A Win is a Win: How Weighted Point Values Don’t Affect Match Outcomes

One of my first SwordSTEM articles was Is It Important To Weigh Target Values?. In this article I tried to correlate a fighter’s win percentage with their preference for scoring high or low value points. In the end it showed that there wasn’t really a correlation between fighters who hit higher value targets and those who won more.

The data was based on 10 events which had a large number of overlapping participants. But times have changed. I have some better ideas on how to test this, and a much, much bigger data set to work with.

A New Adventure

My new approach is to see how many matches would be overturned by flat scoring vs how many would retain the same winners. The methodology was simple:

  • Look up how many times each fighter hit each other.
  • Determine who got more hits in.
  • Compare that against the actual match winner.

Which is all well and good, but how do I know which tournaments to select?

The advantage of working with the 10 events in the first article was that they all had similar rules, allowing them to be treated as the same. Now I am looking at a database of 128 events (541 tournaments), which means that there is a ton of variation.

It is important to filter out tournaments which don’t use weighted scoring, as you are going to see 100% correlation (+ table error) between the number of times hit and the match winners. My first thought was to use the highest point value seen in the tournament. But I know for a fact that scorekeepers make mistakes, and sometimes organizers add extra exchanges to correct things. A tournament with a few hundred 1-point exchanges, and a single 3 point exchange, is still a non-weighted tournament . And thus I moved to looking at the average number of points awarded in a tournament.

But what should I set the threshold at? I decided to sweep through and see at what point the number of tournaments drops off, and…

Why am I seeing about 50 tournaments with an average point value (on scoring exchanges) of less than 1 point? Turns out it is because there are several full afterblow tournaments which are not recording their exchanges correctly. Instead of inputting the proper point values they enter 0 points awarded when both fighters score the same value. So I try again only looking at clean hits, and things look much better.

FYI, not entering your exchanges properly is a violation of the HEMA Scorecard Terms of Use. I’m watching you!

You Haven’t Told Us Anything Useful Yet

Indeed.

Now that I know how I’m going to get my dataset, it’s time to mine some data.

Bam. Looks like there is very little change if we remove weighted scoring. If you disallow ties then you will get the same result 96% of the time. But does it matter how much you are weighing your tournaments? Surely a tournament which awards points from 1-4 will be more likely to overturn results than a tournament which only gives 1-2 points?

Effect of Point Spread

So we repeat the same experiment, while varying the threshold of which tournaments we include. 

Pure Win the Win % when ties are excluded.

Everything seems somewhat stable until we get to an average exchange value of greater than 2.5. After that the weighting seems to become significantly more important. Or does it?

Around 2.5 points per exchange is the region where we get into really small sample sizes. With a few tournaments dominating the narrative the numbers certainly can’t be taken to be indicative of an overall trend. So the original observations stand.

Sanity Check

Earlier I said that I didn’t want to use the maximum points awarded in a single exchange as a criteria to determine if a tournament was weighted or unweighted scoring. But we can use it as a point of comparison with this data, to make sure it is all sensible.

And it looks about the same. After 4 points we are getting into small sample size territory, and we start to see the number of ties increase as a result of our point flattening changes. But overall the same numbers check out.

Why Weight?

This data shows fairly conclusively that weighted scoring really doesn’t affect the outcome of the match very much. Nineteen times out of twenty you will end up with the same overall result. 

But is that even important? Even if the weighting doesn’t affect the match outcome it can still have significant impact on participant behavior. Looking back to Data Mining – SoCal Swordfight Longsword we can see significant changes in the targeting when point values were changed year over year. And this is minor, shuffling the point values within a fairly stable ruleset. Going from tournament to tournament I would expect to see even more variation (as soon as I figure out a good way to parse and wrap my head around it).

Go read the SoCal Data Mining article if you want to know why there is an asterix

Because of its ability to change participant behavior, I still strongly advocate having weighted targets. But it has become very obvious by now that better fencers will get it done regardless of how you award the points.

Stuff for Nerds

Data dumps!

What happens if I look at tournaments with really big score discrepancies.

Number of Eligible Tournaments:

Average Point Theshold All Scoring Exchanges Clean Exchanges Only
0.1 433 415
0.2 433 415
0.3 433 415
0.4 433 415
0.5 433 415
0.6 430 415
0.7 423 415
0.8 413 414
0.9 413 414
1 380 380
1.1 373 373
1.2 369 369
1.3 363 357
1.4 344 337
1.5 318 314
1.6 295 293
1.7 267 262
1.8 241 238
1.9 222 219
2 206 199
2.1 193 185
2.2 163 159
2.3 139 129
2.4 111 106
2.5 86 86
2.6 59 62
2.7 40 48
2.8 32 32
2.9 19 22
3 15 17
3.1 12 16
3.2 11 13
3.3 8 11
3.4 8 8
3.5 5 4
3.6 5 4
3.7 4 4
3.8 4 4
3.9 4 4
4 4 4
4.1 4 4
4.2 3 3
4.3 3 3
4.4 2 2
4.5 2 2
4.6 2 2
4.7 2 2
4.8 2 2
4.9 2 2
5 2 2
5.1 2 2
5.2 2 2
5.3 2 2
5.4 2 2
5.5 2 2
5.6 2 2
5.7 2 2
5.8 2 2
5.9 2 2
6 2 2
6.1 2 2
6.2 2 2
6.3 1 1
6.4 0 1
6.5 0 0
6.6 0 0
6.7 0 0
6.8 0 0
6.9 0 0
7 0 0

 

Number of Matches Affected By Flat Scoring

Average Score Value No Change Tie Different Result
1 16398 602 2071
1.1 16032 602 2067
1.2 15999 602 2053
1.3 15723 596 2004
1.4 14926 575 1922
1.5 13961 555 1789
1.6 13025 533 1650
1.7 11816 470 1412
1.8 10522 439 1279
1.9 9605 404 1175
2 8649 376 1096
2.1 7961 351 1037
2.2 6781 296 940
2.3 5147 226 761
2.4 4134 197 654
2.5 3198 166 552
2.6 2016 134 449
2.7 1379 99 369
2.8 883 68 299
2.9 577 62 210
3 479 55 193
3.1 459 55 190
3.2 353 52 181
3.3 291 51 151
3.4 199 49 134

 

Number of Matches Affected By Flat Scoring

Max Score Value Greater Than No Change Tie Different Result
1 16398 602 2071
2 13464 563 1824
3 6571 337 1041
4 3692 163 597
5 946 29 292
6 696 17 214
7 358 11 149
8 248 10 136
9 197 8 131
About Sean Franklin 78 Articles
Sean has a Bachelor's Degree in Mechatronic Systems Engineering, and is currently employed as a Controls Engineer. He is passionate about developing more analytical ways to view sword fighting, wishing to develop evidence based standards for protective gear and rule sets informed by tournament statistics. His martial arts history includes competitive success, medaling in international competitions for Longsword, Messer, Grappling, Rapier, and Cutting. In addition to competition Sean has been invited to instruct at a number of events across North America and Europe.