Dale vs. Daytona: Was the year Dale Earnhardt beat Daytona the best year of his career, or was he never meant to beat that track? Amanda Adams Statistical Reasoning in SPorts Period 1 February 20 th, 2014
Dale vs. Daytona: Which year was Earnhardt s best? 2 Table of Contents Intro...3 Raw data...5 Dotplots...8 Confidence Intervals...9 Conclusion...10 References...12
Dale vs. Daytona: Which year was Earnhardt s best? 3 Intro Dale Earnhardt may be the most recognized name in NASCAR, second only to Jeff Gordon or Jimmie Johnson. He holds the record along with Richard Petty for the most Sprint Cup/Winston cup wins of all time (one above Jimmie Johnson) with 7. Dale was an iconic NASCAR driver, with an enormous fan base that supported his near instant success, winning the championship the first year he raced in all the winston cup races, a feat not accomplished by any other driver. Earnhardt was an instant star. I chose to investigate Dale because his success came long before I ever started watching NASCAR with my dad (more like listening to NASCAR while I did my homework on Sunday afternoons). Dale s success amazed me, he was more successful than Jimmie Johnson who was already breaking all kinds of records. A few weeks ago, I heard on NASCAR radio some people talking about how Dale Earnhardt had only ever won one Daytona 500: in 1998. That s the reason for my choosing to investigate the year 1998, and for a comparison, I chose the year that he was paid the most. I thought it would be interesting to look at what motivated him more; finally beating the course that had always beaten him, or making a record amount of money. I got my stats from racing-reference.info and espn.com. In the years before 2000, The Sprint Cup that we know today was known as The Winston Cup which is why some of the graphs and tables have Winston Cup as their title instead of Sprint Cup; however, they are in essence the same thing.
Dale vs. Daytona: Which year was Earnhardt s best? 4 I think that my results will show that he had a greater ability to place higher in 1998, because he was younger then and he was riding the high of finally beating Daytona. Questions of Interest: 1. What was Dale Earnhardt s true ability to place in the 1998 Winston Cup? 2. What was Dale Earnhardt s true difference in ability to place between the 2000 and 1998 sprint/winston cup series?
Dale vs. Daytona: Which year was Earnhardt s best? 5 Raw Data Dale Earnhardt 1998 2000 total Top 10 13 24 37 Not top 10 20 10 30 total 33 34 67 1998: Race Place Daytona 500 1 GM Goodwrench Service Plus 400 17 Las Vegas 400 8 Primestar 500 13 Transouth Financial 400 12 Food City 500 22 Texas 500 35 Goody s Headache Powder 500 4 Diehard 500 36 California 500 Presented by Napa 9 The Winston 19 Coca-Cola 600 39 MBNA Platinum 400 25 Pontiac Excitement 400 21 Miller Lite 400 15 Pocono 500 8 Save Mart/Kragen 350 11 Jiffy Lube 300 18 Pennsylvania 500 7 Brickyard 400 5 The Bud at the Glen 11 Pepsi 400 Presented by Devilbiss 18 Goody s Headache Powder 500 6 Farm Aid on CMT 300 9 Pepsi southern 500 4 Exide Nascar Select Batteries 400 38 MBNA Gold 400 23 Napa Autocare 500 22 UAW-GM Quality 500 29 Winston 500 32 Pepsi 400 10 Dura Lube/Kmart 500 3 ACDelco 400 9 Napa 500 13
Dale vs. Daytona: Which year was Earnhardt s best? 6 2000: Race Place Daytona 500 21 Dura Lube/Kmart 400 2 Carsdirect.com 400 8 Cracker Barrel Old Country Store 500 1 Mall.com 400 3 Food City 500 39 DirecTV 500 7 Goody's Body Pain 500 9 Diehard 500 3 NAPA Auto Parts 500 17 Pontiac Excitement 400 10 The Winston 3 Coca-Cola 600 3 MBNA Platinum 400 6 Kmart 400 2 Pocono 500 4 Save Mart/Kragen 350 6 Pepsi 400 8 ThatLook.com 300 6 Pennsylvania 500 25 Brickyard 400 8 Global Crossing @ The Glen 25 Pepsi 400 Presented by Meijer 6 GoRacing.com 500 4 Pepsi Southern 500 3 Chevrolet Monte Carlo 400 2 Dura Lube 300 Presented by Kmart 12 MBNA.com 400 17 Napa Autocare 500 2 UAW-GM Quality 500 11 Winston 500 1 Pop Secret Microwave Popcorn 400 17 Checker Auto Parts/Dura Lube 500 9 Pennzoil 400 20 NAPA 500 2 The data that I ve chosen to investigate is numerical, I ll be getting Earnhardt s average place for each season and calculating which season was better based on that. The
Dale vs. Daytona: Which year was Earnhardt s best? 7 formula for calculating a confidence interval with numerical data is: x ± 2 s n when comparing the seasons to each other, the formula for calculating the difference in means confidence interval is: x A -x B ±2 S A 2 + S 2 B n A n B
Dale vs. Daytona: Which year was Earnhardt s best? 8 Dotplots Dale Earnhardt's Finishes Sprint/ Winston Cup 1998 2000 0 10 20 30 40 50 Mean 2000 Median 2000 Mean 1998 Median 1998 Dale Earnhardt's Finishes Sprint/Winston Cup 0 10 20 30 40 50 Mean 2000 Median 2000 Mean 1998 Median 1998 For the 1998 distribution, the minimum is 1, maximum is 39, Q1 is 8.25, Q3 is 22 and the median is 13. The 2000 distribution has a minimum of 1 and a maximum of 39 as well. Q1 is 3 and Q3 is 11.5, with the median at 6. Indicative of his higher placing in 2000. The 1998 distribution is more uniform than the 2000 distribution which is skewed right. Neither distribution has outliers, the 1998 mean is much higher than the 2000 mean, indicating that Earnhardt finished higher up in 2000 than in 1998. Both graphs have exactly the same range, the 2000 distribution has a smaller IQR of 8.5 compared to the 1998 distribution s IQR of 13.75. The graphs contrast our preliminary answer in showing that Earnhardt appears to have performed better in 2000, not 1998.
Dale vs. Daytona: Which year was Earnhardt s best? 9 Confidence Interval for 1998: mean: 16.235 Standard Deviation: 8.622 Confidence Interval 16.235 ± 2 8.622 = 16.235 ± 3.002 = 13.233-19.237 33 Confidence Interval for Difference in Means 1998-2000: Mean 1998: 16.235 Standard Deviation 1998: 8.622 Mean 2000: 9.2 Standard Deviation 2000: 10.762 16.235-9.2 ± 2 8.6222 33 + 10.7622 = 7.035 ± 4.758 = 2.277-11.793 34 In the difference in means interval, a positive number in the interval means that Earnhardt was better in 2000 (since it is better to have a smaller number as the place you finish). A negative number would mean that Earnhardt performed better in 1998.
Dale vs. Daytona: Which year was Earnhardt s best? 10 Conclusion According to my calculations, I am 95% confident that Dale Earnhardt s ability to place in the 1998 season is contained in the interval 13.233-19.237. I think this is a reasonable estimate given most of Earnhardt s finishes in 98. There could have been quite a few errors in calculating this interval. With the amount of calculations necessary, there was plenty of opportunity for computational error. Because the data was from over 10 years ago there is always the chance that it is not accurate or that it was misrepresented. Of course there are also different explanations for why Earnhardt s performance lies in this interval, but we ll examine that with the next confidence interval. The second interval gives us 95% confidence that Earnhardt s difference in ability to place for the years 1998 and 2000 lay in the interval 2.277-11.793. Because this interval does not contain 0, we have convincing evidence that Earnhardt had a greater ability to place higher in 2000 than in 1998. This means my guess was wrong, but it does not confirm that the reason behind his better performance was the fact that he was paid more. As with the first calculation, this one could have easily had computation errors and incorrectly recorded and reported data. I knew going into this investigation that I wasn t looking at Earnhardt s best years. He finished 8 th in 1998 and 2 nd in 2000 in the final standings. Of course, these aren t bad finishes, but they aren t the years that he won first. To say he peaked in the 80 s wouldn t be right because he placed 1 st in 1980, the year he first started racing in the Winston cup, and he placed 2 nd in 2000, the last year he raced before his
Dale vs. Daytona: Which year was Earnhardt s best? 11 tragic death. In those 20 years of racing, the lowest place he ever got was 12 th, so he never really peaked he was always on top. So, what does this all say about Daytona? Dale and Daytona will forever go down in history because of his fatal crash on that very track that he had finally conquered just 3 years before. Was Dale never meant to beat Daytona? Why did it take NASCAR s greatest driver 18 years to win on the most famous course in the sport when he qualified first nearly every time? We may never know, but the celebration that day he won it was one for the books, an 18 years in the making tribute to NASCAR s greatest driver. Rest in peace, Dale.
Dale vs. Daytona: Which year was Earnhardt s best? 12 Works Cited "1998 NASCAR Winston Cup Schedule." ESPN Sprint Cup. ESPN, n.d. Web. 19 Feb. 2014. "Dale Earnhardt." Career Statistics. USA Today Sports, n.d. Web. 15 Feb. 2014.