*Italian translation at settesei.it*

Clearly, height matters. On average, tall players can serve faster and more effectively than can shorter players. And usually, short players who succeed on tour do so by returning and moving better than their taller colleagues. The conventional wisdom is that height is an advantage, but only up to a point. An inch or two above six feet (a range between 185 and 190 cm) is good, but much more than that is too much. No player above 6’4″ (193 cm, Marat Safin) has ever reached No. 1 in the ATP rankings.

While 5’7″ (170 cm) Diego Schwartzman‘s surprise run to the US Open quarterfinals has brought this issue to the forefront, pundits and fans talk about it all the time. This is a topic crying out for some basic data analysis, yet as is too often the case in tennis, some really simple work is missing from the conversation. Let’s try to fix that.

When I say “basic,” I really mean it. We all know that tall men hit more aces than short men. But how many? How strong is the relationship between height and, say, first serve points won? In this post, I’ll show the relationship between height and each of nine different stats, from overall records to serve- and return-specific numbers.

For my dataset, I took age-25 seasons from 1998 to 2017 in which the player completed at least 30 tour-level matches. (I used only one season per player so that the best players with the longest careers wouldn’t be weighted too heavily.) That gives us 156 player-seasons, from Hicham Arazi and Greg Rusedski in 1998 up to Schwartzman and Jack Sock in 2017. There aren’t very many players at the extremes, so I lumped together everyone 5’8″ (173 cm) and below and did the same with everyone 6’5″ (196 cm) and above. I also grouped players standing 5’10” with those at 5’9″, because there were only four 5’10” guys in the dataset.

That gives us nine “height levels”: one per inch from 5’8″ to 6’5″ with the exception of 5’10”. (The ATP website displays heights in meters, but its database must record and/or store them in inches, because every height translates to something close to an integer height in inches. For example, no player is listed at 174 cm, or 5’8.5″.) Some individual heights are certainly exaggerated, as male athletes and their organizations tend to do, but we have to make do with the information available, and we may assume that the exaggerations are fairly consistent.

Let’s start with the most basic building block of tennis, the match win. There is a reasonably strong relationship here, although the group of players at 6’1″ is nearly as good as the tallest subset. In each of these graphs, height is given on the horizontal axis in centimeters, from 173 (the 5’8″ and below group) up to 196 (the 6’5″ and higher group).

There is a similar, albeit slightly weaker, relationship when we look at the level of single points. Since a small difference in points results in a larger difference in matches won (at the extreme, winning 55% of points translates to nearly a 100% chance of winning the match) this isn’t a surprise. At the match level, r^2 = 0.38, and at the point level, below, r^2 = 0.27:

(If you’re wondering how all of the averages are above 50%, it’s because the sample is limited to player-seasons with at least 30 matches. A fair number of those matches are against players who aren’t tour regulars, and the regulars–the guys in this sample–win a hefty proportion of those matches.)

**Serve stats**

Now we get to confirm our main assumptions. Taller players are better servers, and the gap is enormous, ranging from 60% of service points won for the shortest players up to nearly 70% for the tallest:

As strong as that relationship is (r^2 = 0.81), the relationship between height and ace rate is stronger still, at r^2 = 0.83:

Aces don’t tell the whole story–the stat with the strongest correlation to height is first serve points won (r^2 = 0.92) as you can see here:

But this is where things start to get interesting. Nearly every inch makes a player more effective on the first serve, but opponents are able to negotiate tall players’ second serves much more successfully. There remains a modest relationship with height (r^2 = 0.18), but it is the weakest of all the stats presented here:

It’s nice to be tall, as anyone who has seen John Isner casually spin a second-serve ace out of the reach of an unlucky opponent. But except in the tallest category, height doesn’t confer much of a second-serve advantage. Players standing 6’4″ (193 cm) win about as many second-serve points as do players at 5’9″ (175 cm). That doesn’t mean that the second serves of the shorter players are just as good–they probably aren’t–but that shorter players tend to possess other skills that they can leverage in second-serve points, which usually last longer. For the purposes of today’s overview, it doesn’t really matter *why *short players are able to negate the advantage of height on second serve points, just that they are clearly able to do so.

**Return stats**

We wouldn’t be having this conversation–and David Ferrer wouldn’t be headed to a likely place in the Hall of Fame–if the inverse relationship between height and return effectiveness weren’t nearly as strong as the positive one between height and serving prowess. “Nearly” is the key word here. The relationship between height and overall return points won is almost as strong (r^2 = 0.74) as that of height and overall service points won, but not quite:

Schwartzman is doing more than his part to hold up the left side of that trendline: He is both the shortest player in the top 50 and the best returner. On first serve points, however, there’s only so much the returner can do, so while shorter players still have an advantage, it is less substantial. The relationship here is a bit weaker, at r^2 = 0.63:

It follows, then, that the relationship between height and second-serve return points won must be stronger, at r^2 = 0.77:

The overall and first-serve return point graphs make clear just how much worse the tallest players are than the rest of the pack. The graphs exaggerate it a bit, because I’ve grouped players from 6’5″ all the way up to 6’11”, and the Isners of the sport are considerably less effective than players such as Marin Cilic. Still, we find plenty of confirmation for the conventional wisdom that a height of 6’2″ or 6’3″ (188 cm to 190 cm) allows for players to remain effective on both sides of the ball, while a small increase from there can be a disadvantage.

**A note on selection bias**

It’s easy to lapse into shorthand and say something like, “shorter players are better returners.” More precisely, what we mean is, “of the players who have become tour regulars, shorter players are better returners.” They have to be, because it is nearly impossible for them to be top-tier servers. If they’ve cracked the top 50, they *must* have developed a world-class return game. The shorter the player, the more likely this is true.

The same logic is considerably weaker if we descend a couple rungs lower on the ladder of tennis skill. In collegiate tennis, it’s still an advantage to be tall–as Isner can attest–but a player such as 5’10” Benjamin Becker can serve as well as nearly all the competition he will face at that level.

**One more note on selection bias**

My choice to use each player’s age-25 season might understate the ability of either short or tall players. It is possible that certain playing styles result in earlier or later peaks, meaning that while tall players could be better at age 25, shorter players may be superior at age 28. There are anecdotes that support the argument in both directions, so I don’t think it’s a major issue, but it is one worthy of additional study.

**Further reading**

A guest post on this blog earlier this year posed the question, Are Taller Players the Future of Tennis?

I didn’t mention serve speed in the above, but here’s a quick study of the fastest serves and their correlation with height.