GRF NASCAR Web Site
ATTRITION MODEL RANKINGS OF NASCAR DRIVERS
On this site we present rankings of NASCAR drivers, for each of the
Winston Cup, Busch Grand National, and Craftsman Truck series. We will
add historical rankings as we have time to develop them. These
rankings are based on a Bayesian hierarchical modeling approach,
discussed in a paper submitted to the Journal of the American
Statistical Association and available here. The rankings depend only
on finishing positions in the races of the current season; we do not
award bonuses for leading laps, qualifying well, or any other reason.
One of the pleasing properties of our ranking method is that it
emphasizes very good finishes and especially wins, and does not punish
very poor finishes as strongly as does the official NASCAR points
system. (The best of example of this through ten Winston Cup races in
2002 is Rusty Wallace, who has not finished worse than 18th, but
neither does he have a top 5 finish. He is fourth in the official
NASCAR standings but only tenth for us.) It is also possible to use
our results to generate simulated races and seasons. This can be used
to provide well-defined measures of how much better certain drivers
have been than others. Note that our system is not a "points system":
in particular, drivers do not have to participate in all the races to
attain a high rating, although it helps. For those who find this
distasteful, it is also possible to rank the drivers according to our
'SimPts' (simulated points) column.
For more on Bayesian statistics, see, for example, Gelman et al....
We obtain the race results from NASCAR's web site, www.nascar.com,
and do not profit from these rankings.
- Prev: rank of the driver before the most recent race. 'NA' means that
the driver was unranked (because the most recent race was his or
her first race of the year).
- Rank: rank of the driver after the most recent race.
- Driver: name of the driver.
- Mean: Posterior mean of the attrition model ability parameter. Drivers
with higher values in this column are estimated to be better.
- SD: Posterior standard deviation of the ability parameter. A lower
in this column means that we are more certain about the value of
the driver's ability parameter.
- Races, Wins, Top5, Top10: numbers of races, wins, top 5 finishes, and
top 10 finishes for the driver
- AvgFinish: average finishing position for the driver
- SDFinish: standard deviation of the driver's finishing positions
- Finishes: list of the driver's finishing positions in order
- Points: driver points according to the NASCAR points system. Our
total will sometimes differ from the official NASCAR standings,
because we most often use unofficial points as of the end of
the race, before they are updated to include penalties, post
- SimPts: Average number of points attained by the driver in 1000
seasons using our attrition model. If you dislike the fact
that drivers with few races can attain high rankings, this
column can be used to rank drivers and avoid this problem.
You can also compare Points to SimPts to see if drivers have
been relatively lucky (with respect to the points system).
- SimWins: Average number of wins by the driver in the same 1000
- SimChamps: Number of times out of the 1000 simulated seasons that the
driver emerged with the simulated points lead.
- Graves, T.L., Reese, C.S., and Fitzgerald, M. (2003) "Hierarchical Models for Permutations: Analysis of Auto Racing Results", to appear in the Journal of the American Statistical Association.
- Graves, T.L., Reese, C.S., and Fitzgerald, M. (2002) "Hierarchical Models for Permutations: Analysis of Auto Racing Results", A slightly longer version with more technical details.
- The Data which the paper was based on. They consist of all race results for the Busch Series and the Winston Cup for 1996-2000. A description of the fields is included with the data.
C. Shane Reese
Department of Statistics
Brigham Young University