Two of the four Monkton entries at NSR 2009 were fastest non-qualifiers for their events. (See Regatta Results on a later page.)
Until fairly recently, school crews that had trained for months in order to challenge other crews at the National Schools Regatta or at Henley looked forward to racing knowing that, barring accidents, they would take part in these important events. Times have changed. NSR and HRR are now so overwhelmed with entries that there are often 'Qualifiers' which take the form of processional races which put crews in order of speed. Normally the fastest 12 crews at NSR or the fastest 32 crews at HRR qualify to proceed to ordinary races. To make later rounds more interesting, the times of the crews that qualify are not published by NSR until after the next round. HRR do not publish these times. However, times of crews which do not qualify are published to give them some idea about how they got on. Over the years, at both of these events, Monkton has on more than one occasion been the fastest non-qualifying crew - surely one of the most frustrating positions to finish in.
During the qualifying race, concerned coaches can be seen near the start and finish, recording unofficial times so they can tell their crews the good or bad news in advance of the official results. For a crew that just misses qualification, this unofficial time can give a reasonably accurate indication of how much faster they needed to be to qualify. The times recorded by coaches and by the regatta frequently disagree by a small amount, and occasionally the crucial order in which crews are placed by the two timing teams does not agree. There can be much gnashing of teeth.
One hopes that both timing teams produce reasonably accurate results, but if they are using stopwatches rather than, say, transponders or time-stamped video, then human error creeps in.
As an example, here is an imaginary set of times for four crews in a qualifying race. Three times are shown for each of the four crews. Time A is the accurate time which would have been recorded electronically to a high degree of accuracy if expensive equipment had been available; Time R is the time as recorded by the regatta. For the purposes of this exercise we will assume that the regatta has one watch at the start and another at the finish, and that the overall time is calculated from the times on the two watches. Note that TWO times have to be recorded to obtain the overall time of a crew for the course by subtraction. Time U is similarly obtained by an unofficial team of coaches, again using a watch at the start and another watch at the finish.
| Crew | Accurate | Regatta | Unofficial | |||||
|---|---|---|---|---|---|---|---|---|
| Pos | Time | Pos | Time | Error | Pos | Time | Error | |
| Crew 1 | 4 | 5:12.125 | 4 | 5:12.3 | 0.275 | 4 | 5:10.9 | -1.225 |
| Crew 2 | 2 | *5:09.731 | 2 | *5:09.6 | -0.131 | 3 | 5:08.9 | -0.831 |
| Crew 3 | 3 | 5:09.817 | 3 | 5:09.9 | 0.983 | 2 | *5:08.8 | -1.117 |
| Crew 4 | 1 | *5.07.438 | 1 | *5:07.3 | -0.138 | 1 | *5:06.6 | -0.762 |
| Crew 2 beats Crew 3 by: | 0.086 | BR=0.3 | BU=-0.1 | |||||
Notice that the unofficial times are all about one second fast; this is perhaps because the unofficial timing team is not placed exactly on the start and finish lines. This does not invalidate the unofficial exercise because it is only the order of speed that matters. In this particular race two of the four crews qualified. Qualifying crews according to the three systems are marked with stars, and, as can be seen, there is disagreement.
Human beings do not use stopwatches with complete accuracy. A study of a large number of times recorded by experienced timekeepers at the Head of the River Race indicates that the standard deviation of the errors in times recorded manually from a watch is approximately 0.1sec.
In the above table, if the accurate times are used, Crew 2 beats Crew 3 by 0.086 seconds; according to the regatta the time difference is BR = 0.3 seconds and according to the unofficial timing the difference is BU = -0.1 seconds. It is the difference in the signs of these last two values which indicates there is disagreement about the finishing order between the timing systems. Note that for each calculation of BR, a total of four stopwatch times is needed (start and finish times for two crews). If BR is treated as a variable, its standard deviation is 2 x 0.1sec.
Assuming the standard deviation of errors on a single stopwatch is 0.1sec, various probabilities may be estimated.
Firstly, let us ignore the unofficial timing team.
Regattas often announce times to the nearest 0.1sec. If times are obtained from one set of watches, the probability that the time given is correct is about 0.4, and claims that times are correct to within 0.1sec must be taken with a pinch of salt.
What is the probability that the regatta will record the correct finishing order of two crews? Clearly, if the real time difference between the two crews is large (say 10 seconds), the regatta will always get the answer correct (** but see caveats below). At the other extreme, if the two crews happen to do exactly the same time according to an accurate atomic clock, and the regatta places them in a finishing order, it will get the answer wrong half the time. The regatta will get the answer correct 99% of the time if the actual difference in the times of the two crews is about 0.5 seconds.
When two timing teams are involved, there are three possible outcomes: the two timing teams agree on the finishing order and are both correct; they agree but are in fact both wrong; they disagree. The only occasons on which there may be an argument between the two timing teams is when they disagree. If the two crews in fact record exactly the same time, the probability of each timing team arriving at the correct finishing order is 0.5; the probability that both timing teams get the answer right is 0.25 and the probability that they both agree (right or wrong) is 0.5.
Disagreement is a major concern only if the discrepancy happens to involve crews near the qualification cut-off point. Unofficial timekeepers may then go to the regatta organisers to query the results. If the different finishing orders are caused by disagreements about a crew's time, and the time difference is more than about a second, one of the two timing teams has made a serious error beyond that caused by the small errors which arise when stopwatch times are recorded. But what about the cases where the time differences are less than about a second? The condition for a legitimate complaint is that the regatta has got the order of crews wrong and the unofficial timekeepers have got it right. The following table gives the probabilities for actual time differences for the crews ranging from zero (dead heat) to 1.0sec:
| actual time difference | 0.0 | 0.10 | 0.20 | 0.30 | 0.50 | 1.00 |
| pr(regatta is wrong) | 0.50 | 0.31 | 0.16 | 0.07 | 0.01 | 0.00 |
| pr(unofficial is correct) | 0.50 | 0.69 | 0.84 | 0.93 | 0.99 | 1.00 |
| pr(legitimate complaint) | 0.25 | 0.21 | 0.13 | 0.07 | 0.01 | 0.00 |
So, if you are the fastest non-qualifying crew and you think you missed qualifying by a small margin, the regatta is almost certainly correct in turning down your appeal. If the times disagree by much more than a second, one of the two timing teams has made a major blunder, and both should consider double-checking their work. The regatta will probably have at least two, and preferably three timing teams giving independent results (Do they, I wonder?), and they will be in a stronger position than you are to eliminate obvious mistakes.
If you find that you are the fastest non-qualifier, don't complain - row faster next time!
** Although the standard deviation of the errors on a single stopwatch is found to be approximately 0.1sec, this estimate from HORR has been calculated after ignoring some wildly inaccurate times. Even experienced timekeepers make blunders, and the frequency of these increases during a long timing session. (The standard deviation of errors is found to remain stable, but the number of times which have be rejected because they are obviously wrong increases.) The HORR uses at least three timing teams, allowing wildly inaccurate times to be ignored. If a head race relies on a single timing team, the published finishing order will be more reliable than the individual times, but without cross-checks with back-up systems, there may be significant errors caused by muddling of crew numbers, transposition of digits in times, major stopwatch errors, etc.
Julian Bewick