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Tuesday, April 19, 2011

A 2:03:02. 3 to 4 min? What effect did the wind have?

2:03:02 dissected.  What effect did the tailwind have? 3 to 4 minutes...?

I don't know the answer to that question.  Let me say that right upfront.  It's insoluble.  But it's too intriguing not to ask, and attempt to answer, and there are a few approaches to it to shed light on a  quite remarkable Boston Marathon, now that the wind has died down and the dust settled on the fastest two marathons in history. Just where do Geoffrey Mutai's 2:03:02 (and, for that matter, Moses Mosop's 2:03:06) rank in the history of marathon performances?

Not a recognized record - why not?

As you'll know, Mutai's record will not be accepted as the official world record.  The main reason is that Boston is a point-to-point course with an overall drop in elevation greater than 1 m per kilometer, a one in a thousand drop (Boston drops by 135 m).  Also, a second criteria for course eligibility is that "The start and finish points of a course, measured along a theoretical straight line between them, shall not be further apart than 50% of the race distance".  This would apply to Boston, because the course is basically a straight line running north-east, and that is why a south-westerly wind, as we saw today, would have such a profound effect.  The image below (click to enlarge), again taken from Letsrun.com in their preview, shows this nicely.  The wunderground.com site had the wind at 14mph westerly, incidentally.

So not recognizing Mutai's time is indirectly influenced by the wind (as indicated by that second clause which would help to prevent a 'wind-aided' record), but it's mainly because of the drop, despite the fact that Boston is actually a slower course than the other Majors, as we'll see below.  But the real meat of this debate is the effect of the wind on the times?  And what would Mutai have run on any other course?

Let's repeat that this question is unanswerable.  We will never know exactly what Mutai would be capable of on a flat, fast course like Berlin or Rotterdam on a still day.  We will never be able to quantify the improvement that might have occurred thanks to the tailwind during today's race.

Equally, we will never know how much Boston's relatively tougher profile, with its Newton Hills in the second half, costs runners compared to the flat and fast courses in Europe and Chicago.  So to ask "What could Mutai have run in Berlin?" is a rather futile exercise.  I know this, and so this is somewhat speculative.  But it's also an intriguing one, and there are some analytical approaches that one can take to help remove guesswork and rather be informed speculation!  And that is the purpose of this post!

So, what effect did the wind have on Mutai, Mosop and co?

The mathematical approach - drag, wind resistance and improvement

I must confess this is not my first approach to the problem, but it is the best one.  My first approach is physiology and the physiological variance in performance, combined with historical context, as you'll see below.  But if you have the physics, then this approach brings some objectivity.

The two problems with this are that you need to make some assumptions about how to treat the runner - a cylinder with a given drag, and an assumed mass and height.  Also, you cannot always know that the wind is from behind, and nor do you know its speed the whole way, so there are estimates, but I still feel you still get valuable information given the length of the course, provided you make valid inputs.  It gets us into the ballpark.

So thanks to djconnel and Giovanni Ciriani for their inputs on this, which I'm pasting directly below:
Assume a human is 1.7 meters tall by 40 cm wide, with Cd close to 1 for a cylinder with normal wind incidence.  That's CdA = 1.5 meters squared.  Then assume the wind is blowing at around 2 m/sec (very fast for road-level given how fast these guys are running) with an air density near 1.2 kg/m-cubed.   That's 6.25 N = 6.25 kJ/km.   Minetti measured close to 3.4 kJ/km/km for running: http://jap.physiology.org/content/93/3/1039.full.  So if a runner weighs 60 kg, that's 204 J/m, of which the tailwind is saving 6.25 J/m, which if speed is proportional to power, is 3.8 minutes saved. (courtesy djconnel).   
 So that's 3 min and 48 seconds.

And then there is this, the wind resistance and relative velocity argument:
Aerodynamic drag for a runner is about 3% of forces acting against him/her. Today's wind in Boston (according to wunderground.com) was 14 mph W to E, which is just about the same speed the top runners were running at. Therefore the runners didn't experience aerodynamic drag. Since their power output remained the same, a 3% advantage translates directly into a 3% higher speed, and a 3% lower time = 3 min and 36 sec. (Courtesy G. Ciriani)
I'm going to work with an engineer to see if it's possible to refine the assumptions a little and work towards a clearer understanding of the physics.  However, we're in the ball park of 2 to 3%, 3 to 4 minutes.  Now, let's compare that to performance variations.

Historical approach.  Understanding the context of performance, Boston vs other marathons

I'm a big believer in history, as it applies to performance.  That's both "institutional history" and individual history.  Historical context is important, because it points to what should be expected in terms of improvements in performance.  Outliers happen, yes, like Bob Beamon almost jumping right over the pit in 1968, but when this happens, there is often an explanation, or at least part of one.  That's the value of context.

And so when you have an outlier, historical lessons become even more valuable.  2:03:02 is an outlier, because it's almost a full minute faster than the current record, and it was achieved on a course that is generally recognized to be slower than the other big city courses (with the exception of NY).

So the first way to examine the effect of the wind on Mutai's performance is to ask how large an outlier it is for the Boston course specifically?  The graph below shows the winning times in Boston since 1990.

The average winning time, excluding today, is 2:09:20, and interestingly, in the last TEN years since 2000, it has been 2:09:30.  Boston is one of the few major marathons where times have NOT plummeted in the last decade.  If you would rather compare Mutai to the best ever in Boston, then the previous record, only one year older, is that of Robert Cheruiyot, at 2:05:52.

So Mutai is 6:18 faster than the average and 2:50 faster than the next best time in Boston's history (with the exception of positions 2,3 and 4 in the same race, of course!).  It's important to start with Boston-comparisons only, because as we'll see shortly, Boston cannot be directly compared to London, Chicago or Berlin without some correction for Boston's hills and slower course.  What is more, the top four today all bettered the previous fastest Boston time by a considerable margin, since Hall finished in 2:04:58 to claim fourth.

Clearly, the wind had a significant effect on today's times, unless you believe that Mutai is genuinely a 2:03:02 guy in Boston, and by extension, that Mosop is at the same level, two minutes faster than the next best ever.  You also have to believe that Hall is a 2:05 or faster runner on a hilly course (which many feel doesn't suit him).

And remember, these are all Boston times, and the flaw in the argument becomes apparent when you consider how "slow" Boston is compared to other big city marathons, as shown below:

So Boston "expects" to be 3 minutes slower than the big European races (Rotterdam is as fast, incidentally - we just don't have the times going back 10 years), and 2 minutes slower than Chicago.  Recall that London has been won in 2:05:10, 2:05:19 and 2:04:40 in the last three years.  Berlin - 2:03:59, 2:06:08 and 2:05:08.  Boston?  2:07:46, 2:08:42 and 2:05:52.  Cheruiyot's sub-2:06 brought that down last year, the gap was 1 minute (I don't know the wind conditions then though), but generally, it's 3 minutes or more (Yes, there are years where Boston is super slow, and there are years when it is much faster, but last year, the 2:05:52 was the first time ever that Boston was within a minute of the other races.  So I don't think it's unreasonable to view Boston as slower)

Mutai vs Boston vs flat courses

This helps us understand where Mutai's performance ranks.   If you believe Mutai is a 2:03:02 man in Boston, then you're either saying that hills don't affect him, or that he could be a 2:01 performer or better in London and Berlin!  So we have something of a circular argument, it has to be said.  If you believe that Mutai is genuinely 2:03:02 material, then you can dismiss the impact of the wind.  But if you believe him to be a 2:05 runner, maybe 2:04:00 on the right day, then you have a wind impact of between 1 and 2 minutes COMPARED TO A FLAT COURSE.  Now add the Boston "disadvantage" due to hills and the wind is again coming out to 2 to 4 minutes, depending on how much Mutai may have been affected by the hills.

The point is, it's not valid, under any circumstances, to compare Boston times to those of London or Berlin.  Normally, it's for the opposite reason - Boston is slower.   Today, it is the other way around, and that is significant because it helps us understand just how big an effect that tailwind might have had.  In other words, the wind was at least sufficient to overcome a historical difference of 2 to 3 minutes on these other races. 

But Boston is now a minute faster - the wind was responsible for overturning a 3 minute deficit and turning it into a 1 minute advantage.  The wind is therefore estimated to be worth 4 minutes, based purely on historical averages (note that this approach assumes equality of strength of the races over the years, as well as the quality of the athletes at the top - I think this is a sound, valid assumption given the short three to five year period, others may disagree.  Certainly, there was a time when Boston attracted "lesser" runners, but the last five years have been comparable to London, Chicago, Berlin)

If one makes the admittedly tenuous leap that Boston is around 2 to 3 minutes slower, then this 2:03:02 in Boston is worth a...better than a 2:01 in London.  Only an extreme optimist would suggest this, and that's partly because we understand that such dramatic improvements don't happen, and because we know the characters.  So next, we need to look at Mutai, Mosop, Hall and co and ask if these individuals are running "out of character"?

Within runners - an error-prone comparison, but valuable with interpretation

Comparing the same runner in two different events can be fraught with danger, but if you are sensible, there's valuable information there too.  The reason for this is physiological variance - elite runners at this level can have bad days, where they are minutes off their best (Kebede in London may be an example of this.  Cheruiyot yesterday is another).  But when they have great days, they don't go minutes faster.  If you are an elite (and by this, we're talking top 20 ever), you don't leap forward by minutes in one race.  That happens to a Keitany, who has run a "slow" marathon in New York on debut, and then blasts 9 minutes faster in London.  That's not that unexpected, given the context.  But for the already established elite, there is such a thing as "acceptable physiological/performance variance".

So we accept the limitations, but use this to give more context to the physics and the history that we've already discussed.  

Let's take Mutai.  He has shown his marathon credentials on the fast, flat European races, first by running 2:04:55 in Rotterdam, and then 2:05:10 in Berlin.  To improve by 1:53, on the toughest of the three courses, that's a huge improvement.  And yes, runners have breakthrough days, but that margin is too large to simply be a "good day".  At this level, once you're in the top 10 in history (which Mutai was even before today) improvements of 20 seconds are remarkable.  Gebrselassie has set two world records, one by 29 seconds, the next by 26.  Those are breakthroughs for this caliber of athlete. 

1:53 is thus artificially high.  So assume that Mutai was in the same condition as Rotterdam and Berlin, when he ran very close to 2:05 both times.  Then, in Boston, he runs 2 minutes faster on a course that is normally about 2% slower than other courses.  If you assume that Mutai was in great shape, 30 seconds faster than Rotterdam (a huge leap forward in performance), then you still have the wind helping him to the tune of 1:30 compared to a flat course...

Knowing your history and where Boston lies, you know have the worst case where you have to also add time for the Boston profile.  2 minutes?  That's a conservative estimate based on history?  Then suddenly you have between a three and four minute difference made by the windI suggested this in my first write-up after the race, and the physics calculations (assumptions and all) support the estimate - 2 to 3%, 3 to 4 minutes.

To return to the earlier example, if you believe the wind was worth only 1 minute today, then you're effectively saying that Mutai is a 2:04 guy in Boston, which means a 2:02 or better performer in London or Berlin (1 to 2% faster).  Either that, or that he is "immune to hills". 

The same is true for Ryan Hall.  A 2:06:17 runner, Hall has raced the marathon numerous times.  In his case, you have two Boston performances to compare to - a 2:09:40 and a 2:08:40.  Maybe Hall continued his improvement and was in 2:08 or even 2:07:40 shape this year.  He still ran a full 3 minutes faster than this. 

Of course there is variability in performance.  Athletes improve, they get worse.  But by seconds, not minutes in this population, and a three minute improvement, suggests to me close to a 3-minute impact by the wind, if not more. 

For an illustration from years gone by, the last time we had such strong tailwinds in Boston was 1994.  That year, Cosmos Ndeti won the race in a course record that was bettered by only two men until this year (both Cheruiyots, one in 2006, and last year).  Now there are four men going under 2:05 in one race.

But back in 1994, America's Bob Kempainen produced a "Beamonesque" performance by running 2:08:47, which was an American record at the time, and would remain so until Ryan Hall broke it.  Kempainen was a good, but not great runner, and his next best time was 2:12:45.  That's a 3:58 improvement, on the tougher Boston course, thanks to a windy day like we had today.

Yes, there are factors that influence this, which is why his numbers alone don't make this case. But when you have Boston's history, plus the comparison between Boston and other races, plus Mutai and Hall's recent racing credentials over Boston AND other courses, then a picture starts to come into focus.

The pacing and 2:03:02 performance in context

So how big an effect did the wind have?  Impossible to say.  Can we conclude that the wind was worth about 3 to 4 minutes? 2 to 3%  I suspect so.

And so while Mutai's time is exceptional, I would interpret it differently.  2:03:02 is superb running - on the hills of Boston, wind or not, it defies belief.  A second half of 61:05 is eye-popping.  But if that wind is genuinely worth 2 to 3%, as I suspect, then the first half of 61:57 is actually worth about a mid-63 minute first half.  In other words, conservative.  That suddenly explains the searing pace in the second half, and it also helps us understand those final 10km.

The final 10km are also mostly downhill and so a 28:25 is extra-ordinary, but with a wind of even 2% (conservative), plus a relatively physiological "conservative" start, and the ingredients were there for a super fast finish, and an amazing overall time!

I guess we'll never know, but we have a great fall marathon season to look forward to!

The fall marathons and the impact of Boston

What will be fascinating is to see how this impacts the Fall marathons, particularly Berlin.  It's like that Geoffrey Mutai will race there.  Maybe even against Emmanuel Mutai.  And Wanjiru.  Will the elite men, having now touched the 2:03 barrier try to go out in 61:30 for the first half?  That would be faster than Boston's first half, without the downhill start and the following wind, so it's adventurous, but does Boston 2011 change the mindset of the elite?

And if the top men, in a race, do go out in 61:30, or even 61:15, will that pace be sustainable?  That's a fascinating question, and it sets the fall marathons up in a big way.  Remember that until yesterday, only Haile Gebrselassie and Emmanuel Mutai had broken 62 for the second half of a major marathon.  Now we have Geoffrey Mutai and Moses Mosop.  Is that possible with a 61:30 first half?  My initial thought is that a first half of 61:15 to 61:30 is just too quick, for now.  61:45, followed by a 62 min is doable, if the weather conditions are perfect in Berlin, perhaps.

But that's all conjecture - let's wait for October to see!  Marathon running has never been healthier!


P.S.  A late addition to the post. In the discussion to the previous thread, we received a comment from Mike with this link to a running calculator based on Jack Daniels' formulas for pace.  In this calculator, if you assume that the wind was 14 mph tailwind, then the predicted time with zero wind is about 2:10.

There are clearly differences in how the wind is assumed to impact performance!  And our 2 to 3% conclusion in the post above, aided by the physics of some readers, seems to be on the conservative side!  I suspect that this calculation is "idealized" and what you'll probably find is that the variable wind speed and direction in "real-world" Boston conditions, combined with shelter, combined with the different physical stature of runners, accounts for differences.  But overall, I'm pretty confident (but never certain) in the estimation of 2 to 3%, or 3 to 4 minutes thanks to yesterday's wind in Boston.


Ralph said...

You could usthe average times of the top 10 (or 100!) runners over their last 3 or 4 years, and then use regression analysis to assess the impact of Boston on their times for each year - then you could assess the impact of the wind (using the historic wind records) and (for years without find) the profile of the race. If you had the time!