The Six Run Average (6RA)

A starting point for getting better at something is to measure where you currently are. If you can measure it, you can improve it. One of our new year resolutions here at EquiRatings is to bring some new 'metrics that matter' to Eventing in 2019. These are metrics that are easy for anyone to measure and understand, and still give real and reliable insight into a horse’s performance. People know all about the power of the FOD now, next stop is the 6RA. 

To calculate your own 6RA, simply take your six previous dressage scores, any level (national or international also works!) add them together and divide by 6 to get your average. That's your current 6RA. 

The science

A 6 Run Average is our new metric for the dressage phase. It is something almost naively simple, but still a great starting point for understanding a horse’s form. In the following analysis the “X Average Previous Runs” is an average of a horse’s previous test scores with the same rider at international events. The average is capped at the last X runs, but where a horse doesn't have X runs, the average is across all of its runs to date. All DR Scores have been adjusted to the 2018 format (i.e. without the multiplier).

So why stop at 6?

For a simple metric like an average of previous tests, there will come a point when averaging over more runs does not yield a better prediction of future performance. This occurs due to a number of factors. The average score smoothens out a horse’s recent form, and after 6 runs the average is pretty stabilised. Also, we know that horses’ DR Scores tend to improve with their number of runs. If we average over too large a number of runs, we may be including tests that occurred a few years ago, and that are not a true representation of a horse’s current ability.

A simple method is to look at the standard deviation (SD) of Prediction Error, against the average of the horse’s previous runs, where Prediction Error is Average Previous DR Scores minus Actual DR Score. The SD is a measure of how accurate the prediction is. For example, if the 6RA has a SD of 3.9 marks, then ~68% of all horses’ scores will fall within 3.9 marks of their 6RA coming into a test.

If we limit the analysis to the top levels (3* and 4* competitions), the predictive power of the “Previous Runs Average” is stronger, but the optimal number of runs to use still stabilises around the same figure of 6-7 runs.

6RA examples at WEG 2018 

So how does this look in a real competition? Below is a table of the top 20 6RA DR tests going into WEG 2018 and the horses’ actual DR Score on the day. Here the average difference of 6RA to DR Score is -0.14 marks, and the SD is 2 marks.

Similarly, if we look at the bottom 20 6RAs at the same competition, we see that the average difference is a full 1.11 marks with an SD of 2.8. This means that at the bottom end of the field, horses scored better than their average coming into the competition. Did these horses save their best performance for the big stage? Did the judges mark this group of higher scoring horses easier than they have done in the past? 

Across the whole competition the average difference between the 6RA and the actual result was 0.14 marks. This is as expected since we are just looking at how much a 7RA is different to a 6RA for the field. The deviation of the error was 2.75 marks, a tighter deviation than we might have expected from a standard CCI4* event.

Conclusion - your 6RA

A horse’s average form is a good starting point for estimating how they might perform at an event, and a maximum of 6 runs is a good range to average over. This number of 6 doesn’t depend on the level a horse is competing at, but a 6RA does lead to a better estimation of future performance for horses that compete at the highest levels.

In addition to your 6RA, learn how to calculate the other Simple Metrics in our toolset.