Can past performance predict future results? This is a question of many fencers, who wonder if the place they currently are is the place they are always going to be, or if one day they will be able to get an A rating or win a tournament. Of course you wish that your past results did not predict your future ones (unless your past results were already amazing–but that is not true for most of us), but also you know that as you try to improve, other fencers are getting better, making it hard for you to catch up.
Can we predict who will be an Olympian from Y10 or Y12 results? Of course that is not a healthy thing to obsess over, but it is natural to wonder if we can.
I have already sort of looked at this question. In my recent posts When Can Youth and Cadet Fencers Make a Breakthrough? and Y-12 Performance Predicts Cadet Performance Surprisingly Well I look at the correlation between seedings at national championships between consecutive years. However, one person suggested that I look at the correlation between results as well, since that would give a better snapshot of someone’s performance on a given day regardless of any lucky ratings or rankings earned.
Pros and Cons
I will admit that results are a more obvious choice, but when I first thought about this question I initially thought that seeding would be better. However, after more carefully thinking about it, I think that both seeding and results have both advantages and disadvantages for measuring the skill levels at fencers at a point in time. Here are (in my opinion) the pros and cons of each:
| Pros | Cons | ||
| Seeding | Result | Seeding | Result |
| Averages performance over long period | Gives nonrandom placement, regardless of whether a fencer has national points or not | Fencers of same rating and no ranking are randomized | Can be messed up by luck of tournaments |
| Not as affected by injury | Less affected by fencer’s financial resources (single result) | Affected by fencer’s financial resources (ability to earn national points) | Very affected by injury |
Predictive powerpower the probability that a study will correctly reject the null hypothesis when it is false, indicating the sensitivity of a test to detect an effect if it truly exists of one year for the next year
My interest was piqued, so I decided to look at the predictive power of previous results for future performance. Methodology is identical to When can Youth and Cadet fencers make a breakthrough? except I use results instead of initial seeding, so you can look at that if you are interested in the details.
As a reminder here is the result from the previous post:
And here is the new result:
The predictive power of results one year to the next is a bit lower than the predictive power of seeding from one year to the next, but it is still moderately correlated which is decent. Again, predictive power seems to increase slightly as the fencers get older but not in too drastic of a manner (except in mens’ fencing for some reason).
Predictive power of Y12 for Cadet (long term)
Here are the results for the longer term correlations. This one is between the seeding for the 2nd year of Y12 and the 1st year of Cadet.
And here is the new one with results instead of seeding:
Just like the other graphs above, the graph that uses results has slightly lower correlations. However, the correlation between Y12 and Cadet results is about 0.5, which still constitutes moderate predictive power. That is quite high considering that so much can change in 3 years, from height to mindset and motivation.
Linear Regression
If one were to move one place up in their Y12 seeding, how much would they expect to move up in their Cadet seeding 3 years later? I did linear regression which basically makes a y=mx+b line from the scatterplot of Y12 seeding to Cadet seeding. Here are the slopes for the lines when looking at both seeding and results:
For each increase of one place in seeding for Y12, there is an approximate 0.67 gain in seeding for Cadet 3 years later, and for each increase of one place in results in Y12 there is about a 0.55 gain in the later Cadet results.
Conclusion
I am not sure what ideas you had coming into this article, but you may have either confirmed your suspicions or changed your mind. Let me know what you think in the comments. I’d say that overall, I think that past performance can do a pretty good job predicting future results.
Here and here are the data if you would like to look at it yourself!
