May 19, 2017

TL;DR Which Types of Partners Win Combined Ratings Doubles

USTA Men’s, Women’s, and Mixed Doubles statistics

We received some very nice comments about the blog series. We also received a request for an “Executive Summary”, we suspect the suggestion came from a reader of HBR or Sloan Management Review. We like the idea and will name these summaries “tl;dr” posts.

  • Who wins doubles matches?
  • 100,000 USTA doubles matches analyzed
    • 2016 season matches
    • 6.0, 7.0, 8.0, and 9.0 NTRP levels
    • Only matches where the sum of both partners’ levels equaled the league level were included
  • Terminology
    • Equal Partners: Both doubles partners have the same NTRP rating, for example, 4.0/4.0, 3.5/3.5, etc.
    • Unequal Partners: Partners have different ratings: 4.5/3.5, 4.0/3.0, etc.
    • Higher Rated Partner (HRP): The Unequal partner with the higher NTRP rating
  • Unequal partners win 56% of the time when playing against Equal partners
  • In Mixed Doubles, when Unequal play Equal
    • Partners with a man HRP win 70% of the time
  • In Mixed Doubles, when both teams are Unequal
    • Partners with a man HRP win 56% of the time
  • The study used only player NTRP ratings
    • In a future post we’ll look at whether dynamic ratings of the players provide more insight


May 11, 2017

Part 5, Unequal vs Unequal Mixed Doubles

Does Gender of the Higher Rated Partner Matter?

We continue our focus on Combined Ratings Mixed Doubles. This post examines Unequal vs. Unequal teams to find out whether the gender of the higher rated partner provides an advantage. That is, does a 4.5 woman partnered with a 3.5 man, for example, win more than a 4.5 man / 3.5 woman when both doubles teams are Unequal? Does gender of the higher rated partner matter?

If you’re new to this blog series, read Part 3 for a recap of the terms used in this tennis blog series. We make every effort to keep the tennis statistics jargon to a minimum.

Part 4 showed that gender of the higher rated partner provides an advantage when Unequal teams play Equal teams. Part 4 also gives a nice recap of the number of matches used in this analysis of USTA matches.

tennis statistics

This chart shows the number of Unequal vs. Unequal Mixed Doubles matches by level that will be used in this analysis. The distribution of matches between levels is very similar to the distribution of men’s, women’s, and overall mixed doubles with most matches in 7.0 and 8.0. The total number Unequal vs. Unequal matches in all 4 levels: about 7,800.

The first chart in Part 4 shows the same info along with Equal vs. Unequal. Unequal vs. Unequal matches are not nearly as common as Equal vs. Unequal. This fact may provide an advantage to readers of this series and especially to users of Tennis League Analytics Team and Player Reports.

First, let’s look at how USTA team captains put together Unequal Mixed Doubles partnerships. In Part 4 we saw that men were the higher rated partner (HRP) in 67% of the matches where Unequal partners played Equal partners. Of course, captains do not know whether their opponents will use Equal or Unequal teams in their lineup.

When looking at matches of Unequal vs. Unequal, the table below shows that men are the HRP in 66% of lineups. This is consistent and expected.



Table 1 - HRP of Mixed Doubles Unequal vs. Unequal Teams (both teams)

Gender of HRP Number of Teams
Men 10,320 66%
Women 5,280 34%
total 15,600 100%



But it only makes sense to look at matches that involve HRP of opposite genders. For example, if the league is 8.0, one team has a 4.5 woman and the other team has a 4.5 man. 3,330 of the 7,807 matches from the previous chart are like this - see the next chart.

tennis statistics

To clarify what this chart shows, let’s look at the 7.0 level. The bar shows that about 1,500 matches were played where the genders of the higher rated prater for each team were opposites. One side had a woman HRP and the other had a man HRP. And similarly for the other levels.

Again, the distribution of matches follows a similar pattern to all the other groups this blog series has examined - this is a good thing and makes the statistics folks feel warm and fuzzy. So, does gender of the higher rated partner make a difference? If gender does not make a difference, the statistical expectation is that both types of teams would win about 50% of the time.

tennis statistics

The chart shows the gender win percentage by Mixed doubles league level. The horizontal red line shows that, overall, teams with men as the HRP win about 56% of the time.

A reasonable conclusion of this series would be for USTA team captains to assemble teams that pair higher rated men with lower rated women.

But what if you knew more than just the USTA ratings of potential team members. What if you were not limited to just the standard 1/2 point increments of USTA ratings, e.g., 3.5, 4.0, 4.5, etc.

What if you knew that a players true strength rating was 3.4, 3.9, or 4.4? Would knowing those details change how a captain would assemble a team or lineup? We’ll address those questions in future posts.

If you like this type of information, please tell your tennis playing friends. And follow us on Twitter or Facebook to know when the latest blog post is available.



April 17, 2017

Part 4, Unequal Mixed Doubles: Does Gender of the Higher Rated Partner Matter?

Which Partnerships win more tennis matches?

So far it seems that Unequal partnerships have an advantage when playing against Equal partners. Now we’ll focus on Mixed doubles to see if the gender of the higher rated partner (HRP) makes a difference. Of course, to do this we’ll look only at matches that involved at least one Unequal partnership. If these terms don’t make sense, read Part 3 of this blog series (scroll down to find that post).

We started this blog series with a little over 100k combined ratings doubles matches at the 6.0, 7.0, 8.0, and 9.0 levels. Of those, about 72k were Mixed doubles as shown in Part 1 of this series. And we found that about 37k of the Mixed doubles matches involved at least one Unequal partnership. Next we’ll drill down to matches of Unequal vs. Equal partners. The chart below shows the split by level and by partnership type.

tennis statistics 1

The chart shows that a very large proportion of Mixed consisted of Equal partnerships vs Unequal on both an overall and per level basis. Unequal vs Equal totals about 30k matches. The math and statistics gurus will like that we have a number of matches that’s big enough to give meaningful conclusions.

Before we look at the gender split of the higher rated winning partner, let’s first look at which gender is more common in the higher rated slot. We’ll check all Unequal partnerships that played Equal partners. This number will help frame the conclusion of this post.



Table 1 - HRP of Mixed Doubles Unequal Teams (vs Equal)

Gender of HRP Number of Teams
Men 20,000 67%
Women 10,000 33%
total 30,000 100%




This table shows that of the about 30k Unequal partnerships that played against Equal partners, the HRP was a man in about 67% of the doubles teams. Team captains seem to choose men 2-to-1 as the higher rated doubles partner. And if the numbers seem too “neat” or “well rounded” to be true, the numbers were rounded to make them easier to read, but were very close to the numbers in the table. Now let’s see the gender split of the winning teams’ HRP.

tennis statistics 1

This chart shows the gender splits of the HRP for Winning Unequal teams. The horizontal line shows the overall split for Men at 70%. Correspondingly, the overall split for Women is 30%. So does this mean that Unequal teams with a man as the HRP have much more success than Unequal teams with a woman as the HRP? The answer is yes, but not as much as you might believe at first.

Remember Table 1 above? It shows that 67% of all Unequal teams had a man as the HRP. So it’s expected that 67% of winning (and losing) teams will have a man HRP. The actual percent of the time that a doubles partnership with a man HRP wins is 70% overall. And the chart shows a similar win percentage within each doubles level. So, yes, a man as the higher rated partner appears to give a Unequal team a better chance of winning when they play an Equal team.

For the tennis-playing data-science types reading this blog - the rest of you can skip this paragraph - the chi-square test blows away the null hypothesis. There is a relationship between gender of the HRP and the match result for these types of matches.

The difference between 70% and 67% may not seem like a big advantage - only 3 percentage points. But a casino would love that small advantage. These 3 percentage points provide an advantage of about 4.5%. That’s in the range of a casino’s advantage for slots and video poker.

If you like this type of tennis information, let us know. And let your tennis playing friends know.

We have one more type of match to look at in this series: Unequal vs. Unequal.




April 2, 2017

Part 3, Is a 4.5/3.5 partnership better than a 4.0/4.0?

Does Gender Make a Difference?

In Part 2 of this series, we looked at 2016 combined ratings doubles league matches and found that, overall, partners with Unequal ratings won about 56% of the time when playing against partners with Equal ratings. The win percentage for Unequal partners in 7.0, 8.0, and 9.0 was similar (see the last chart in Part 2).

It is challenging to write about combined rating system doubles and some terms are used that may be unfamiliar. If you’ve not read Parts 1 and 2 of this series, you may find doing so now beneficial. If you want to skip Parts 1 and 2, here are a few terms that will make this post easier to read.

Combined rating system: A system that limits the combined ratings of doubles partnerships in a doubles league. For example, if the league is identified as 8.0, doubles partnerships may be 4.0/4.0, 4.5/3.5, or 4.0/3.5. Generally, a partnership cannot be separated by more than 1.0 in level, so a 5.0/3.0 would not be allowed. And of course a 4.5/4.0 partnership would not be allowed because it exceeds the league level.

Unequal partners: doubles partners that do not have the same rating, such as a 4.0/3.0, or 4.5/3.5 partnerships.

Equal partners: doubles partners that have the same rating, such as 4.0/4.0, or 3.5/3.5 partnerships.

We now need to ask whether gender affects the results. And eventually we’ll determine how the strength of a player relative to other players of the same rating affects the results. But for now, the focus is gender.

In Part 1 we saw a chart that showed the number of Men’s, Women’s, and Mixed doubles matches that were played in 2016 by four levels - 6.0, 7.0, 8.0, and 9.0. Overall, about 71% of these matches were mixed doubles. And the ratio of men’s-to-women’s-to-mixed appeared graphically similar in each level. So, how does gender affect the likelihood of winning a combined ratings doubles match?

We’ll start with Unequal vs. Equal matches by Men’s, Women’s, and Mixed. Look at the chart below.

tennis statistics 1

This chart shows the Unequal partners win percentage when playing against Equal partners in combined ratings leagues. The winning percentages across each league type are similar. And since Mixed is by far the largest group (71%), it makes sense that its winning percentage of 56.5% is very close to the overall average of 56%. So far these results are consistent with what we found in the previous blog post.

Let’s see what the winning percentages look like when grouped by doubles league rating level.

tennis statistics 1

This chart shows the Unequal partners’ winning percentage vs Equal partners by combined ratings level and league gender. The overall average of 56% appears in orange.

A few observations are:

At the 7.0, 8.0, and 9.0, Unequal partners appear to have an advantage, particularly in Mixed and Men’s. In fact, the only groups where Unequal teams do not win more than 50% of the time are the Men and Women at 6.0 - this is one of the two observations that jump out.

The second observation that jumps out is that at the 9.0 level, Women’s Unequal teams have the highest winning percentage (vs. Equal teams) at 61.4%. We’ll look at why in a future post.

Our next post will focus on Mixed Doubles and whether the gender of the higher rated Unequal partner makes a difference.




March 27, 2017

Part 2, Is a 4.5/3.5 partnership better than a 4.0/4.0?

Combined Rating Doubles Matches: Partners with Equal vs. Unequal Ratings

In the previous post we looked at the types of matches and players included in this statistical analysis to answer the question, "Is a 4.5/3.5 doubles partnership better than a 4.0/4.0?" Keep in mind that that we're looking at not only 8.0 combined ratings doubles but also, 6.0, 7.0, and 9.0 leagues. Now let's delve into the findings. And if you have not read the previous post, you may want to now.

We'll start with some simple observations that lead up to the answers. Of the 100k+ combined ratings doubles matches, the chart below shows the number of matches where all players had the same rating. For example, 3.0/3.0 vs 3.0/3.0, or 4.5/4.5 vs 4.5/4.5.

tennis statistics 2

This shows that in each level, there were more matches played where all four players had the same rating. Overall, in 57% of the matches, all four players had the same rating. Is this because players tend to play more often and form closer ties to other players with the same rating? The data does not tell us. Regardless, are partnerships of equal ratings the best way to form competitive teams for Combined Rating Doubles? We'll see.

Keep in mind that any matches that involved a doubles team whose combined rating totaled less than the league rating was not included (see the previous post for more on this).

It's interesting that at the 9.0 level, the ratio of "Equal-to-Unequal" matches is not as large as for the other levels. We'll look into why in a future post.

Now, let's look only at matches that involved at least one doubles team with unequal ratings. For example, a 4.5/3.5, or 3.0/4.0 partnership. The natural question to ask is, "How many of those matches pitted Equal partners against Unequal partners?"

tennis statistics 3

Overall, of the approximately 100,000 combined rating doubles matches, about 35,000 were Equal vs. Unequal. There are relatively few matches of Unequal vs. Unequal pairs. But those will be interesting to look at when we examine whether the gender of the higher rated player makes a difference.

35,000 matches is a nice sample size to work with and should give interesting results. So, who wins more often when Unequal partners play Equal partners. Another way to ask the same question is, "When Unequal partners play against Equal partners, how often do Unequal partners win?"

tennis statistics 1

Overall, Unequal partners win about 56% of the time. At this point it seems that, over all 4 combined ratings doubles, Unequal partners have an advantage. But we won't know with certainty until we complete some more checks. Let's see if the winning percentage differs by league level since the 7.0 and 8.0 leagues seem to show more wins than the 6.0 and 9.0 leagues.

tennis statistics 4

For 7.0, 8.0, and 9.0, the winning percentage for Unequal doubles partners ranges from 56% to 58%, similar to the overall winning percentage. For 6.0, the percentage is closer to 51%.

Does this mean that in, for example, an 8.0 league you should try to field teams of 4.5/3.5 partnerships rather than 4.0/4.0? Before we draw conclusions, we need to look at whether gender makes a difference. And even then, we may find that we need to take some other factors into account. For example, does knowing which 3.5, 4.0, and 4.5 players are stronger, respectively, than the average 3.5, 4.0, and 4.5 make a difference?




March 22, 2017

Is a 4.5/3.5 partnership better than a 4.0/4.0?

Doubles Matches and Partners with Equal vs. Unequal Ratings

This and the next few posts examine combined rating doubles to determine whether certain level and gender combinations win more often than others. And, more importantly, why?

If you've played in USTA combined rating system leagues, and especially if you've captained a team, you have likely wondered whether it's better to pair players with equal or unequal ratings (e.g., a 4.0 with a 4.0, or a 4.5 with a 3.5).

And in mixed doubles, is it better for the man or woman to have the higher rating?

One school of thought is that a 4.5 player can dominate play. Others feel that a 3.5 player becomes a target for a solid 4.0 doubles pair.

To answer these questions we looked at a little more than 100,000 USTA doubles league matches played in 2016. Only matches where both doubles teams had a combined rating equal to the league rating level were included. So, for an 8.0 league, matches with partnerships of 4.0/4.0 or 4.5/3.5 were included. Any other combinations, such as 4.0/3.5, were not included.

So before we see the answers, let's get a feel for what types of players and matches were examined.

2

This shows that about 80% of the matches were played in 7.0 and 8.0 leagues. This makes sense since most USTA players fall into the 3.5 to 4.0 rating levels.

Next, let's look at the breakout by gender and rating level. This may surprise readers who live in a section or district that offers combined rating leagues only for mixed doubles.

1

Mixed Doubles is by far the most popular format for the combined rating system, accounting for about 71% of matches played. This is more clearly shown the the next chart.

3

Again, the questions are:

  1. What combination of ratings wins more often, unequal (such as 4.5 & 3.5) or equal (such as 4.0 & 4.0)?

  2. For unequal partners, does a partnership with a man or a woman in the higher rated slot win more often? That is, does a partnership of a 4.5 woman/3.5 man win more than 4.5 man/3.5 women?

We'll start to answer these questions in the next post.