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**Early Season Speed Ratings and
a Brief Overview of Speed Ratings**

* Bill Meylan*
(September 3, 2005)

This article is somewhat repetitive in regards to other articles already posted
... It addresses some recent inquiries concerning my speed ratings with
regards to their application and accuracy ... As requested, a brief summary
overview of speed ratings is presented ... Remember, the purpose of this
methodology is to determine how fast people are running relative to each other
at different courses.

__ Early Season Speed Ratings__
... In general, the most difficult time of the season to calculate comparative
speed ratings is in the beginning of the season ... The reason is lack of data
... The overall process is data-dependent which basically means that the
accuracy of speed ratings improve as more and more data becomes available (which
can only occur as the season progresses) ... In early season, data are limited
and statistical "margins-of-error" may be high resulting in

__Speed ratings can be generated ONLY if one (or a
combination) of following are available__:

(1) A good **Course Conversion Table** for the cross
country
course being considered (more about this later in the article) ... This method
is useless for new courses, courses that have been modified, or courses where I
have inadequate (or no) prior data evaluation.

(2) **Speed Data on Individual Runners** ... For the
first race of the season, there are no prior speed data for the current season
... I will look at XC speed data from the previous year, but that data is last
year's data and must be used with reservation (it might be helpful, but it can
also be inaccurate for the current season).

(3) **Complete Race Results** containing appropriate
groups of runners for statistical sampling ... In practice, I graph the race
results and try to identify various sub-groups of "average" runners that
correspond directly to sub-groups of "average" runners of known speed ability (I
can also use "above-average runners") ... This can be very difficult in small
invitational races!! (and may be impossible) ... Early season races add another
problem - early season races contain a mix of runners ready to race good times
(because they have been running much of the summer) and runners who are not
in-shape (but will be later in the season), and this makes race graphs difficult
to interpret.

__Bottom-Line for Early Season__ ... The most
"inaccurate" speed ratings are likely to occur early in the season because the
statistical "margins of error" can be high ... Often, I make my best "educated
guess" and go from there ... As the season progresses and more teams and
individuals cross-over in invitational races (race teams from other leagues and
sections), the accuracy improves ... Also as the season progresses, the overall
process becomes increasingly a statistical number-crunching operation with few
educated-guesses on my part.

__Noteworthy Side Consideration__ ... I receive e-mails
from coaches and runners wondering **why some teams or individuals are NOT
included in my database or ranking lists** ... __Reason One__ - some
sections and leagues historically have limited (or NO) results available ...
I can NOT speed rate races with insufficient data (and this occurs frequently
within NY State, especially within certain sections) ... When I do not know the
course, individuals or quality of a race (with some degree of acceptability), I
do NOT rate it ... __Also__ - available race results for some races may go
only 10 or 25 runners deep - therefore, I do NOT have results for other
runners in the race ... Available race results means "readily" available through
Armory Track, the various sectional web-sites, the timing-company web-sites,
on-line newspapers, or other web-sites making it "readily" known that results
are being posted there.

__Brief Overview__
(Speed Ratings)

**Where do Speed Ratings come from??** ... Speed
Ratings for an individual race are generated by the following method:

(1) Get the actual final times for a race.

(2) Determine how fast or how slow the race times are compared to a standard base-line race of known speed ... the determination is a number of seconds (plus or minus) which is known as the correction.

(3) Add or subtract the correction to each of the actual times ... for example, if the correction is 10 seconds faster than the standard base-line race, then add 10 seconds to all of the actual race times ... this produces the "adjusted" race times for each runner.

(4) The method could stop at (3) above ... however, I use the "adjusted" times for a variety of comparisons and other processes involving mathematical calculations ... performing math on race times is a "pain-in-the-neck" compared to using regular numbers, so I convert the "adjusted" times to a number called a "speed rating" (for those familiar with horse racing and the Daily Racing Form, this is similar to the Beyer Speed Figures) ... My speed ratings use the following conversion equation:

Speed Rating = (1560 - Adjusted Time (in seconds)) / 3

1560 is the number of seconds in 26 minutes ... so in effect, the speed rating is how much faster the adjusted time is than 26 minutes (in seconds) divided by three ... the "divided by three" simply means that one speed rating point equals three seconds.

__ Determining Race Corrections__ ...

**(1)** * Course Conversion Tables* ... course
comparison tables compare the speed of different race courses to each other
based upon statistics or historical observation ... I use the SUNY Utica course
as my standard or base-line course (and compare all other courses to it) ... Some current course comparisons on my
tables are:

SUNY Utica 0 (base-line course) Bowdoin Park -5 to -15 Sunken Meadows -3 to -13 Saratoga Park -70 to -80 Bear Mountain 2004 -63 to -78 McQuaid Invite -75 to -85 Van Cortlandt Park (2.5) -230 to -238 (boys) Van Cortlandt Park (3.1) -13 to -25 (Footlocker) Elma Meadows -5 to -20 Chenango Valley St Park -20 to -30 Bethpage St Park -25 to -35The negative numbers mean faster than the SUNY Utica course ... I actually have separate tables for boys and girls (the table above is primarily boys ... the girl's ranges are similar for most, but do vary).

**Limitations of Course Comparison
Tables **... My comparison tables (and anybody
else) are only approximations ... they typically consider only
normal/good running conditions ... and you must assume the course
distance doesn't change from year to year ... Daily variations with
respect to weather and other factors MUST be considered.

Conversion tables are NOT my first choice in determining race
corrections ... I prefer using them as a check on calculations from the other
methods ... __However__, the tables are useful for courses that are consistent in
speed ... I commonly use the average table correction for Van Cortlandt Park
(2.5 mile) ... Saratoga Park typically has a race correction of 75 seconds under
normal conditions (for both boys and girls) - For example, Nicole Blood broke
the Saratoga course record at the 2004 Suburban Council Championships by running 16:41.9
... the speed rating was calculated as follows:

16:41.9 + 75 seconds = 17:56.9 ... 17:56.9 = 1076.9 seconds ... Speed Rating = (1560 - 1076.9) / 3 = 161

I do not know the Saratoga course record for boys; however, a 15:00 time would typically yield the following:

15:00 + 75 seconds = 16:15 ... 16:15 = 975 seconds ... Speed Rating = (1560 - 975) / 3 = 195

**(2)** *Reference Runners*
... This increasingly becomes the method of choice (within NY State)

For every race, I keep track of how fast every runner runs
relative to every other runner on the same day at the same course ... I then
extend it with results from other race courses so I can compare how fast any
runner has run relative to any other runner on a single day or throughout the
season ... It is just keeping track of time differences and final times ... It
requires a computer program for the scale of comparison I do within NY State,
and it's done on a race by race basis to see how fast a particular race is
compared to other races based on how fast individuals have run ... Hence,
the **individual runners are the reference for determining the race speed**
... the time differences and final times are statistically evaluated to find
median course correction values.

In addition, I frequently apply a modified "Reference
Runner" methodology as follows (because it is easier and takes less time) ...
(a) Use the actual race times to calculate "unadjusted speed ratings" by
assuming **zero** correction ... (b) Get the existing overall speed rating for each
individual from the current Rankings (or database) ... (c) Find the difference between the
"unadjusted speed rating" and the current overall speed rating ... (d) Find the
statistical median of the difference as the correction ... (e) apply the
correction to the "unadjusted" ratings ... Here is an example:

Overall Unadjusted Seasonal Rating SPEED Time Speed Rating Speed Rating Difference RATING ----- ------------ ------------ ---------- ------ Runner 1 15:30 210.0 195 +15.0 186.0 Runner 2 15:40 206.7 183 +23.7 182.7 Runner 3 15:43 205.7 185 +20.7 181.7 Runner 4 15:45 205.0 180 +25.0 181.0 Runner 5 15:50 203.3 171 +32.3 179.3 Runner 6 15:52 202.7 176 +26.7 178.7 Runner 7 16:00 200.0 165 +35.0 176.0 Runner 8 16:05 198.3 173 +25.0 174.3 Runner 9 16:10 196.7 180 +16.7 172.7 Runner 10 16:12 196.0 172 +24.0 172.0For this made-up example, the statistical median of Rating Differences is about 24 speed rating points (or 72 seconds) ... The race correction becomes 72 seconds faster than the standard course, therefore, 72 seconds is added to each actual race time ... and the "adjusted race times" are used to calculate the normal Speed Rating.

This example Reference Runner method assumes the majority
of runners are consistent in speed ... this assumption is reasonable __after__
the majority of individuals have had the opportunity to achieve a decent level
of fitness ... In the early season, many runners have __not__ achieved an
appropriate level of fitness (so this must be taken into consideration).

Additional information on Reference Runners is available in a separate article.

**(3)** *Statistical Sampling of Groups*
... This method does NOT use any individual runner data ... Often, it is the
only method available to compare races from different sections of NY State or
other states ... It requires complete race results (and sometimes that's not
enough to adequately compare races) ... It requires statistical assumptions (as
will be explained) ... Generally, it involves

The Articles Page contains a list of the articles on this web-site, and several articles have examples of graphing races (so I am not going to repeat that here) ... the most recent article has some basic sampling information and examples concerning NTN 2004.

Here is a quick example of Statistical Sampling of Groups ...
Consider a large group of high school students from many different schools
(small, medium, large ... good, average, bad) ... Results of standardized exams
allow educators to identify the "A", "B", "C", "D" and "F" students based on
relative scores ... the "C" students are the largest group and can be visually
identified on the classic "bell-shaped" graphs ... __Results of cross country
races are similar__ - in any large invitational race, the majority of runners fall
in the "average" class (or "C" class) ... since the "C" class is large, it can
be further divided into "C-plus", "C-average" and "C-minus" classes ... Assuming
we already have the results of a large standardized race, then we already know
how fast the "C-plus", "C-average" and "C-minus" runners will run.

Therefore, in any large invitational race (similar in quality to the standardized race), if we can identify the "C-plus", "C-average" and "C-minus" classes, then we can calculate with reasonable precision how fast one race is compared to other ... and we do NOT need to know anything about the individual runners or the race courses!

The **assumption is that groups of runners are equal in
quality** ... and the primary focus is identifying the classes. __
Direct__ graphical comparison of races is NOT possible unless that assumption
is accurate.

**Note** ... Graphical interpretation of race results
is part statistical and part "art" (which means experience is necessary) ...
Sometimes the graphs are obvious in their comparisons (those are the examples
posted on this web-site) ... but occasionally, the appropriate interpretation is
NOT obvious (usually due to an unbalanced or non-homogenous mix of "A", "B",
"C", "D" and "F" runners).

For those viewers who have asked about the **computer
software I use** .... For statistical evaluation, I use a combination of **
ProStat** (Poly Software International),
which is also my primary graphing software, and **Microsoft Excel** ... The
actual cross country databases are maintained as WordPerfect **Corel Paradox**
databases ... I have written series of
programs (in **Microsoft Visual C++**) that do a variety of operations such
as generating the actual output for placement on web-pages, calculation of speed
ratings for entire races, and generating output for uploading into ProStat or
Excel.