First and Third Trinity Boat Club
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The Club's Results

Pembroke Regatta, Lent Term 2018

2nd men's VIII (2nd division)

Coxed by: Marcus Roberts

Beat Christ's M2 (Canvas)

Preparations for the great struggle began on the evening of 16th. Crew pasta was very good all you can eat fusilli, meat and sauce followed with cake. Well-fed and rested, our warriors gathered in early morning of 17th. They were joined by the new coach Seb, who was wearing a FaT jacket. This confused and demoralised people from Sebs old club and thus made us very happy. The first opponent was Caius M2, who we brushed away. One by one all our rivals fell. The crews who had beaten us in Bedford were no match to us in the regatta. When others asked who we beat, our cox Marcus gave one word: EVERYONE. And as always in such occasions he was thrown into the river. If such starts can be repeated or improved on, then the Bumps look easy as pie.

This was an exciting win, not least for what it says about our odds heading into Bumps. Our starting position is in Division II:

4Caius II
5Lady Margaret II
6Jesus II
7Corpus Christi
9First and Third II
11Downing II

An "M2 headship" is theoretically within reach, although to reach it in four bumps might require Corpus to go up by three as well. Perhaps more importantly, it would require us to be quite quick.

Just how quick is an interesting question. For two boats stationed 1 1/2 lengths apart (30 m) to meet by the end of the course (2.2 to 2.6 km), the chasing crew would have to average a speed at least ~1.15% greater than that of the crew ahead; ~1.36% greater if covering the full 2.6 km, as we would from 9th position. That's a difference of 1-2 seconds per 500 m split. The chasing crew will also be rowing in wash, requiring some additional amount of effort to make speed.

By comparison our side-by-side results with Jesus and Caius were 1/2 and 3/4 of a length over a 1100 m course, whereas a bumping crew would on average have closed about 2/3 of a length (1.1/~2.4 * 1.5 lengths) over that distance (and in wash). It's hard to say what bumping odds those margins indicate, given how different a regatta is from bumps, and how variable a crew's performance can be. But we've got a shot at this.

On the topic of variable crew performance, it is perhaps worthwhile to note that some amount of variability day-to-day might actually make it easier for the faster crews to bump up. Bumps is unusual among races in that it has a non-zero threshold for success, and certain pathological possibilities arise from that fact: one might, for example, imagine a division in which each crew was slightly faster than the crew above, though not quite enough to bump, and thus the headship crew could be 20 or so splits slower than the sandwich boat. In a world where crew performance was perfectly consistent, such pathological rankings would in fact be stable over the week. But in reality, where crew performance is stochastic, that very stochasticity helps to ensure that smallish differences in speed rise to the threshold needed for a bump.

It may be counter-intuitive that a random element can help to give more accurate rankings. Certainly it doesn't help when the random element is very large; in the lower divisions for example the rather high frequency of reciprocal bumps might suggest an excess of randomness. But where we are, in the upper half of Div II, reciprocal bumps are quite rare, while bumps in general are more frequent than in the divisions above, and row-overs more rare. Insofar as one expects day-to-day consistency to increase with skill in the higher positions, one wonders if we are near the "sweet spot", a position where a moderate amount of consistency allows bumps to most efficiently sort crews by speed. Analytically one would expect this to be true when the random element alone would induce bumps at about the same rate as would the non-random element, as is generally the case for systems in so-called "stochastic resonance." But that would take some effort to measure. It is however nonetheless encouraging to think that, in a very real sense, we might have luck on our side.
(A.J.O. Lewis)

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