An Evaluation of
Performance Figures (PFs) vs Beyer Speed Figures (BSFs)
in the 2001 Kentucky Derby

This study was undertaken to compare Beyer Speed Figures (BSFs) and Performance Figures (PFs) in the context of the 2001 Kentucky Derby.  For those unfamiliar with speed figure technology, both BSFs and PFs convert the raw time of a race into a mathematically derived number taking into account variations in inherent track speed.  Ideally, the resulting numbers may be used to compare levels of performance from race to race, track to track and horse to horse regardless of how fast or slow a track plays on a particular day and independently of characteristics unique to the surface.

The two approaches differ mainly in that BSFs are based only on the final time of a race while PFs are based on an integration of final time and fractional time.  In other words, PFs incorporate a significant pace factor while BSFs do not.  The general methodologies are similar to the extent that both use variants from an expected level of performance to fine tune the raw numbers.  These variants from the norm may be derived by comparison with par values for the class of race or, in the case of BSFs, projecting an expected figure based on the past history of an individual horse.

The two approaches also differ in that the higher the BSF the better, while the more negative the PF the better.

The races included in the study are all the graded prep races in 2001 contested by each Derby starter, excluding Express Star, which did not race in North America.  One other major prep was added as well – the listed Lone Star Derby.

Table 1 displays the PFs and BSFs for the sixteen three-year-olds in each of their prep races plus the Kentucky Derby.  There are no Derby numbers for Talk Is Money since he did not finish the race.  The figures are listed in post-position order by name of horse and include the race as well as the PF and BSF assigned to the horse in that race.  The pre-Derby BSFs are those published by Daily Racing Form, Inc.  The Derby BSFs are based on the assigned value to the winner of BSF 116.  We calculated Derby BSFs for the other horses by adjusting the winner's figure according to the beaten lengths formula in "Beyer on Speed", by Andrew Beyer, Houghton Mifflin Company, Boston and New York, 1993.

Table 1. 2001 Kentucky Derby and Graded Prep Race PFs and BSFs

We used the data first to perform a direct comparison by plotting the BSF vs. the PF for each of 47 races assigned a figure in Table 1.  The results are shown in Chart 1.

Chart 1.  Comparison of BSFs vs. PFs

The correlation is linear and quite good.   The R² value is 0.866, equivalent to a correlation coefficient of 0.931.  The general relationship between PFs and BSFs is expressed by the equation: 

BSF = -0.3531 x PF + 84.48. 

Thus, when PF = 0, BSF = 84.48.  As we might expect from a strong correlation, these two values do in fact represent essentially the same level of performance.  PFs around 0 are par for a $10,000 older male claimer at many tracks as are BSFs between 83 and 85. 

Having established the strength of the correlation between BSFs and PFs, we next examined the Derby prep races to see if relative performance in the preps correlates with relative performance in the Derby.  Table 2 lists the horses in order of decreasing best BSF in a prep race, also showing the horse's finish  in the Derby.  BSF Rank refers to the relative position of the horse's best BSF among all the horses.  For example,  Millennium Wind's BSF 114 in the Blue Grass Stakes was tops among all the horses while Arctic Boy's BSF 101 was 10th best.   The Table presents similar data for the best PF.   There are obvious differences between the two systems.  In the PF case, Millennium Wind's PF -65 was 5th best while Arctic Boy's PF -56 ranked 8th.

Table 2.  Best BSFs and PFs in Derby Prep Races Ranked From Best to Worst

An immediate difference may be seen in the top quartiles by speed figure rank.  The horses with the top four best BSFs finished 11th, 14th, 16th and 5th in the Derby - for an average of 11.5.  Those with the top four best PFs finished 3rd, 4th, 1st and 14th - for an average of 5.5.

Plotting the best BSF or best PF vs. order of finish for the field affords Charts 2 and 3, respectively.  Not unexpectedly, there is significant scatter as reflected in the low R-squared values of the best straight lines derived by linear regression.  Even so, the PF-Finish plot has a higher R-squared value, indicating a better correlation.  However, it is the slope of the line that is relevant here.  In the case of BSFs, the slope is negative, representing an inverse correlation between best BSF and order of finish.  On the other hand, the correlation between best PF and order of finish is positive.  In other words, the relationship between pre-Derby speed figures and actual Derby performance is much stronger for PFs than it is for BSFs.

Chart 2.  Best Derby Prep Race BSF vs. Derby Finish

Chart 3.  Best Derby Prep Race PF vs. Derby Finish

Table 2 and Charts 3 and 4 are similar to those for the best BSFs and PFs, except this time we are looking at the the figures for the last prep race immediately before the Derby.  The results are identical to those found with the "best" figures.  The upper quartile of last BSFs corresponds to an average Derby finishing position of 11.5 while the upper quartile of last PFs corresponds to an average Derby finishing position of 5.5.   The R-squared values are again low but better for the PFs.  And finally, the BSF vs. Derby finish trend line indicates a negative correlation while that for the PF vs. Derby finish is again positive.

Table 2.  Last BSFs and PFs in Derby Prep Races Ranked From Best to Worst

Chart 4.  Last Derby Prep Race BSF vs. Derby Finish

Chart 5.  Last Derby Prep Race PF vs. Derby Finish

No general conclusions about the value of BSFs or PFs should be drawn from these singular results.  BSFs have stood the test of time.  They are certainly a profound improvement over raw time as a measure of performance.  Nevertheless, the results do suggest that other approaches may be at least as accurate and equally useful. 

More information about PFs may be found here.