Caroline Hood winning the North Georgia Championships earlier this year in the fastest girls speed rating of the season

# Introducing Meet Speed Ratings

# by Mason Arbery

Every cross country runner understands the importance of a course's difficulty on the time they end up running. Running a 20:00 5K at Asics is one thing, but repeating that time at Carrollton is another story altogether. Many factors--most of them outside of the control of the athletes--determine the ultimate speed a runner ends up running. Weather, hills, the "softness" of the racing surface, amount and degree of turns, and the quality of competition can all affect the times that runners produce. Because of all these factors, it can be difficult to compare times across meets and courses. MileSplit does have a feature that allows you to compare races to each other, but only between meets across different years. However, I have developed a system to attempt to rank and compare the difficulty across courses, and therefore compare times across courses.

Methodology:

How do you begin comparing courses against each other, especially when an entirely different set of runners may compete at one race from another? The answer is to assume that the general population of runners has the same talent in one race as another. Extremely fast or slow runners can skew the picture, so I disregarded the extreme fast or slow runners from my analysis entirely. This means that all numbers that you'll see in the rest of the article are calculated for the average runner.

Now, how did I go about doing my analysis? First, I gathered the results for every meet in Georgia with at least 400 boys participating to make sure my sample size for each race was large enough. If the meets had multiple races within them (such as varsity and JV), I just combined them as if they were in a single race. However, I kept boys' and girls' races separate. Then I made a plot of the race with the place of the runner on the x-axis and the finish time of that runner on the y-axis. For example, here's what the boys' results at the AT&T Starr's Mill Panther XC Meet looked like.

As you can see, the runners who finished towards the back cause a large change in the trajectory of the graph. It's a bit difficult to see above, but the runners at the front do as well. To account for that, I decided to only look at the middle 50% of runners, or runners who finished between the 25th and 75th percentiles. For Starr's Mill, there were 669 boys who competed, so the middle 50% of runners ranged from 168th place to 502nd place. Here's what the plot looked like when I had adjusted it.

The graph looks extremely linear, so I fit a line of best fit to the graph. The slope of that line represents how many seconds separate each place from the next one on average. I was most interested in the y-intercept of the best fit line, however. That y-intercept represents how fast the runner in first (or technically zeroth) place would be expected to run assuming that the linear trend holds true all the way to the front. Of course, the fastest runners are always going to be faster than this prediction, but the y-intercept gives us a number that we can use to compare between meets. For Starr's Mill, the y-intercept on the boys' side was about 997. That means that based off of this model, the runner at place 0 would be expected to finish in about 997 seconds, or 16:37. The slope is less than 1, so the runner in first place could be expected to finish within a second of that. The R-squared value tells us how good of a fit the linear model is for the data, with 1 meaning a perfect fit. As we can see, the R-squared value is above 0.99, which means it describes the data extremely well.

I recorded the intercept for girls and boys at every meet this season that recorded at least 400 boys racing, which ended up at 15 meets. I wanted to keep the sample size high to make sure that a race was not skewed by more fast or slow runners participating. I then averaged the intercept for the boys and girls to produce the final meet intercept. I turned that value into a Speed Rating where a higher Speed Rating represents a faster meet and a lower Speed Rating represents a slower meet. A Speed Rating of 85 indicates a roughly average score. Every increase of 1 in Speed Rating indicates a faster course by about 2 seconds.

Results:

Before we look at the Meet Speed Ratings, a few notes. First, these are speed ratings for meets, not courses. That's important because a meet could have had difficult weather conditions, for example, and run slower than usual. Therefore, these ratings are only accurate for 2022 races. This is also the reason why we see differences between races run on the same course, such as Pickens Preview and Pickens & Grinnin' Invitational. Second, these speed ratings are predicated on the results of average runners. I calculated the speed rating for the GHSA state meet, but it's much higher than Carrollton Orthopaedic Invitational, which was on the same course. Why? That's mostly because the "average" runners at the state meet are much better than the average runners at Carrollton Ortho, since only the top seven runners on each team could qualify for state. Therefore, the Carrollton Ortho result is a better comparison across meets than the GHSA State results. I just included GHSA state as a comparison.

As expected, the Milton Invitational clocks in as the slowest meet among these 15, with Carrollton Orthopaedic close behind. On the other end, Asics ranks as the fastest meet with a rating of 115, while Coach Wood ranks second with a score of 105. Now, an increase of 1 in speed rating corresponds to a two-second faster course. That means the difference between Asics and Milton courses Is 115.1 - 32.9 = 82.2, and 82.2 * 2 = 164.4, or 164 seconds. That's over 2 minutes and 40 seconds! Now, that difference is for the average GA cross country runner. If you're a faster runner than average, then the difference should be smaller. If you're a slower runner than average, the difference should be even larger. These ratings take into account the boys and girls results together. For boys, the difference in times between courses tends to be smaller than for girls.

The neat thing about these Meet Speed Ratings is that you can use them to compare times across different meets. Using the intercept for boys and girls, I calculated the course-adjusted time for the 15 meet winners. For the individual times, I used a separate adjustment for boys and girls. This was because the differences in course adjustments for boys and girls are much larger for the very fastest runners.

Joe Sapone of Holy Innocents and Alex Arrambide of East Forsyth dominate the top four course-adjusted times for meet winners. Tommy Latham's very close second place finish at Coach Wood would rank fourth if it were shown. We can also see that Ben Bergey's 17:11.7 at the Milton Invitational is on the same level as Taylor Wade's 15:28.7 that he ran at Bob Blastow.

On the girls' side, there may be a slightly surprising result at the top with Caroline Hood's performance at the North Georgia Championships back in August ranking an entire fifty seconds ahead of second place. While that may seem unreasonable, she actually won that race by 57 seconds over Clodagh O'Bryant and finished 80 seconds ahead of Carmel Yonas. Unfortunately, she suffered an injury after than meet and didn't run again until region. I especially enjoy the fact that the top seven results are by seven different girls, which shows how many girls battled for the fastest times throughout the season.

Editor's Notes -

Speed ratings were first invented by Bill Meylan in New York, see his website for more info on how they began - http://tullyrunners.com

The Author wanted to find a way to bring these to Georgia and also drew inspiration from this article he found online - https://mixcspeedratings.com/2019/07/03/how-are-speed-ratings-calculated/