A tennis court is 23.77m long and 8.23m wide. A ping-pong table is 2.74m long and 1.525m wide. A tennis racket is up to 0.394m long and 0.317m wide. A ping-pong bat is actually allowed to be any size, but most are around 0.25m long and 0.15m wide. A tennis ball is around 0.067m in diameter, and a ping-pong ball is 0.040m. A tennis net is 3.07m tall and a ping-pong net stands at a lofty 0.1525m.1
Thus we can find an approximate scale factor for these games.
Net height: \[ \frac{3.07}{0.1525} = 20.1 \]
Playing surface length: \[ \frac{23.77}{2.74} = 8.68 \]
Playing surface width: \[ \frac{8.23}{1.525} = 5.40 \]
Racket width: \[ \frac{0.317}{0.15} = 2.11 \]
Ball diameter: \[ \frac{0.067}{0.040} = 1.68 \]
Racket length: \[ \frac{0.394}{0.25} = 1.58 \]
The difference in net height is a whopping 20x. The field of play is 5-10x the size, and the rackets and balls are 1.5-2.5x the size. This makes some sense because tennis rackets twice as large as they currently are would be pretty unwieldy, as would ping-pong paddles at half the size.
We also know that the size of the humans involved is the same, so the scale factor for humans is 1. In general, things “closer” to humans (that they interact with more directly) like the balls and rackets have less of a difference in scale than the playing surface or the net.
This trend informs the general playing styles of the games: in ping-pong, everything is fairly nearby at all times, which lends itself to rapid returns, generating lots of spin to trick opponents within small reaction windows, and so on. Tennis involves a lot more running, physical exertion, and wider distances to cross.
Which brings us to volleying. Imagine a singles tennis point. The serve goes in and is returned. The server hits an approach shot back and rushes the net. The returner decides to hit a zippy line drive just over the net rather than risk a lazy lob. If volleying is disallowed, the point is over. The server must watch the ball go by, where it inevitably bounces far behind the net (thanks to trigonometry and the disproportional net height mentioned). Unless the server has superhuman speed to get to where the ball is bouncing, the point is over.
Likewise, in ping-pong imagine a point with volleying. The serve hits deep with lots of spin, catapulting it high into the air. The returner gets it back, but the server can volley, essentially setting up a wall at the net, reaching far forward to get angles (both wide and short) that are typically impossibly good.
Volleying rules can be thought of as dependent on the scale of the game. Is there a middle ground, a crossover point where volleying starts to make sense? Interestingly, we have an example of a mid-sized solution: pickleball.
In pickleball, there is an area called the “non-volley zone” (or more affectionately, the “kitchen”) between the net and a line on the court. If any part of a player is within this zone, volleying is considered a fault. This rule exists for many of the reasons mentioned above, as it makes the game more fair.
One can imagine infinite gradations between tennis (where the non-volley zone is infinitesimal), and ping-pong (where the zone is infinite). It would surprise me if one of the three games mentioned somehow precisely nailed the goldilocks non-volley zone. We should begin a search of this space immediately! Who knows, we could discover an even-more-fun racket sport.