TullyRunners - Article
Distance & Speed Ratings
by Bill Meylan (August 18, 2012)
One common inquiry sent to me involves the use of distance in speed ratings ... Typically, somebody wants to know how I incorporate the distance of a cross country race into the speed ratings ... or does the distance of the race affect the speed ratings??
The short answer is ... The distance of a race is not used in any way ..... As long as the distance is roughly between 2.75 and 3.1 miles, it really doesn't matter ... I like to know the general distance, but I never use the distance explicitly in any calculation ... As the distance gets shorter, especially near 2.5-miles (or 4K), the derived speed ratings may need to be scaled somewhat to more accurately reflect comparison with longer distances (the Manhattan Invitational is a good example ... scaling is discussed later in this article).
High School Cross Country Courses & Reported Distance ... When initially forming a speed rating methodology for high school cross country races, I knew that course distances varied ... I also knew that many reported 5K courses are not really 5K running distances ... One problem is how course distances are measured.
The distance of many courses was determined by measuring a "line" approximating a mid-course position throughout course ... sometimes a line may have been painted on the course showing runners where to go, but the line did not "cut-the-tangents" utilizing the shortest possible distance a runner could run ... Therefore, a runner who did "cut-the-tangents" ran a shorter distance than the "mid-course" measurement of 5K (or whatever reported distance).
Many road races are "certified" 5K courses ... This means the course was measured "cutting-the-tangents" and that any runner has to run a minimum of a 5K distance ... Measurement of high school courses is currently moving in this direction prompted by a 2012 rule change by the NFHS (National Federation of High Schools) as follows:
NFHS Track and Field
and Cross Country Rules Changes 2012:
How Much Distance is Saved by Cutting-the-Tangents??
Using track & field as an analogy ... If you run in the second lane of a standard 400-meter track for one lap, how much longer than 400 meters do you run?? ... A look at the stagger-lines gives you an idea ... If you run one lap in lane 4, you run quite a bit longer than 400 meters ........ Now think about running a cross country course by following a line drawn at a mid-course position (not cutting-the-tangents).
I am aware of several courses that have been measured by both an approximate mid-course position (or about 2 to 5-meters off shortest possible around curves) and by shortest possible line (cutting-the-tangents) ... The distance saved by cutting-the-tangents are as follows:
Cortlandt Park 5K Course: 80-95 meters (measured by wheel & GPS).
The distances saved are approximate, but fairly consistent from measurements by different people (guess which one I measured) ... It takes a high school runner roughly 1.8 to 2.5 seconds to cover 10 meters during an XC race, so I use 2 seconds per 10 meters because it's an even number ... so cutting-the-tangents at Van Cortland Park can save 16-19 seconds ... 50 meters at Saratoga Park saves 10 seconds.
Side-Note ... Saratoga Park is typically listed as 3.04 (or 3.05) miles in length ... From a second-hand source, I heard that one "cutting-the-tangents as tightly as possible" measurement last year was 4854 meters (3.016 miles) ... a difference of 0.03 miles equals 48.2 meters ... In the last few years, Saratoga Park has been running roughly the same speed as the McQuaid Invitational course (in good weather) which is 3.0 miles cutting-the-tangents.
Whether the course is 3.01 or 3.04 miles makes no difference to me in terms of calculating the speed ratings ... the speed ratings are determined by the final times of the runners and how the final times relate to other runners on this course and other courses.
Bottom-Line ... Course distance can not be used explicitly in speed rating calculations because the "exact" distances of corresponding courses are unknown (or uncertain) ... Another problem is course changes from year-to-year.
Course Changes ... Last year, I received nearly a dozen e-mails from meet directors or coaches describing changes (modifications) to courses for specific meets (they thought it might be useful in making the speed ratings) ... That information is definitely helpful because course changes can cause in a change in the "inherent speed" of the course ... typically, the course gets a bit longer or shorter, so the course runs slower or faster based on distance change alone.
I maintain profiles for individual courses and races ... When I see a significant change in speed from previous races or years, and it does not appear to be weather-related, it's good to know the course was modified.
Reasons for most course changes are fairly common such as (1) construction at the school or park, (2) weather-storms messed-up a section of the course, so it was altered, and (3) making it safer for runners and spectators, etc.
Small Changes?? ... At times, seemingly "minor" changes can affect a course's inherent speed more than realized ... One re-occurring example is to round a very tight turn to make it safer (e.g. groups of runners bunch-up and slow noticeably to go around a turn) ... Even minor rounding can cut-off 10-15 meters of distance (it does not seem it until you measure it) and the rounding itself allows runners to run faster (no slowing down), so a "minor" change can speed-up a course by a few seconds.
Often when I make comments about specific courses, I catch grief from people who "love" that course and think I'm personally criticizing the course (well, maybe Portland Meadows, but that has nothing to do with this discussion) ... In the early 2000s, I noticed the 2.5-mile course at Van Cortlandt Park was running faster ... At Footlocker Northeast (when it was still at Van Cortlandt Park), I talked to several runners & parents and a worker who actually worked at the park ... a follow-up phone call to the Van Cortlandt Park offices confirmed that "minor" changes had been made to the cross country courses to make them the correct metric distances (4K, 5K, 6K, 8K) ... the 2.5-mile course was now a 4K course which means the course was shortened by roughly 25 meters (e.g. roughly 5 seconds faster which is about what I was seeing) ... But "everyday" runners and coaches at the course said I was wrong ("crazy") about the course shortened when I mentioned it ... All I know is the course got faster and workers at the park said the course was shorter ... Just another reason why course distance can not be used explicitly in speed ratings.
Side-Note ... Even back in the early 2000s, there was more than one 2.5-mile course used in Van Cortlandt Park by the different associations (PSAL, AIS, CHSAA) and Manhattan Invitational ... Last year (2011), at least two (maybe three) different variations of a 2.5-mile (or 4K) course were used, and it was noticeable from the final times of the races.
Scaling Speed Ratings for Shorter Races
Speed ratings are a measure of the time differences between runners ... In longer races, the differences can be spread-out more; e.g. the better runners have more time to increase their margins over the slower runners ... In shorter races, the margins can be smaller ... So in shorter races, the evaluation accuracy of speed ratings can be enhanced by scaling the ratings with a math equation.
For many 4K races at Van Cortlandt Park, I don't bother scaling the ratings for two reasons, (1) in some 4K races, the runners simply spread-out as much as in a 5K race, and (2) I'm only looking at certain portion of runners from a race for upload to my database, and they're spread-out enough.
The Manhattan Invitational needs scaling due to the quality & number of runners ... So How Do I Scale Ratings?
Early on, I did not scale 4K races ... I simply ignored them when the championship portion of the season came (knowing the ratings might be too high for many runners) ... But evaluation of 4K State Meet results from other States for NXN purposes and complaints about Manhattan Invitational ratings changed that.
For nerds who like math ... So I did what most scientists and engineers would do ... I put available data into a statistical computer program and statistically "fit" the data to a useable math equation ... The initial "fit" used the Manhattan Invitational and every runner in my existing database with known inherent speed (which is many runners from NY) ... for "known inherent speed", I used each runner's overall speed rating going into the Manhattan Invitational (runners with limited data were excluded to improve data quality) ... I speed rated the Manhattan Invite, as in the past, without scaling ... I then statistically related the unscaled-ratings to the known overall speed ratings to determine a scaling equation.
I eventually settled on a basic scaling equation that works for any shorter race and allows for manipulation (e.g. a secondary fit for any particular race) ... The basic equation can be seen in the scaling equations for the 2011 Manhattan Invitational which are:
Boys Scaled Rating = Unscaled Rating - (175 - Unscaled Rating)*0.11
In these equations, the 175 (for boys) and 145 (for girls) are focal points that change from race to race ... the focal point needs to be lower than the top runner(s) in the race, but typically in the upper 25% of the unscaled ratings (e.g. at a point where a majority of unscaled ratings equal the overall ratings) ... The 0.11 (for boys) and 0.06 (for girls) are plain multiplying factors that change from race to race.
For Manhattan 2011, I entered the unscaled ratings and known overall ratings into my stat program ... I arbitrarily selected a focal point and derived the best-fit multiplying factor ... I tried different focal points to find better overall fits if possible ... the unscaled ratings may need some manipulation as well ... requires some trial-and-error, but it's not too time consuming when necessary ... and it doesn't need to be precise, just reasonably close.