Mapping NTRP to WTN - Women's Doubles

The USTA has started publishing the new World Tennis Number (WTN) for players on their profile on usta.com.  I did some initial analysis last week, but now I'm able to do a bit more thorough and complete analysis so this begins a sequence of posts with that.

My process for this analysis is to look at a sampling of the USTA League players who received a 2021 year-end rating/level and look at the distribution of WTN levels for each different gender, discipline, and level.

By limiting it to players that received a 2021 year-end level I am only considering players who got a recent NTRP rating so that I'm not using stale NTRP levels in the comparison.  Since NTRP levels don't change again until the end of 2022, a player could have gotten better or worse in the 6 months since ratings were published, but this seems like a reasonably consistent approach to doing this mapping.  Ideally this would be done using WTN ratings at the time the NTRP ratings were published, but we haven't had WTN until now so we do the best we can.

In this post, I'm looking at WTN's for women's doubles.  What you will see in the chart below is the count of players at each WTN level in total and broken out by NTRP level.  So let's have it!

(You likely want to click on the image to see a larger version of it).

Looking at the general distribution, we see a typical normal distribution to the left of WTN 25, but to the right, things aren't quite as prototypical.  There is a significant drop from 25 to 26 and 27, and then is somewhat as expected through 33, but then it is missing the long tail we expect from a normal distribution.  It is certainly possible this is the skill level profile of women doubles players, and it could be that the players that would be in the long tail aren't playing competitive matches and so aren't in the WTN system.

We also see as you move towards single digits, the women fall off quickly.  While there are a good number of women with a WTN of 20, less than a quarter of that number are a WTN 15 and at 12 or lower, there are hardly any.  It will be interesting to compare this chart with the men's to see how different it is, which will give us an idea of how WTN handles gender neutrality.

But looking at the counts by NTRP level is what is perhaps more interesting and will give us an idea of how NTRP maps to WTN.

As you'd expect there is for the most part the expected normal curve within each level, that is until you get to 3.0 and 2.5, where it doesn't tail off at the higher WTNs as noted above.  What is perhaps not expected is how wide each NTRP level is.

There are a reasonable number of 4.5s ranging from 12 to 26 (4 to 32 for all) with an average of 18.7 and standard deviation of 3.8.  If there was a direct and perfect conversion from NTRP to WTN, one NTRP level would correlate with about 4 WTN levels, so having a range of 15 levels, with some players even beyond that, seems very high.

Similarly, there are a reasonable number of 4.0s from 15 to 29 (4 to 33 for all) with an average of 21.9 and standard deviation of 3.3.

The explanation of course is that NTRP and WTN use different algorithms and there is no direct mapping.  And WTN could argue that their algorithm is better and these large ranges are actually correct and more accurate, but that would be indicting NTRP as not being accurate then.

One key algorithm difference is that WTN calculates separate singles and doubles ratings, and that can certainly be the reason for some variance, e.g. someone could be good at doubles and bad at singles but play both.  Their NTRP will be somewhere in the middle but WTN will have the individual ratings farther apart.

Additionally, what matches the USTA includes for WTN has not, to my knowledge, been shared yet.  If WTN includes matches that NTRP does not, that could be contributor to differences between the two systems.

The other thing you can do with this chart is see how many NTRP levels there are at a given WTN level.  For example WTN 25 has a noticeable segment of players from 2.5 to 4.5.  If WTN were to be right, it would be saying the 2.5s and a 4.5s with WTN 25 would have a competitive match.  That seems hard to believe, but perhaps there really are some edge cases where a 4.5 has a rating that is lagging their ability and the WTN algorithm, despite being updated weekly, hasn't caught up with the 2.5's improvement.  But this seems a bit of a stretch.

Which is right?  WTN or NTRP?  I can't say at this point, but stay tuned, I'll keep doing analysis.  And it is likely that neither is "right" or "wrong" and they are just different.

And stay tuned for this same post for the Men's Doubles, Women's Singles, and Men's Singles.

Update: I posted an update that looks at only high confidence WTNs here.