Mapping NTRP to WTN - Men's Singles

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 men's singles.  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 17, but there isn't a true peak in the middle, and to the right of 20 there are some strange drops.  It is certainly possible this is the skill level profile of men 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, there isn't the strange blip that the men's doubles had.

The above is including all players, but if we limit it to those with a high confidence WTN, the chart is at follows:

This looks a bit better, but a bit of a strange step from 14 to 16.

What is dramatically different is the number of players drops over 85%.  It would seem there are very few men that play enough singles to get a high confidence WTN.

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.  What is perhaps not expected is how wide each NTRP level is, although they are probably not as wide as the doubles players.

There are a reasonable number of 4.5s ranging from 8 to 18 with an average of 13.6 and standard deviation of 2.6.  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 11 levels, with some players even beyond that, seems a little high.

Similarly, there are a reasonable number of 4.0s from 11 to 22 with an average of 16.8 and standard deviation of 2.6.  Both of these are significantly better than the doubles and approaching what you might expect.

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 18 has a noticeable segment of players from 3.0 to 4.5.  If WTN were to be right, it would be saying the 3.0s and 4.5s with WTN 18 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 3.0'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.

See the prior post for Women's Doubles, Men's Doubles, and Women's Singles.