585
0.488
0.645
0.595
0.622
-0.137
0.597
0.407
0.423
0.488
0.692
0.693
0.475
0.586
0.577
0.722
0.633
0.783
0.558
0.477
0.602
0.503
0.809
0.756
0.794
0.665
0.630
0.452
0.801
0.221
0.528
0.754
0.651
p
0.087
0.051
0.401
0.000
0.000
0.000
0.000
0.000
0.381
0.000
0.006
0.004
0.000
0.000
0.000
0.001
0.000
0.000
0.000
0.000
0.000
0.000
0.001
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.002
0.000
0.152
0.000
0.000
0.000
PRACTICE, QUALIFYING, AND PAST SUCCESS IN NASCAR AND F1 26 Appendix B Spearman rs (and their p values) used to construct Figure 3
Grand Prix
Variables
Finish and Practice
Spearman's rs
Australia
Malaysia
China
Bahrain
Spain
Monaco
Turkey
Great Britain
Germany
Hungary
Europe
Belgium
Italy
Singapore
Japan
Brazil
Abu Dhabi
0.300
0.427
-0.260
0.130
0.251
0.515
0.523
0.654
0.320
0.496
0.281
0.067
0.529
0.505
0.349
-0.515
0.425
p
0.197
0.060
0.267
0.582
0.285
0.019
0.017
0.001
0.168
0.030
0.229
0.776
0.016
0.023
0.142
0.019
0.061
Finish and Qualifying
Spearman's rs
0.087
0.630
0.514
0.739
0.804
0.476
0.730
0.830
0.452
0.370
0.720
0.621
0.524
0.715
0.849
-0.007
0.628
p
0.714
0.002
0.020
0.000
0.000
0.030
0.000
0.000
0.045
0.118
0.000
0.003
0.017
0.000
0.000
0.974
0.002
Finish and Points
Spearman's rs
-0.440
0.558
0.288
0.665
0.558
0.424
0.577
0.695
0.595
0.334
0.474
0.162
0.366
0.459
0.658
0.390
0.566
Note. The degrees of freedom for all races was 18 except for Hungary (df= 16) and Japan (df = 17).
p
0.051
0.010
0.216
0.001
0.010
0.062
0.007
0.000
0.005
0.175
0.034
0.494
0.111
0.041
0.002
0.088
0.009
PRACTICE, QUALIFYING, AND PAST SUCCESS IN NASCAR AND F1 27 Appendix C Spearman rs (and their p values) used to construct Figure 5
Race
Variables
Finish and Practice
Spearman's rs
Daytona
Fontana
Las Vegas
Atlanta
Bristol
Martinsville
Texas
Phoenix
Talladega
Richmond
Darlington
Charlotte
Dover
Pocono
Michigan
Sonoma
New Hampshire
*Daytona
Chicago
Indianapolis
*Pocono
Watkins Glen
*Michigan
*Bristol
*Atlanta
*Richmond
*New Hampshire
*Dover
Kansas
*Fontana
*Charlotte
*Martinsville
*Talladega
*Texas
*Phoenix
Homestead
0.067
0.514
0.544
0.369
0.386
0.630
0.333
0.460
-0.048
-0.144
0.186
0.517
0.285
-0.031
0.323
0.209
0.530
-0.239
0.219
0.192
0.428
0.615
0.033
0.254
-0.052
0.261
0.694
0.377
-0.040
0.287
0.183
0.261
0.021
0.046
0.204
0.156
p
0.776
0.020
0.013
0.108
0.092
0.002
0.150
0.041
0.840
0.543
0.431
0.019
0.222
0.894
0.164
0.376
0.016
0.309
0.352
0.416
0.059
0.003
0.889
0.279
0.825
0.265
0.000
0.100
0.865
0.219
0.438
0.265
0.929
0.845
0.387
0.510
Finish and Qualifying
Spearman's rs
-0.255
0.392
0.478
0.187
0.073
0.350
0.569
0.578
0.069
0.272
0.172
0.467
0.269
0.209
-0.070
0.362
0.547
0.535
0.431
0.541
0.436
0.326
-0.115
0.230
0.081
0.699
0.449
0.204
0.395
0.317
0.550
0.335
-0.240
0.021
0.293
-0.141
Note. The degrees of freedom for all races was 18.
The * denotes that drivers had raced at that track earlier in the season.
p
0.276
0.086
0.032
0.427
0.757
0.129
0.008
0.007
0.771
0.245
0.465
0.037
0.251
0.376
0.767
0.116
0.012
0.014
0.057
0.013
0.054
0.160
0.626
0.329
0.733
0.006
0.046
0.387
0.084
0.172
0.011
0.148
0.306
0.929
0.209
0.552
Finish and Points
Spearman's rs
0.192
-0.073
0.018
0.230
0.242
0.350
0.470
0.285
-0.279
0.169
0.374
0.001
-0.010
0.209
0.269
0.031
0.547
0.535
0.294
0.204
0.436
0.279
-0.022
-0.103
0.067
0.436
0.434
0.555
0.559
0.500
-0.126
0.493
-0.240
0.043
0.390
0.299
p
0.416
0.757
0.939
0.328
0.302
0.129
0.036
0.222
0.232
0.475
0.103
0.994
0.964
0.376
0.251
0.894
0.012
0.014
0.207
0.387
0.054
0.232
0.924
0.663
0.776
0.054
0.055
0.010
0.010
0.024
0.595
0.027
0.306
0.855
0.088
0.199
PRACTICE, QUALIFYING, AND PAST SUCCESS IN NASCAR AND F1 28 Appendix D R values (and their related F statistics and p values) used to construct Figure 9
Race
Model
Finish = α + β1Practice + β2Qualifying
Daytona
Fontana
Las Vegas
Atlanta
Bristol
Martinsville
Texas
Phoenix
Talladega
Richmond
Darlington
Charlotte
Dover
Pocono
Michigan
Sonoma
New Hampshire
*Daytona
Chicago
Indianapolis
*Pocono
Watkins Glen
*Michigan
*Bristol
*Atlanta
*Richmond
*New Hampshire
*Dover
Kansas
*Fontana
*Charlotte
*Martinsville
*Talladega
*Texas
*Phoenix
Homestead
Finish = α + β1Practice + β2Points
R
F
p
R
F
0.169
0.609
0.359
0.537
0.478
0.720
0.591
0.642
0.084
0.404
0.289
0.652
0.626
0.691
0.706
0.576
0.623
0.569
0.624
0.638
0.823
0.586
0.383
0.440
0.398
0.595
0.602
0.599
0.477
0.494
0.585
0.508
0.219
0.273
0.674
0.590
0.589
11.817
2.963
8.120
5.929
21.572
10.735
14.055
0.144
3.921
1.825
14.854
12.932
17.829
19.934
9.941
12.689
9.580
12.762
13.763
42.177
10.463
3.453
4.818
3.779
10.968
11.404
11.235
5.893
6.490
10.448
6.989
1.016
1.612
16.701
10.725
0.559
0.000
0.063
0.001
0.005
0.000
0.000
0.000
0.866
0.027
0.174
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.041
0.013
0.031
0.000
0.000
0.000
0.005
0.003
0.000
0.000
0.371
0.212
0.000
0.000
0.293
0.594
0.332
0.658
0.591
0.741
0.575
0.719
0.135
0.654
0.432
0.650
0.609
0.699
0.743
0.557
0.594
0.579
0.738
0.667
0.812
0.621
0.528
0.629
0.567
0.798
0.740
0.797
0.652
0.617
0.526
0.772
0.219
0.472
0.725
0.697
1.883
10.943
2.485
15.275
10.779
24.496
9.882
21.429
0.374
14.954
4.614
14.654
11.848
18.649
24.775
9.014
10.908
10.117
24.030
16.089
38.863
12.614
7.734
13.130
9.492
35.141
24.339
34.917
14.792
12.323
7.689
29.671
1.016
5.734
22.241
18.917
p
0.165
0.000
0.096
0.000
0.000
0.000
0.000
0.000
0.690
0.000
0.015
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.001
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.001
0.000
0.371
0.006
0.000
0.000
PRACTICE, QUALIFYING, AND PAST SUCCESS IN NASCAR AND F1 29 Appendix D (continued) Race
Model
Finish = α + β1Qualifying + β2Points
Daytona
Fontana
Las Vegas
Atlanta
Bristol
Martinsville
Texas
Phoenix
Talladega
Richmond
Darlington
Charlotte
Dover
Pocono
Michigan
Sonoma
New Hampshire
*Daytona
Chicago
Indianapolis
*Pocono
Watkins Glen
*Michigan
*Bristol
*Atlanta
*Richmond
*New Hampshire
*Dover
Kansas
*Fontana
*Charlotte
*Martinsville
*Talladega
*Texas
*Phoenix
Homestead
R
F
p
0.337
0.532
0.305
0.650
0.578
0.687
0.630
0.676
0.162
0.655
0.430
0.580
0.552
0.708
0.681
0.527
0.607
0.565
0.762
0.711
0.796
0.642
0.518
0.631
0.566
0.814
0.736
0.796
0.652
0.625
0.575
0.776
0.217
0.478
0.717
0.628
2.573
7.902
2.058
14.656
10.044
17.944
13.211
16.876
0.542
15.044
4.540
10.179
8.785
19.703
17.347
7.704
11.672
9.427
27.735
20.450
34.635
14.052
7.344
13.255
9.432
39.286
23.777
34.720
14.812
12.857
9.913
30.424
0.997
5.943
21.214
13.051
0.008
0.001
0.141
0.000
0.002
0.000
0.000
0.000
0.586
0.000
0.016
0.000
0.000
0.000
0.000
0.001
0.000
0.000
0.000
0.000
0.000
0.000
0.001
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.377
0.005
0.000
0.000
Finish = α + β1Practice + β2Qualifying + β3Points
R
F
0.342
0.631
0.364
0.671
0.608
0.742
0.635
0.719
0.166
0.655
0.514
0.681
0.638
0.716
0.754
0.616
0.623
0.586
0.762
0.712
0.826
0.667
0.532
0.643
0.567
0.818
0.741
0.798
0.652
0.631
0.589
0.779
0.222
0.478
0.736
0.697
p
1.726
8.606
1.994
10.676
7.627
15.926
8.818
13.974
0.372
7.153
3.427
11.296
8.962
9.741
17.131
7.952
8.249
6.821
18.047
13.371
28.086
10.443
5.137
9.187
6.170
26.336
15.852
22.948
9.629
8.605
6.923
20.101
0.678
3.864
15.377
12.308
0.177
0.000
0.130
0.000
0.000
0.000
0.000
0.000
0.733
0.000
0.017
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.004
0.000
0.001
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.570
0.016
0.000
0.000
Note. The degrees of freedom for the two- and three-variable models were (2, 40) and (3, 39), respectively,
for all races except Pocono (df = 2, 39 and 3, 38). The * denotes that drivers had raced at that track earlier in the
season.
PRACTICE, QUALIFYING, AND PAST SUCCESS IN NASCAR AND F1 30 Appendix E R values (and their related F statistics and p values) used to construct Figure 8
Grand Prix
Model
Finish = α + β1Practice + β2Qualifying
Australia
Malaysia
China
Bahrain
Spain
Monaco
Turkey
Great Britain
Germany
Hungary
Europe
Belgium
Italy
Singapore
Japan
Brazil
Abu Dhabi
Finish = α + β1Practice + β2Points
R
F
p
R
F
0.300
0.630
0.635
0.789
0.810
0.536
0.749
0.837
0.478
0.501
0.741
0.660
0.587
0.718
0.866
0.542
0.633
0.845
5.597
5.773
14.108
16.231
3.432
10.881
20.019
2.524
2.523
10.441
6.574
4.490
9.053
24.111
3.551
5.702
0.446
0.013
0.012
0.000
0.000
0.055
0.000
0.000
0.109
0.113
0.001
0.007
0.027
0.002
0.000
0.051
0.012
0.579
0.681
0.418
0.730
0.589
0.572
0.612
0.809
0.608
0.523
0.467
0.103
0.612
0.575
0.576
0.707
0.623
4.308
7.353
1.804
9.705
4.538
4.147
5.113
16.159
5.003
2.826
2.380
0.091
5.102
4.210
3.986
8.522
5.407
p
0.030
0.005
0.194
0.001
0.026
0.034
0.018
0.000
0.019
0.090
0.122
0.913
0.018
0.032
0.039
0.002
0.015
PRACTICE, QUALIFYING, AND PAST SUCCESS IN NASCAR AND F1 31 Appendix E (continued) Grand Prix
Model
Finish = α + β1Qualifying + β2Points
Australia
Malaysia
China
Bahrain
Spain
Monaco
Turkey
Great Britain
Germany
Hungary
Europe
Belgium
Italy
Singapore
Japan
Brazil
Abu Dhabi
R
F
p
0.523
0.694
0.523
0.801
0.805
0.538
0.740
0.839
0.603
0.320
0.730
0.626
0.547
0.721
0.879
0.447
0.662
3.217
7.925
3.203
15.234
15.690
3.467
10.331
20.265
4.863
0.859
9.700
5.478
3.643
9.254
27.418
2.127
6.664
0.065
0.003
0.066
0.000
0.000
0.054
0.001
0.000
0.021
0.443
0.001
0.014
0.048
0.001
0.000
0.149
0.007
Finish = α + β1Practice + β2Qualifying + β3Points
R
F
0.583
0.702
0.651
0.805
0.811
0.579
0.755
0.855
0.613
0.529
0.745
0.685
0.626
0.724
0.896
0.713
0.664
p
2.755
5.183
3.937
9.882
10.289
2.701
7.087
14.518
3.222
1.822
6.653
4.724
3.452
5.889
20.498
5.516
4.226
0.076
0.010
0.027
0.000
0.000
0.080
0.003
0.000
0.051
0.189
0.003
0.015
0.041
0.006
0.000
0.008
0.022
Note. The degrees of freedom for the two- and three-variable models were (2, 17) and (3, 16), respectively,
for all grands prix except Hungary (df = 2, 15 and 3 ,14) and Japan (df = 2, 16 and 3, 15).
PRACTICE, QUALIFYING, AND PAST SUCCESS IN NASCAR AND F1 32 Appendix F R values (and their related F statistics and p values) used to construct Figure 9
Race
Model
Finish = α + β1Practice + β2Qualifying
Daytona
Fontana
Las Vegas
Atlanta
Bristol
Martinsville
Texas
Phoenix
Talladega
Richmond
Darlington
Charlotte
Dover
Pocono
Michigan
Sonoma
New Hampshire
*Daytona
Chicago
Indianapolis
*Pocono
Watkins Glen
*Michigan
*Bristol
*Atlanta
*Richmond
*New Hampshire
*Dover
Kansas
*Fontana
*Charlotte
*Martinsville
*Talladega
*Texas
*Phoenix
Homestead
Finish = α + β1Practice + β2Points
R
F
p
R
F
0.273
0.460
0.547
0.421
0.306
0.639
0.597
0.587
0.085
0.513
0.317
0.596
0.427
0.241
0.396
0.466
0.672
0.504
0.462
0.465
0.552
0.544
0.145
0.259
0.105
0.736
0.541
0.156
0.543
0.330
0.418
0.308
0.204
0.113
0.191
0.273
0.689
2.283
3.641
1.840
0.883
5.879
4.726
4.479
0.063
3.036
0.952
4.706
1.902
0.528
1.589
2.362
7.024
2.909
2.319
2.356
3.740
3.582
0.184
0.611
0.095
10.058
3.532
0.213
3.562
1.040
1.800
0.894
0.371
0.111
0.322
0.689
0.515
0.132
0.048
0.189
0.432
0.011
0.023
0.027
0.939
0.074
0.405
0.023
0.179
0.599
0.232
0.124
0.005
0.081
0.128
0.125
0.045
0.050
0.833
0.554
0.909
0.001
0.052
0.810
0.057
0.375
0.195
0.427
0.695
0.895
0.729
0.515
0.196
0.435
0.544
0.336
0.351
0.640
0.532
0.463
0.288
0.242
0.555
0.433
0.415
0.292
0.539
0.352
0.680
0.443
0.334
0.244
0.541
0.524
0.066
0.230
0.160
0.445
0.544
0.551
0.564
0.271
0.400
0.342
0.134
0.206
0.108
0.205
0.340
1.990
3.573
1.085
1.195
5.903
3.359
2.320
0.769
0.532
3.788
1.965
1.777
0.795
3.491
1.205
7.314
2.082
1.074
0.540
3.527
3.219
0.038
0.477
0.225
2.103
3.583
3.721
3.967
0.679
1.620
1.131
0.158
0.378
0.101
0.375
p
0.716
0.167
0.050
0.360
0.326
0.011
0.058
0.128
0.478
0.597
0.043
0.170
0.199
0.467
0.053
0.324
0.005
0.155
0.363
0.592
0.052
0.065
0.962
0.628
0.800
0.152
0.050
0.045
0.038
0.520
0.227
0.345
0.855
0.690
0.904
0.692
PRACTICE, QUALIFYING, AND PAST SUCCESS IN NASCAR AND F1 33 Appendix F (continued) R values (and their related F statistics and p values) used to construct Figure 9
Race
Model
Finish = α + β1Practice + β2Qualifying
R
F
p
Finish = α + β1Practice + β2Points
R
F
p
Daytona
0.338
1.102
0.354
0.338
0.692
0.570
Fontana
0.345
1.153
0.339
0.460
1.433
0.270
Las Vegas
0.434
1.981
0.168
0.578
2.681
0.081
Atlanta
0.390
1.532
0.244
0.447
1.339
0.296
Bristol
0.275
0.697
0.511
0.351
0.754
0.536
Martinsville
0.343
1.134
0.344
0.640
3.704
0.033
Texas
0.633
5.703
0.012
0.655
4.021
0.026
Phoenix
0.577
4.246
0.031
0.589
2.846
0.070
Talladega
0.287
0.767
0.479
0.288
0.483
0.699
Richmond
0.302
0.857
0.442
0.530
2.087
0.142
Darlington
0.475
2.479
0.113
0.535
2.378
0.108
Charlotte
0.494
2.749
0.092
0.597
2.968
0.063
Dover
0.359
1.261
0.308
0.447
1.332
0.298
Pocono
0.360
1.271
0.305
0.384
0.927
0.450
Michigan
0.350
1.189
0.328
0.552
2.341
0.111
Sonoma
0.430
1.939
0.174
0.476
1.564
0.236
New Hampshire
0.549
3.680
0.047
0.680
4.591
0.016
*Daytona
0.519
3.134
0.069
0.543
2.238
0.123
Chicago
0.536
3.431
0.056
0.543
2.232
0.123
Indianapolis
0.527
3.285
0.062
0.528
2.067
0.144
*Pocono
0.493
2.737
0.093
0.552
2.347
0.111
Watkins Glen
0.425
1.879
0.183
0.544
2.253
0.121
*Michigan
0.159
0.221
0.803
0.159
0.139
0.935
*Bristol
0.242
0.532
0.597
0.278
0.448
0.722
*Atlanta
0.146
0.187
0.830
0.163
0.147
0.930
*Richmond
0.749
10.875
0.000
0.753
7.001
0.003
*New Hampshire
0.382
1.457
0.260
0.548
2.299
0.116
*Dover
0.573
4.166
0.033
0.583
2.750
0.076
Kansas
0.461
2.301
0.130
0.678
4.545
0.017
*Fontana
0.325
1.005
0.386
0.355
0.772
0.526
*Charlotte
0.626
5.489
0.014
0.643
3.771
0.031
*Martinsville
0.401
1.633
0.224
0.404
1.043
0.400
*Talladega
0.248
0.559
0.581
0.253
0.366
0.778
*Texas
0.203
0.366
0.699
0.206
0.237
0.868
*Phoenix
0.177
0.277
0.761
0.191
0.203
0.892
Homestead
0.266
0.651
0.534
0.363
0.812
0.505
Note. The degrees of freedom for the two- and three-variable models were (2, 17) and (3, 16), respectively,
for all races. The * denotes that drivers had raced at that track earlier in the season.