Initial analysis of NTRP to WTN mapping - Much larger ranges than you'd think!

The USTA launched showing player's WTN on their profile earlier this week and I made some anecdotal observations yesterday, but have now started to do a more scientific analysis and while it is by no means complete, I wanted to share some initial results from it.

For this analysis I'm looking at male players with a 4.0C or 4.5C year-end rating for 2021.  The theory is that since NTRP is only published once a year, this is the most recent rating/level and should be the most relevant to compare with.  Yes, I'm doing the same for 4.0 and 4.5 females, it will come shortly.

With this population of players, I can then look at the range of WTNs for each level to see how things map in practice.  I've included the average and standard deviation here too:

• 4.0 singles - range: 32.2 to 4.4, average: 17.6, standard deviation: 3.2
• 4.0 doubles - range: 34.0 to 3.3, average: 21.4, standard deviation: 4.1
• 4.5 singles - range: 32.3 to 5.1, average: 14.4, standard deviation: 3.4
• 4.5 doubles - range: 31.1 to 2.4, average: 17.2, standard deviation: 4.9

The first thing that jumps out is some pretty astonishing ranges.  If a single NTRP level can span up to 30 WTN levels, it makes interpreting a WTN very difficult to say the least.  It could of course be that WTN is far better and the NTRP levels for these players is way off as well, but ranges this large make you go hmmm and require further analysis.

On the other hand, the averages do kind of make sense.  It is interesting that within a level, the singles WTN is significantly better than doubles, in fact on average this has a 4.0 singles player being rated about the same as a 4.5 doubles player.  Given there are separate singles and doubles ratings, I don't know that one can actually compare them as I'm not sure there is any correlation between them.

But the wide ranges could be due to a handful of edge cases and the general population is more consistent.  The standard deviations help here and, assuming a normal distribution, means that about 68% of 4.0 singles ratings are going to be between 20.8 and 14.4, and that is a lot more palatable, but still 68% leaves a significant number outside of that range.  And that range is wider than the Game zONe (generally about +/-2) meaning even by the USTA's definition, some portion of this 68% won't be evenly matched, let alone those outside of it.  And the doubles standard deviations are significantly higher.

But, the above is looking at all players.  The WTN does have a confidence number that is presumably based on number of matches played and gets higher (up to 100) as the algorithm considers a WTN to be more accurate.  If I do the same stats as above but for WTNs with a confidence of 70 or higher, it is better but still broad ranges.

• 4.0 singles - range: 27.4 to 10.1, average: 16.8, standard deviation: 2.6
• 4.0 doubles - range: 31.7 to 3.9, average: 20.4, standard deviation: 3.5
• 4.5 singles - range: 25.7 to 6.7, average: 13.7, standard deviation: 2.6
• 4.5 doubles - range: 28.4 to 3.3, average: 15.8, standard deviation: 3.9

It is interesting that the average gets better in every case by around a point as the confidence gets higher.  The standard deviations drop but are still above the +/-2 the Game zONe tends to be.

More analysis to come including getting this data in some charts, but I wanted to share initial observations right away.