Jul 10, 2010

Actuarial Limit 100m Sprint

In June 2009 Professor of Statistics John Einmahl and (junior) actuary Sander Smeets, calculated the ultimate record for the 100-meter sprint. The actual World record - at that time - was set by Usain Bolt at 9.69 seconds (August 16, 2008, Beijing, China).

With help of the extreme-value theory and based on 'doping free' World Record data (observation period:1991 to June,19 2008) Smeets and Einmahl calculated the fastest time that a man would be ultimately capable of sprinting at: Limit = 9.51 seconds.

As often in actuarial calculation, once your model is finally set, tested and implemented, the world changes...

Or, as a former colleague once friendly answered when I asked him if his ship (project) was still on course:

In this case, the 'model shifting event' took place in Beijing, exactly one year later, on August 16, 2009: Usain Bolt sets a new astonishing 100m World Record in 9.58 seconds !

Of course 9.58 secs is still within the scope of Smeets' and Einmahl's model limit of 9.51 seconds...

Nevertheless, as a common sense actuary, you can see coming a mile away, that this 9.51 secs-limit will not hold as a final future limit.

As is visual clear, one can at least question the validity of the 'extreme-value theory approach' in this 100m sprint case.

Math-Only Models
In this kind of projections (e.g. 100m world records) it's not enough to base estimations only on historical data. No matter how well historical data are projected into future data, things will mesh up!
Why? Because these kind of 'math-only models' fail to incorporate the changes in what's behind and what causes new 100m World Records. To develop more sensible estimates, we'll have to dive into the world of Biomechanics.

To demonstrate this, let's have a quick -amateur - look at some biomechanical data with respect to Usain Bolt's last World Record:

Let's draw a simple conclusion from this chart:

Hitting 9.50 secs seems possible

Just like Bolt stated in an interview: "I think I can go 9.50-something", appears to be realistic:
  • 0.026 secs faster by improving his reaction time to the level of his best competitors: 0.12secs, instead of  0.146secs
  • 0.060 secs faster by reaching his maximum speed (12.35 m/s) at V50 and maintaining this speed for the remaining 50 meters. 

Biomechanical explanations
On top of this, Bolt outperforms his competitors on having a higher step length and a lower step frequency. This implies there must be deeper biomechanical factors like body weight, leg strength, leg length & stiffness (etc), that need to be included in a model to develop more realistic outcomes.

Newest biomechanical research ("The biological limits to running speed are imposed from the ground up" ) shows maximum (theoretical?) speeds of 14 m/s are within reach, leading to potential World Records of around 9 secs on the long run.....

Based on this new biomechanical information output in combination with an appropriate chosen corresponding logistic model, we can now predict a more realistic ultimate World Record Estimation (WRE) in time.

Curvefitting at ZunZun with the 1968-2009 data (including Bolt's 9.58 secs record) on basis of a Weibull CDF With Offset (c), led to the next, best fit equation:

With: y=WRE in seconds, x=Excel date number, and:
a =  -3.81253229860548
b =  41926.0524625578
c =  8.97894916004274 (=final limit)

As we may learn more about biometrics in the near future, perhaps the ultimate 9 seconds (8.9789 seconds, more exactly) can possibly be reached faster than we currently estimate (year 2200).

Now, just play around with (estimate) world records in this Google time series plotter:

As actuaries, what can we learn from this 'sprinting example'?
Well... Take a look at estimating future (2030 a.f.) mortality rates.

Just like with estimating World Records, it seems almost impossible to estimate future mortality rates just on basis of extrapolating history.

No matter the quality of the data or your model, without additional information what's behind this mortality development, future estimations seem worthless and risky.

Although more and more factors affecting retirement mortality are being analysed, (bio)genetic and medical information should be studied by actuaries and translated into output that strengthens the devlopment of new mortality estimate models.

Actuaries, leave your comfortable Qx-houses and get started!

Related links and sources:
- Ultimate 100m world records through extreme-value theory
- 90 years of records
- Usain Bolt: The Science of Running Really Fast
- Biomechanics Report WC Berlin 2009 Sprint Men
- BP WC Berlin 2009 - Analysis of Bolt: average speed 
- The biological limits to running speed (2010)
- Limits to running speed in dogs, horses and humans (2008)
- Improving running economy and efficiency
- Factors Affecting Retirement Mortality and Their Impact ... 
- Cheetah Sets New World Record 100 meter sprint2009 (6.130 sec)
- 100m World record data and WRE (xls spreadsheet)

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