THE BIRTH OF THE BLINCOE PERFORMANCE RATING
‘Stick and ball’ sports in the United States are steeped in mathematical performance rating systems. To illustrate: the NFL has Sagarin ratings; NCAA basketball has the RPI, Pomeroy Ratings, etc.; NCAA football incorporates an official rating system for the Bowl Championship Series; and the MLB has so many rating systems it would be a disservice to even name but a few. So why aren’t statistical performance rating systems nearly as prevalent in motorsports as they are in traditional sports? Sure, motorsports have their unique points tables, race classifications, etc. to provide an idea of the relative levels of performance between entries in any given series; but with the multitude of statistical information available, wouldn’t a mathematical performance rating system make better sense of everything that goes on at the track?
THE BPR EVOLVED
The “Blincoe Performance Rating”, or BPR, was initially crafted for an undergraduate statistics project and designed to formulate performance ratings in the various sportscar racing series of the world; such as the American Le Mans Series, Le Mans Series, and FIA GT1 Championship. However, in late 2008, Trey focused on adapting the BPR to evaluate the pinnacle of motorsport: Formula 1. Throughout the 2009 F1 season, a dry-run was performed with an evolution of the BPR specifically formulated to evaluate the unique and ultra-competitive world of Grand Prix racing. To incorporate the rules changes set in place for the 2010 F1 season, the BPR formula has been further evolved to its current state.
THE FORMULA EXPLAINED
The BPR formula rates the performance of each driver for each round relative to a theoretical perfect score of 100. The perfect score is “theoretical” because it is based on the premise that the fastest and/or winning driver represents the maximum possible performance in any given race weekend.
The data for each driver incorporated into the BPR formula includes: (1) fastest qualifying lap time; (2) fastest race lap time; (3) mean race lap time; (4) finishing position; and (5) laps completed. Each discrete data-set is weighted to reflect its correlation to finishing position. For instance, a driver’s mean race lap is correlated to finishing position at a rate approaching 3x that of its fastest qualifying lap.
A “Reliability Rating” is incorporated into the BPR formula to reflect the ratio of laps each driver has completed over the course of the season. Any driver not classified by the FIA at the end of a race will be given an “NC” designation and not receive a BPR score for that particular round (there are various reasons for doing this, mainly related to the statistical flaws which arise when comparing complete and incomplete data sets). However, the laps completed by a driver will be counted towards the Reliability Rating regardless of classification.
In the event a driver does not complete a representative qualifying lap, the BPR formula’s qualifying lap input will be calculated with the fastest practice lap set under like or similar track conditions.
THE BPR TABLE
The BPR table is designed to efficiently display an otherwise confusing set of statistical outputs. Entry number, driver name, and team name are the first columns displayed left-to-right and should be self-explanatory.
The first numerical column is arguably the most important number in the BPR table: the “Power Rating”. The Power Rating incorporates three BPR data sets for each driver in its formulation: (1) performance over the entirety of the season to date; (2) three-race performance trend; and (3) the Reliability Rating. The Power Rating is the most accurate reflection of a driver’s current level of performance, and is therefore the single best predictor of future results. You will notice that the Power Rating column is highlighted in decreasing shades of blue-to-white to reflect correlation to statistically possible/probable finishing positions of each driver/entry:
- Darkest blue and white lettering reflects possible race-winning performance (Power Rating of 90+);
- Second-darkest blue and white lettering reflects possible podium performance (Power Rating of 89.999-85);
- Third-darkest blue with black lettering reflects regular points-scoring performance (Power Rating of 84.999-80);
- Fourth-darkest blue and black lettering reflects possible points-scoring performance (Power Rating of 79.999-75); and
- Non-highlighted with black lettering reflects non-points scoring performance (Power Rating of 74.999-0)
Next to the Power Rating column is the “Average Rating” column. The Average Rating is the full-season performance of each driver to date, calculated without reflecting current trends or reliability. It follows that the Average rating is the best indicator of full-season driver/entry performance.
Next to the Average column is the “Reliability Rating” column. Described earlier, the Reliability Rating reflects the reliability of each entry and is used to calculate the statistical likelihood that a driver will not complete the full race-distance for any reason. The Reliability Rating is displayed to give the viewer a concept of driver reliability is factored into the Power Rating.
The next three columns reflect the rankings of the drivers based on the Power Rating, including +/- changes in rank from the previous round and numerical change in Power Rating from the previous round.
Finally, the remaining columns display the per-round BPR output for each driver based on the results of the round; including once again the driver’s best qualifying lap time, best race lap time, mean race lap time, and finishing position.
For a visual explanation of the BPR table, see the image below.