Are A-rated fencers more consistent than E-rated fencers? They should be, but how can we know? Luckily, I have tens of thousands of bouts in my dataset, and I can answer this question (and answering such questions is the basis of the blog)! In this post, I will explore how the distribution of scores varies based on the ratings of two fencers and uncover valuable, and possibly unexpected insights! As usual, the full data is available at the end.

If you enjoy this post, I recommend checking out this one, which looks at score differences across division and weapon:

Why Fencing Is Often So Disappointing: 12% Of Bouts Are Lost by One Point

## Score difference in pool bouts

Let’s begin our exploration by examining the average score differences in pool bouts between fencers of varying ratings. Based on national tournaments bouts from 2017-2020, the average score difference for fencers who are one rating apart is approximately 1.11 points. As the rating differentials increase, we observe a progressive increase in the average score difference between the fencers. For instance, when the rating difference jumps to two, the average score difference rises to 1.81 points. This progression continues, with score differences of 2.43, 3.00, and 3.34, for three, four, and five rating differentials, respectively.

This is all pictured below in the following graph. Each bar between two columns represents the average score difference between those two ratings in a 5 touch bout. For example, the bar that connects the red A column with the orange B column represents that the average score difference between an A and B rated fencer is 1.36 points in a pool bout. Note that for all of these averages, a loss is counted as a negative value, so if an A loses to a B the average score difference will decrease.

In general, barring comparisons of a rating with U, the lines become shorter as we move towards the right. This suggests that the gap between lower ratings is less than that between higher ratings. It also implies that earning a higher rating progressively becomes more difficult, which makes sense.

## Score difference in DE bouts

#### Boxplots

For DEs, I am going to use boxplots to visually represent the distribution, central tendency, and spread of the dataset. Each box represents the interquartile range (IQR), which is the range within which the central 50% of scores fall. The line inside the box indicates the median value, or the middle value when scores are arranged in ascending order. The whiskers extend to 1.5 times the IQR, and outliers are represented by dots outside the min/max.

These boxplots tell an interesting story about the performance of different rated fencers. Let’s break it down:

#### A-rated fencers

A-rated fencers display a high level of consistency against D-, E-, or U-rated fencers, winning on average with a score of around 15-7 for all of them. Each box also has a small IQR, indicating that it’s rare for scores to fall to far out of the 5-10 touch differential range. This shows that A-rated fencers are very consistent, answering the question posed in the title.

#### B-rated fencers

B-rated fencers, show the smallest IQR when fencing another B rated fencer. This indicates that Bs are fairly homogenous in skill. Surprisingly, Bs tend to have a lower average score against lower rated fencers, as compared to As, meaning that A rated fencers are a lot more consistent in beating weaker fencers than Bs.

#### C-rated fencers

C-rated fencers are interesting as they sit in the middle of the skill spectrum. The scores reflect that, as they generally lose to As by almost the same margin as they beat Us. The graph is also relatively symmetrical.

#### D-rated fencers

D-rated fencers tend to perform consistently poorly against both As and Bs (the IQR is small), which indicates a big difference in skill between even proficient Ds and weak Bs.

#### E-rated fencers

This graph is fairly similar to the D-rated fencer graph, but the E-rated fencers have slightly worse outcomes as expected.

#### U-rated fencers

Lastly, the U-rated fencers tell quite a tale. They show a wide range of scores against other Us, which points to it being a heterogeneous group. They lose to As, Bs, and Cs by a similar, and consistent amount.

## Weapon differences

In Unveiling Fencing’s Winning Odds by Rating, I found that Epee fencers had the lowest chance of beating a lower rated fencer. Likewise, in Why Fencing Is Often So Disappointing: 12% of Bouts Are Lost by One Point I found that Epee fencers have closer bouts than the other weapons.

Unsurprisingly, when looking at the score difference for “adjacent ratings” (ratings that are different by one letter), I found that Epee fencers beat lower rated fencers by less than the other weapons.

**Check out the full data here**