The model uses head race results as the primary data source. We include the Fairbairn Cup (first boats only) and Lent term events with at least three college crews. We’d like to include Pembroke Regatta and other side-by-side events, but the model doesn’t currently support it. Adding this is on our list of future improvements.
The main analysis is a linear regression to predict each crew’s average speed in each event. This analysis divides the crew’s average speed into three components: the crew’s true speed (which is what we care about); the event and its conditions; and unmeasurable variation.
The main goal of the statistical model is to estimate a crew’s true speed. However, a crew races at most a few times each term, which isn’t enough data to estimate its speed reliably. Therefore, we use a Bayesian hierarchical model. This model uses hypotheses based on our experience of college crews and analysing past results.
We start with a hypothesis of each crew’s speed before considering any race results. We use the expected speed of a crew at their bumps start position. If we have to predict a club we have no data for (normally small clubs like ARU or Addenbrookes), this is all we use.
The other main hypothesis is that, for any club/sex combination, if one of their boats is fast (or slow) then their other boats are too. For example, if your club’s M1 is much faster than normal, your M2 is too. We also suppose that the gaps between each crew are similar: so that the gap between an M1 and M2, or M2 and M3, are similar between clubs.
When there’s little data about a crew, we rely on assuming these hypotheses are true to make predictions. More data refines these hypotheses by indicating the correct amount of information sharing, answering: how much does a college’s M2 tell us about the speed of their M1 and M3? More crew-specific data reduces our reliance on information sharing.
Next, we want to include event-specific factors like the weather and its length.
We currently estimate event conditions based on crew performance relative to expectations. In the future, we want to include additional data (e.g. wind and stream speed), but we’re struggling to measure these reliably, especially for off-Cam races, and to determine when each division ran to relate weather data to speed data.
The adjustment has two components: one for the overall event and one for the specific division, applied similarly within the Bayesian hierarchical model.
The intuition is that, if crews A and B had similar speeds in the same division last week but different speeds this week, we’d assume some of the difference is due to changing conditions. With just two crews this would be impossible, but by considering all race times, we can estimate this. When there isn’t enough data, we assume the events are similar, but with wide uncertainty.
View our adjustments for each division on our events page and view our adjusted times for each result in our database.
We allow a term for unmeasurable variation. That’s everything else, including subs, daily performance differences, issues crews had (e.g. crabs), and within-division condition changes.
To simulate one division on one day of Bumps, we estimate a crew’s speed, apply the random variation factor, and calculate when bumps will occur. This determines if a bump occurs before the participants are involved in another bump or the chased boat rows over. We include the starting positions of each boat and the luck inherent in making contact. The most important factor is the relative speeds of the crews.
We simulate each set of Bumps 10,000 times to create crew-by-crew probabilities. These probabilities account for our uncertainty about the crews’ relative speeds and daily performance variation.
Our overall prediction is the simulation with the highest expected BumpIt score. The scoring heavily penalizes being very wrong (e.g.: predicting an overbump when one doesn’t happen), so the prediction tends to be conservative and not predict as many bumps.
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