• One-Swap Method
  • Discussion
• Two-Swaps Method
  • Discussion
• Other Considerations
• Resources

Seat racing is a method employed in rowing to identify the fastest athletes in crew boats. A popular format is to race two crews of four athletes against each other six times. By swapping athletes between boats after every race the method aims to identify the relative strength of athletes. This is constrained by the fact that in rowing boats, unlike in sculling boats, an athlete rows either on stroke or bow side and a crew must contain two of each.

Below we are presenting and discussing seat racing methods. The One-Swap Method is the traditional format. For practical purposes, six races are typically conducted. More races would provide more data but also lead to considerable fatigue.

The one-swap method swaps after every race one rower from one boat against another rower from the other boat. The change in winning margin in the next race is attributed to the two athletes who swapped between the boats.

As an example, we are racing in two boats R, and Q, with 8 athletes: a to d are rowing on bow side, and 1 to 4 are rowing on stroke side. Each crew is comprised of two stroke and two bow siders. A swap either swaps a stroke sider or a bow sider between boats.

We observe the following results (in seconds) over 750m with a rolling start. Further details like a cap on the stroke rate and the involvement of a cox could be agreed but is does not matter for the analysis as long as both crews are racing under the same conditions. This requires that they race side by side or in sequence but at the same time to avoid changing conditions.

In the table above, each athlete (a to d, 1 to 4) is assigned a boat, R or Q; and for each boat a race time is recorded in seconds. The Margin is the time R is faster than Q (positive margin), or slower (negative margin). For example, in Race 2 the margin is 5.0 seconds, so R was faster by 5 seconds. After every race two athletes swap boats. We observe how the margin changes.

For Race 2, b swaps from R to Q and c from Q to R. The margin changes from 0.3 in Race 1 to 5.0 in Race 2, so a change of 4.7s. This change is attributed to the swap: The margin increased by 4.7s, so R became faster relative to Q by 4.7s; this change is attributed as "c is 4.7s faster than b". For all races:

We can also compare Race 6 and Race 1 because their crews differ by one swap. All other pairs of races, like Race 3 and Race 5, differ by more than one swap and so the change in margin can't be attributed to two athletes.

In summary, we found these athletes speeds from faster to slower:

• c (faster by 4.0 than) d (faster by 0.7 than) b
• 2 (faster by 3.3 than) 3 (faster by 4.6 than) 4

We can't observe the speed of athletes a and 1 relative to other athletes on their side.

• The appeal of the method is the connection between change in winning margin and the previous swap. At the same time, this could lead swapped athletes to work harder after a swap, knowing that they will be judged on the current race.

• In the example, athletes a and 1 are not observed, and are racing together in the same boat for all six races in R. It could be argued that this does not create equal and fair conditions. A different swap plan could address this but we need to be careful to maintain the desirable property that we can observe six pairs or athletes.

• We compare athletes c and b directly in Race 2, but also indirectly in Race 6 (b,d) and Race 4 (c,d). In this case the result is the same but this is not a given and can lead to ambiguous results.

• The method does not lead to a complete ranking within the two groups. Thus, we need to plan ahead which athletes we are interested in and which not.

• Over the six races, conditions may change and athletes become tired. This may lead to absolute racing times to change. For example, after a swap both boats are slower than in the previous race. This method does not take this into account and only looks at the winning margin and its changes.

In the two-swaps method after each race, two athletes from each boat move into the other boat and vice versa: one from each side. For each rower, the total time he or she is racing is added up. Unlike in the one-swap method, every race counts for everyone.

The total time each rower accumulated defines their position in the ranking - separately for each side.

The athletes in this example are the same as in the previous one. Now we can see how athletes a and 1, for which we had no data, are ranked. Given the small differences, athletes b and d, as well as 1 and 3, are effectively of similar speed.

• The appeal of the method is that it provides a full ranking of each side with the same number of races as before and therefore extracts more information from the same number of races.

• A potential disadvantage could be that this method only indirectly compares athletes.

• Athletes use a specific shell different number of times. This could bias results. In particular, b stays in R for all races.

• The analysis of the result is simpler compared to the one-swap method.

• The fastest crew is potentially {c,d,2,3} but this crew never raced together and therefore this is a hypothesis and not an observation.

The swap matrix above has some desirable properties:

• Athlete "a" races with each athlete from his/her group two times. So "a" and "b" will have two races together. And "a" will have three races with each athlete from the other group. For example, "a" will race three times with "1". Likewise for all other athletes: two races with anyone on the same side and three races with each athlete on the other side.

• Ideally, each athlete would have three races in each shell. But this is not possible while maintaining the symmetry above. In the matrix above 4 athletes have 3/3 races, 3 athletes have 4/2 races and one athlete has 6/0 races.

    a b c d 1 2 3 4
    _ _ x x _ _ x x
    x _ x _ _ x _ x
    _ x x _ _ x x _
    x x _ _ _ _ x x
    _ x _ x _ x _ x
    x _ _ x _ x x _

    3 3 3 3 0 4 4 4

Another matrix is possible where two athletes split their races between the two boats 5/1.

    a b c d 1 2 3 4
    x x _ _ x x _ _
    x _ x _ _ x _ x
    x _ _ x x _ _ x
    x x _ _ _ _ x x
    _ x _ x _ x _ x
    _ x x _ x _ _ x

    4 4 2 2 3 3 1 5

Seat racing produces a ranking per (stroke, bow) side. Could we obtain single global ranking over all athletes? We can't in the case of rowing. If we assume that the speed of a boat is a function of the power the crew produces, consider: when we keep crews the same but take away 50W from every stroke-side rower and add it to a bow-side rower, the total power in each crew would be the same as before but the ranking over all rowers would be different. So seat racing can't infer the power contribution of individual rowers without making additional assumptions.

If the two shells are not identical, this could impact results: not all athletes are racing the same number of times in both shells. In particular, in the example athlete b never switches shells.

Seat racing results can be sabotaged by collusion. If an athlete believes or knows that they can't benefit from the result they could decide to help or hinder someone else. In highly competitive situations it is thus unwise to create a situation where this could happen without consequences.

• D.J. Holland - one-swap method
• World Rowing - one-swap method but based on fixed time of racing.
• British Rowing - a description of the one-swap method.
• Christian Lindig - a look at the math behind seat racing with the two-swaps method.
• Mike Purcer - two-swaps method, including spreadsheets for download.
• Row2k - stories from coaches, this suggests that people have strong beliefs about this but this does not have a lot of details.