It is well-known that the result in a 4x100 relay race is dependent both on the speed of the runners as well as the efficient passing of the baton. A team with four reasonable runners can beat a team with better sprinters by out-performing them in the "handoff zone."
Imagine markers placed at 100, 200 and 300 metres from the starting point. Ten metres on both sides of these markers (a total of 20 metres) constitute the handoff zones. Another ten metres before the start of a handoff zone constitute the "acceleration zone." A runner is allowed to start running in the acceleration zone but the baton must be passed in the handoff zone. Teams which make best use of this 30-metre stretch (times three, since there are three handoffs) will, most likely, win the race.
One of the biggest shocks of the recently concluded IAAF World Championships was China taking silver in the 4x100 men's relay. With no runner of top-class pedigree (their best, Bingtian Su, placed last in the 100 metres final), they still managed to beat more fancied teams like Canada, France, Germany, Great Britain and USA. Obviously, this could have happened only because China's baton passing was superior to the others. But how do we quantify "superior"? I've devised a metric that seems to work well.
I'll explain with a simple example before looking at actual performances. Consider a team of four runners, all with a personal best (PB) of 10.00 seconds. Adding these four times gives a total of 40 seconds. Unless someone runs way below their best, they should finish in a time somewhat less than 40 seconds. How much less depends on how slickly they pass the baton. The more efficiently they use the 30-metre zones (acceleration + handoff), the more their time will fall below 40 seconds. I propose to use the difference between the sum of the personal best times and the actual time run as a measure of "baton-passing efficiency" (BPE). So if the race is run in 38.25 the BPE would be 40.00 � 38.25 = 1.75.
In the final, China's four runners were Mo (PB 10.35), Xie (10.25), Su (9.99) and Zhang (10.00) for a total PB (TPB) of 40.59. They finished in 38.01 for a BPE of 2.58 (40.59 � 38.01).
Canada was represented by Brown (10.05), De Grasse (9.92), Rodney (10.28) and Warner (10.09) for a TPB of 40.34. They ran the final in 38.03, earning a BPE of 2.21 and taking the bronze medal.
Germany, with a TPB of 40.51 (all their runners' PBs were over 10.00, the best being 10.05) finished fourth in 38.15 and a BPE of 2.36. France, with a TPB of 40.27 finished fifth in 38.23 and a BPE of 2.04.
Interestingly, Antigua and Barbuda, with a TPB of 41.30 (average 10.33 per runner) finished sixth and had a BPE of 2.69, the best of all the teams. Just to reach the final was an amazing feat for them given that the PB of one of their runners is 10.89! Even Michelle-Lee Ahye (10.85) and Kelly-Ann Baptiste (10.83) have better PBs than that. Just goes to show that a high BPE can let you punch way above your weight class, to use a boxing term.
Jamaica (Carter � 9.78, Powell � 9.72, Ashmeade � 9.90 and Bolt � 9.58) had a TPB of 38.98 and won in 37.36 for a BPE of 1.62. If they had reached a BPE of just 2.15, they would have broken their own world record of 36.84. Interesting, when Jamaica (Carter � 9.78, Frater � 9.88, Blake � 9.69, Bolt � 9.58) set the world record at the 2012 London Olympics, they did so with a BPE of 2.09.
As another example, T&T's national record is 37.62, set by Thompson (9.82), Burns (9.96), Brown (9.99) and Callender (10.05). They did so with a BPE of 2.20.
It appears that good baton-passing will get you a BPE of about 2.00. Anything over 2.50 is excellent as demonstrated by China and Antigua. It would be amiss of me if I didn't mention that in the semi-final, Antigua clocked 38.01 with a BPE of 3.29! Had they done the same in the final, they would have had the same time as second-placed China.
In a general way, we know that better baton-passing would increase a team's chances of winning. With the BPE metric, we can quantify what we mean by "better" and make more meaningful comparisons of baton-passing efficiency between teams.
Noel Kalicharan