As part of BPR F1’s ongoing season wrap-up, I thought that reviewing the correlation between the BPR POWER rating and the actual on-track results during the 2010 Formula 1 season would be a worthwhile exercise.
For the less mathematically-inclined, correlation is a study of the relationship between two sets of variables (a good, brief explanation of correlation can be found here). In evaluating the POWER rating’s relationship to on-track results, I used one of the most common methods of displaying correlation: a correlation coefficient. A correlation coefficient ranges from -1.0 to +1.0. The closer the coefficient is to +1 or -1, the more closely the two sets of variables are related. Once again, the foregoing link provides a good explanation of what a correlation coefficient represents.
My main purpose in running a correlation analysis was to evaluate how well the BPR POWER rating predicted the next round’s results throughout the 2010 Formula 1 season. It wouldn’t make sense to run a correlation between the individual-round BPR ratings and the on-track results from that same event, as the BPR formula is based solely on on-track performance and inherently correlated. Therefore, I ran the “CORREL” function in Microsoft Excel for the POWER rating preceding each round against the next round’s results. To illustrate: the post-Bahrain POWER rating was correlated to the results of Australia, the post-Australia POWER rating was correlated to the results of Malaysia, and so on. For those that are interested, Excel’s CORREL function uses the covariance of the variable sets and the standard deviations of each set to arrive at its correlation coefficient output.
I evaluated the POWER rating’s correlation to the finishing position of all 24 driver/entries at subsequent rounds in two ways: by utilizing the actual POWER rating as well as the rankings based on the POWER rating which are included in each BPR table posted on BPR F1. The results of each correlation analysis are provided in the tables below, with the corresponding results being utilized to generate a line plot also displayed below. The POWER rating’s correlations were inversed from negative to positive to allow for continuity in graphing.
BPR POWER RATING / RACE FINISH POSITION CORRELATION TABLE
BPR RANKING / RACE FINISH POSITION CORRELATION TABLE
COMBINED CORRELATION LINE PLOT
(Note that because there was no pre-round POWER rating for the season-opening Bahrain Grand Prix, that round does not have a corresponding correlation coefficient. Asterisks next to round abbreviations indicates a year-to-year change in track configuration, and the letters in parentheses next to some round abbreviations indicates the track used for events which have alternated tracks in recent history. Coefficient boxes shaded in light-blue indicate a race that was run in wet conditions.)
With nearly identical average coefficients of 0.779 and 0.778, the POWER rating and its associated rankings are certainly correlated to finishing positions at consecutive races. Take the correlations one step further and the POWER rating is indeed a “predictor” of future results. However, the POWER rating was never designed to be a prediction model and its predicting abilities are solely related to its reflection of current performance trends prior to each consecutive race.
With the foregoing in mind, I intend to adapt the existing BPR formula to create a predictor model for the 2011 Formula 1 season. At this stage, the model will incorporate the POWER rating as well as a separate formula based on track-type performances which positively correlate to other rounds. Including the second calculation is intended to address the simple fact that there are completely different tracks on the Formula 1 calendar which tend to produce different results based on individual car and driver characteristics. Although it’s relatively obvious that the results of the Monaco Grand Prix are unlikely to reflect the results of say, the Italian Grand Prix at Monza, result relationships amongst other tracks aren’t as obvious. Therefore, I decided to run a correlation of all the BPR scores for each round on the 2010 Formula 1 calendar to find which events’ results correlate. Remember that the BPR incorporates a lot of data for all 24 participating drivers at each round and therefore the correlation results should be fairly dependable.
BPR RATING / BPR RATING CORRELATION TABLE
(Note the light-blue shading used once again to show races which ran in wet conditions, with darker blue shading indicating a strong correlation between two races which were run in the wet.)
I’ll let the reader digest some of the more interesting correlations in the above table and what they entail, but I highlighted all correlation coefficients of 0.900+ as being especially relevant.
Look for the upcoming BPR predictor at BPR F1 in addition to the regularly-posted BPR materials throughout the 2011 Formula 1 season.
posted by Trey Blincoe