2015 TC 1 Mile Champions Garrett Heath and Heather Kampf |

The Medtronic Twin Cities 1 Mile is one of the
premier road miles in the United States.
It has hosted Olympic medalists and has borne witness to several
sub-four-minute miles. In addition to a
top-flight pro race, the TC 1 Mile features several "open" waves,
which usually total over two thousand finishers. The traditional course was flat and very
fast. This year, the installation of a
new light-rail transit line forced the course through downtown Minneapolis to
be changed, likely permanently.

This course change was announced a few months ago,
and after researching the elevation profile of the new course, which gains
about 30 feet of elevation in the first half mile before flattening out, I
published an article in which I predicted the new course would be five to eight seconds slower.

The race itself, which happened last Thursday, was
held on a cool, rainy evening with slight winds. Weather data pegs the exact conditions at 54
degrees F, light rain, and 9 mph winds at race time—certainly not conducive to
the very fastest times, but not terrible.
The winner, Garrett Heath (a Minnesota native), took the win in 4:08,
which was a sharp contrast to Nick Willis' blistering 3:56 course record the
last time the race was held. Heath
himself was runner-up in that race with a 3:57.

By looking just at the pro results, the new course
looks substantially slower than the old one, but you could chalk this up to
cautious tactics early in the race, or just a fluke from a small sample
size. To get a real answer on how much
slower the new course was, and how accurate my prediction was, we'll have to do
some statistical analysis.

The rest of this article will go in detail on the
methods I used to compute how slow the course actually was, but if you're just
looking for a quick conversion, here it is: For competitive runners, the 2015
TC 1 Mile was

**13 ± 3 seconds slower**than the 2013 course. A more accurate conversion is to**multiply your 2015 race time by 0.9581**to get the equivalent 2013 time and multiply your time by 0.009 for the uncertainty.
Statistical
methods of comparing the two courses

Broadly, there are two ways of going about looking
at the relative competitiveness of a given time on the old course versus the
new one. The first and more simple
method is a place-by-place analysis—compare both races and analyze what it took
for 1st place, 10th place, 50th place, and so on. This looks merely at how competitive a
certain finishing position is, with no regard to how specific runners performed
year-to-year. While simple, this method
is vulnerable to being swayed by the size of the race. Perhaps because of the poor weather, this
year's TC 1 Mile had only 1,600 finishers compared to 2013's 2,500 (the race
was cancelled last year because of stormy weather). This might shift the bell curve of
competitiveness towards slower times. In
some years, the TC 1 Mile has played host to the USATF Road Mile Championships,
which would also draw a more competitive field.

A workaround for this would be to compare the race
times of individual runners who competed in both races. Though some runners are surely in better
shape this year, some are also slower, so when averaged out over many, many
runners, this gives us another way of looking at the relative speed of the
course.

Another question to ponder is whether we want to
develop a simple conversion that uses a static value to "convert"
from one race distance to another—e.g. "The 2015 course is

*x**seconds slower"—or whether we want to use a multiplier ("The 2015 course is**y**percent slower"). Strictly speaking, the multiplier method should be more accurate, since runners of different speeds are on the course for longer or shorter periods of time. A four-minute miler is probably not going to be slowed down as much as a six-minute-miler.*
Instead of deciding which way to process the data,
I decided to do run several combinations of methods and compare the
results. Surprisingly, I found that

*any*reasonable way of comparing the courses results in about the same result, with roughly the same margin of error!
The data
and the results

What follows is a brief overview of the methods
used to calculate the conversion factors for all seven statistical methods I
tested.

Place-by-place
analysis: static and multiplier

For the place-by-place model, I examined 1st,
10th, 20th, 50th, 100th, and 250th place finishing times from both races. In
each case, I either subtracted the 2013 time from the 2015 time to get a static
conversion factor (a certain number of seconds) for each place, or I divided
the 2013 time by the 2015 time to get a multiplier conversion factor (a
percentage). The places I chose were of
course arbitrary; I stopped at 250th because I wanted to limit model to
relatively fast runners—250th place this year was a hair over six minutes. In

*all*cases, the 2015 time for a given finishing place was slower than in 2013. The confidence intervals ( ~95%) were developed by using twice the standard error of the sample mean (I'm pretty sure this is the correct method but it's been quite a while since I've taken a formal stats course, so by all means let me know if I've veered off course!).

__Result:__
Static: The 2015 course was

**10.7 ± 3.7 seconds**slower

Multiplier: Your 2015 time multiplied by

**0.9649 ± 0.008**gives the equivalent 2013 time
Descriptive
statistics: static and multiplier

When we talk about "descriptive
statistics," we're talking about the mean, standard deviation, and
standard error of a population of measurements.
In the present case, we're talking about the population of runners who
competed at the TC 1 Mile in both 2013 and 2015. As with the place-by-place analysis, I
restricted my data to only include runners who finished in the top 250 places
in

*both*years. This left some 65 runners whose performances I could analyze. Of these, only ten (15%) ran faster in 2015 than they did in 2013. For the static conversion, I computed the time difference between 2015 and 2013 (including the fifteen negative numbers) and determined their standard error. For the multiplier, I divided the 2015 time by the 2013 time and likewise calculated error margins.
Note that, for fast runners, the result here gives
the most generous conversion out of all the statistical methods used. You might think that this is because of the
inherent flaws of a static conversion a six-minute miler is on the course a lot
longer than a four-minute miler, so a static conversion will be overly generous
for the faster runner) but even if you only look at runners who ran under five
minutes in 2013, their mean difference in race time for 2015 was actually

*higher*(14.0 seconds).

__Result:__
Static: The 2015 course was

**13.0 ± 2.9**seconds slower
Multiplier: Your 2015 time multiplied by

**0.9601 ± .009**gives the equivalent 2013 time
Linear
regression: multiplier

A more statistically accurate way of determining a
multiplier conversion factor is to use a statistical method known as linear
regression. Instead of taking the raw
mean of each data point, we use a least-squares regression line to determine
the "best fit" for a line that best represents our data. A full linear regression model would be a
line function like you might remember from algebra class, with the form

*y**= m*where**x**+ b**and x are your 2013 and 2015 times, respectively.***y**m*would be the slope of the line, and*b*would be its y-intercept. In this context those numbers don't really mean anything, they're just a model.
A more simple way to do this would be to force the
y-intercept to equal zero, which simplifies the equation to

*y**= m*. This makes the conversion process easier, but we need to make sure we aren't giving away too much in the way of statistical power by making this simplification. We can do this by comparing the coefficient of determination, also called the R**x**^{2}value. This just tells us how much of the variation in times from 2013 to 2015 can be explained by our model. In this case, the full linear model (with a y-intercept) has an R2 of 0.767, while the simple linear model (no y-intercept) has an R2 value of 0.726, meaning we only lose 4.1% of our explanatory power. Pretty good—and better, this allows us to compare the results from linear regression conversion to our simple mean results from the other models.
I used linear regression to determine a multiplier
only (and not a static value) because finding the analogous value for a static
value is harder—meaning, not automated in MS Excel. I'm sure there is a one-dimensional analogy
to least-squares (minimum distance, probably) but I don't see much value in manually
computing this. In fact it might just be
mathematically identical to the sample mean, but I'm not sure. At this point, I'd rather keep poring over
results than do that proof!

__Result:__
Multiplier: Your 2015 time multiplied by

**0.9581****± 0.009**gives the equivalent 2013 time.
Pro results
only: static and multiplier

Maybe you're a snob who thinks that the pitiful
peons in the open race may have been slowed by the uphill course, but the pros
are a different breed. To answer that
challenge, I looked at only professional runners who competed in both the 2013
and the 2015 race. There were only six:
Garrett Heath, Craig Miller, Jonathan Peterson, Scott Smith, Heather Kampf, and
Meghan Peyton. Despite this, the results
for both static and multiplier conversions were astoundingly similar to the
results from the much larger sample of open runners (and place-by-place
analysis)!

__Result:__
Static: The 2015 course was

**10.2 ± 2.9 seconds**slower
Multiplier: Your 2015 time multiplied by

**0.9616 ± 0.012**gives the equivalent 2013 time
All conversion summarized

The table above presents the result of all seven conversion methods I developed. By visual inspection, and by plugging in different race times, you can see that their results are all very similar and the margin of error is relatively small.

Discussion
and limitations

All in all, it was fairly surprising to me how
well the final results from the seven different statistical models agreed with
each other. Every conversion gives a
time which within the confidence intervals of all of the other conversions, and
the lengths of the confidence intervals themselves are fairly short.

The one major downside to this type of analysis is
that it does tell is

*what*about the course actually caused the ~10 second slowdown from 2013 to 2015. It's a very good bet the 30-foot elevation gain from start to finish played a major role, but some people might argue that the weather had a major impact. True, it was raining, and the temperature was not ideal, but it was actually*colder*in 2013! Race-time temperature was 48 degrees in 2013 compared to 54 degrees this year. You might be able to negotiate and hand-wave your way to chalking up about 2-3 seconds of the slowdown to the rain this year, but not much more than that.
You can play around with the conversion factors to
your heart's content, and I won't bore you with lengthy tables comparing dozens
of equivalent performances. Instead, to
illustrate how well all of these models come together, I'll present a forest
plot that shows what a 4:00.0 in 2013 would be equivalent to on the 2015
course. After seeing this, you can
understand why nobody came close to a sub-four mile! Heath's 4:08.3 from this
year converts to almost exactly the same time he ran last year—the linear
regression multiplier conversion pegs his performance this year as equal to
3:57.9 (plus or minus 2.2 seconds), and his actual time last year was
3:57.1. Not bad!

Conclusion:
A new course?

For competitive runners, this year's Twin Cities 1
Mile was about 10-12 seconds slower than the previous course. Some of this could be explained by the rainy
conditions, but temperatures were not substantially different between 2013 and
2015, so the uphill route remains as the best explanation for the slowdown in
times. In February, I predicted a 5-8 second slowdown based on data from submaximal treadmill tests. If anything, I actually

*underestimated*how slow the course would be by a few seconds! Chalk that up to the rain, I suppose. So far, I've resisted the urge to say "I told you so," but...well, there, I said it. If you're a race director, I'm available for consulting...
Even in perfect conditions, it will remain
extremely difficult to run fast times on the new TC 1 Mile course. This is very unfortunate, as it was a very
special opportunity for elite runners to be in the local spotlight. Additionally, breaking the still-standing
course records will be nigh impossible.
This will detract from the ability of Twin Cities in Motion to recruit
top-flight runners, given that the $10,000 bonus for a course record is out of
reach. Heath's converted time is within
a second of Willis' course record, and women's pro winner Heather Kampf's
converted time was only three seconds off Sara Hall's record from 2011. Finally, we shouldn't underestimate the
marketing potential of being able to see a four-minute mile in person. People in the general population are only
vaguely aware that it is possible for a handful of humans to complete that
task—imagine strolling along Hennepin Avenue on a Thursday evening, only to
discover that four or five men are about to run one before your very eyes!

This is not to say that Twin Cities in Motion did
a bad job. I ran in the race this year,
and TCM did an excellent job with every aspect of the event. It was a great race and I'd love to do it
again. I do with they'd change the
course, though! Given that the new light rail schedule puts the old course
permanently off-limits, selecting a new course is in order. There are a few critical criteria: the course
has to start and finish in an area that can accomodate a few thousand people,
have space at the start for a staging area with port-a-potties, registration
tents, and

**it must be as flat as possible**and should have very few turns. For competitive professional races, the course must not have a net elevation gain of more than ten feet.
To prevent absurdly fast times, the course should
not be a significant net downhill either, though drops of up to about twenty
feet are permissible (as a rough rule of thumb, a downhill will speed you up by
about 2/3 the amount that an equivalent uphill would slow you; by this rule, if
this year's race were simply reversed, times would be about 7-ish seconds
faster than 2013).

There are a lot of good locations in Minneapolis
that could play host to a road mile. If
TCM wants the race to be through downtown, it should be easy to set up a course
heading southeast or northwest, perhaps along Washington Avenue or 6th
Street. These streets run parallel to the
light rail tracks so that should be not an issue. My own humble suggestion is to consider
running the race through the heart of Uptown.
A course starting and/or finishing near Calhoun Square would be a great
"tour" of the uptown area, and there are plenty of bars and
restaurants to host post-race festivities.
The Uptown area plays host to several road races, but all of them just
go along Lake Calhoun—none actually run on the streets!

At the very least, if TCM does not move the course
next year, they should start over with a new course record. According to the statistical models developed
above, breaking Nick Willis and Sara Hall's records would take the equivalent
of a 3:46 and 4:20 mile effort on flat ground.
We can be fairly certain

*that's*not going to happen anytime soon.
looing girl like running man ... be strong

ReplyDeleteSo i thinks this allows us to compare the results from linear regression conversion to our simple mean results from the other models.

ReplyDelete