Building a Modified Elo Rating System for NASCAR

Introduction:

No sport alters its playoff system quite like NASCAR. Remarkably, NASCAR has changed its process of crowning a champion four times since 2004. NASCAR first divided its season schedule between a regular season and a postseason by instituting “The Chase” thirteen years ago. By resetting points for postseason qualifiers, “The Chase” introduced some variance into who could win a NASCAR title. For the first time, it was not certain that the “best” driver would be crowned champion. Beginning in 2014, a new “winner-take-all” playoff format was introduced to NASCAR that significantly damaged how reflective NASCAR’s standings were of overall driver and team performance. Simply, a fluke win could propel a team into the 16-driver playoffs and advance a driver through the playoffs’ sequential elimination rounds (of 12, 8, and 4). Whether this is exciting or damaging to the sport is up to the fans to decide. This season the NASCAR playoff formatting changed once again by adding a form of seeding called “playoff points” giving better regular season drivers an advantage in the playoffs. Regardless, the recent playoff rules’ propensity to create fluke playoff drivers or even “less deserving” champions has increased the potential utility of an Elo rating system for NASCAR to measure driver performance.

After collecting data from driveraverages.com for the 2017 Monster Energy NASCAR Cup Season (MENCS), I created my own modified and live updating Elo rating system. I compared my Elo ratings to current season point standings and included a win probability estimate for the upcoming final championship race on Sunday, November 19th at Homestead-Miami Speedway in Homestead, Florida.

Results:

Figure 1: A static Elo rating updated through 11/12/17.

11/12/17 2017 MENCS Elo Ratings
ELO Rating DRIVER Win Probability
1375 Martin Truex Jr. 39%
1286 Kyle Busch 23%
1259 Kevin Harvick 20%
1253 Kyle Larson
1250 Denny Hamlin
1236 Brad Keselowski 18%
1218 Chase Elliott
1147 Joey Logano
1127 Clint Bowyer
1127 Matt Kenseth
1113 Kurt Busch
1092 Jamie McMurray
1090 Ryan Newman
1087 Ryan Blaney
1069 Jimmie Johnson
1063 Daniel Suarez
1051 Erik Jones
1040 Ricky Stenhouse Jr.
1023 Austin Dillon
996 Aric Almirola (#43 Car)
990 Paul Menard
988 Kasey Kahne
985 Trevor Bayne
964 Ty Dillon
955 Dale Earnhardt Jr.
944 Michael McDowell
937 Chris Buescher
933 A.J. Allmendinger
885 Danica Patrick
879 David Ragan
850 Landon Cassill
842 Matt DiBenedetto
814 Cole Whitt
749 #23 Burger King Racing
737 #15 Premium Motorsports
652 Jeffrey Earnhardt (#33 Car)
Playoff Finalist
Top 16 Elo-Did not make playoffs
*Only Chartered Teams Included

Figure 2: An Elo chart that should automatically update after the Homestead race.

https://docs.google.com/spreadsheets/d/e/2PACX-1vTILvLd3pkisnj78DW3-36h9tKxWmlwlIDQNc8a6cz3y0q3a89eNdc4gXhy8nlz6eZY7yhP4OJZA4OZ/pubhtml?gid=2067488086&single=true

Figure 3: Elo throughout the 2017 MENCS season categorized by racing team. (Note that scales between graphs vary.)

big graph

Commentary:

The first Elo rating chart (Figure 1) contains Elo ratings for the 2017 season before the championship race. Additionally, this Elo rating chart includes win projections for the championship contenders. Since the championship will be awarded to the top performer of the upcoming Homestead race among the four finalists, the win probability only considers how these drivers will perform against one another. In other words, the projections state that Martin Truex Jr. has a 39% probability of beating Brad Keselowski, Kyle Busch, and Kevin Harvick at Homestead.

However, current Elo ratings also demonstrate something remarkable about the final four contenders: all drivers in the final four seem to be “deserving.” This Sunday, the top three Elo drivers will compete for a championship alongside the sixth highest-rated driver. Frequently, NASCAR fans have claimed that recent playoff systems have attempted to generate excitement at the expense of crowning a truly deserving champion. In 2014, these claims certainly seemed convincing as winless Ryan Newman almost “stole” the championship. Yet, these Elo ratings show that NASCAR fans have little reason to complain (at least this season). Certainly, another “Ryan Newman contender” could emerge in future seasons. However, I hypothesize that the introduction of playoff points and stage points will mitigate the risk of a “Ryan Newman” champion. Certainly, both playoff points and stage points helped Martin Truex Jr. build a nearly insurmountable points lead, and also, the playoff points and stage points system punished fluke win drivers like Austin Dillon. Moreover, the “winner-take-all” regular season only removed three top 16 Elo drivers from the playoffs (Joey Logano, Clint Bowyer, and Daniel Suarez). Perhaps, NASCAR finally has found what has seemed like an elusive balance between excitement and deservedness in its 2017 points system.

Methodology and Modifications:

 Named after its creator Arpad Elo, the Elo rating system measures the relative skill of competitors or teams. Although Elo ratings were first used in chess, FiveThirtyEight and others have popularized the use of Elo ratings for American football, basketball, and baseball.

While Elo rating systems are used frequently in many sports, the rating system itself is not naturally suited to analyze matches that involve many players and one winner. Elo ratings are instead designed for matches between two competitors. Generally, the equation is as follows:

New Rating = Previous Rating +K(Event Score – Expected Event Score)

The event score is the score awarded to the competitor for a win, loss, or place finish. In a field of 36 to 40 competitors, the event score cannot be a simple 1 or 0 for a win or loss. Rather, positive or negative values are attached to specific place finishes. The expected event score for a general Elo rating is calculated with the following equation:

Expected Event Score = 1/(10-(Previous Rating – Opponent Rating)/400+1)

Now, many elements within these equations must be modified to accommodate NASCAR races that feature up to 40 competitors. As was previously mentioned, place values must be assigned for each individual finishing position. Using logic from Gautam Narula, who created a multiplayer Elo rating system for the board game, Settlers of Catan, I assigned positive values to the first twenty drivers. Negative values were assigned to the next twenty drivers. The list of values assigned to each position follows:

Final Position Value Assigned
1 1
2 0.9
3 0.75
4 0.65
5 0.55
6 0.45
7 0.35
8 0.25
9 0.2
10 0.15
11 0.125
12 0.1
13 0.085
14 0.075
15 0.065
16 0.055
17 0.045
18 0.035
19 0.025
20 0.012
21 -0.012
22 -0.025
23 -0.075
24 -0.1
25 -0.125
26 -0.135
27 -0.145
28 -0.155
29 -0.175
30 -0.195
31 -0.215
32 -0.235
33 -0.255
34 -0.295
35 -0.345
36 -0.435
37 -0.55
38 -0.7
39 -0.8
40 -0.9

Unfortunately, varying driver participation exists in NASCAR. This season, I did not change the value of the ratings that were awarded if only 36 drivers participated in a race. This is problematic in that drivers in races of 36 drivers were punished less for finishing last. Additionally, the values assigned are somewhat arbitrary. What value positions should receive is subjective, especially since I did not run my final Elo rating system against multiple seasons of data.

Even after new values are assigned to accommodate the many finishing positions found in a multiplayer race, the Elo rating equations still must be modified to function in a multiplayer race. Intuitively, one might consider creating many pairwise matches within a race to preserve the Elo rating system. In other words, driver A’s performance and Elo rating would be calculated by examining individual matches between drivers B, C, and D, etc. As Narula and others demonstrate, this modification can overrate winners and underrate losers. In essence, this modification multiplies the effect of winning a race by creating many individual matches within one race. This multiplication is, of course, improper and results in improper Elo ratings. Thus, some different modification is preferable. In the end, I followed the logic of Narula again and chose to modify the expected pairwise score. The modification itself is simple. The expected pairwise score is multiplied by two and divided by the number of participants in a race. It is:

2(Expected Pairwise Score)/N

Where the expected pairwise score is and new rating equations are:

Expected Pairwise Against Avg. Driver = 1/(10-(Previous Rating – Average Driver Field Rating)/400+1)


New Rating = Previous Rating +K(Event Score – ((2)Expected Pairwise Score/Number Drivers)

Now, a K factor must be added so the new modified Elo system can function. I chose a K factor of 25. Since I only used data from 2017 and had all drivers start at an Elo of 1000, I felt that it was necessary to use a higher K factor. In this case, a high K factor allowed skilled drivers to adequately separate themselves from small teams that consistently run behind top drivers by multiple laps. My K factor is most likely not perfect, but it did produce reasonable results.

Fortunately, next season I will be able to use final Elo ratings from this season to begin as starting rankings. However, the K factor might have to be adjusted to avoid erratic and noisy rankings.

Data from:

http://www.driveraverages.com/

Sources for methods and formula modification:

https://fivethirtyeight.com/features/introducing-nfl-elo-ratings/

https://www.gautamnarula.com/rating/

 

David D’Ambrisi is an OPIM major in the McDonough School of Business, Class of 2020.

Email: djd95@georgetown.edu

 

 

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