“Jules Goux won in 1921 with this Ballot 3L racer the first Italian Grand Prix near Brescia.”
Source: Autorennen : Die Grossen Preise der Welt ….. von 1894 bis Heute / Adriano Cimarosti; p. 53.
The drawing of the Ballot-desmodesign with the text (translated from German into English):
Right The Desmodromic valve actuation from the three liter Ballot from 1921, is taken from the same source.

ballot3 ballot4

ballot1text ballot1 ballot6

Cimarosti doesn’t work in a scientific way and so he does not directly mention the sources for his data and assertions. This is also the case of his text by the picture on this page. Since he is the only one with this desmo-statement and since there is no other text nor are there any pictures from the supposed desmo-engine, we must face the possibility that Ballot never produced a desmo-engine.
Reason to transfer this Brand from “Systems” to “Supposed desmo, but actually non-desmo”

Further comment by Sebastien Faures, a Vintage car specialist from France:
Ballot was an engine manufacturer only before WWI, his first cars appearing after WWI. In 1919, Ballot launched its famous twin-cam 8 cyl. 5 liters racing car on the Indy track.
For 1920 and 1921, this racing car was scaled down to 3 liters to be in accordance with new Indy and Grand Prix regulations.
All these cars were designed by the Swiss engineer Ernest Henry.
Ernest Henry was previously the designer of the famous racing Peugeot twin-cam 1912-1914. As it has been demonstrated by Griffith Borgeson, none of the Peugeot’s was Desmo. As it is clearly shown on Ballot drawings, neither the 1919 nor the 1920 Ballot cars were Desmo, and there is a very high probability that the 1921 car was identical to the 1920 car. For 1921, Ernest Henry designed the Ballot 2 liter twin-cam (4 cyl only) as well, which was the first commercial touring car ever with a twin-cam engine. This was the Ballot 2LS. This engine was neither a Desmo. Before the end of 1921, Ernest Henry left Ballot for Sunbeam where he designed the 1922 Sunbeam Grand Prix car. This car also was not Desmo. After 1922, Ernest Henry never designed any engine again.
At Ballot, at the end of 1921, after the departure of Ernest Henry, a new chief engineer called Louis Germain (from Panhard-Levassor) was entrusted to design a more simple car and so cheaper touring car for mass production than the 2LS. This became a 2 liter 4 cyl. with a single overhead camshaft and vertical valves. The car was called the Ballot 2LT and was presented at the end of 1922. Later Ballot wished to replace the sporty 2LS as it was too expensive to produce. Several studies were made by Louis Germain to create then a sporty derivative of the 2LT. The result was the Ballot 2LTS: same cylinder-bloc as the 2LT (so 4 cyl and 2 liter), with as well a single overhead camshaft, but with sporty hemispherical combustion chambers allowed by V-shape valves (internal angle: 45°) driven by the overhead camshaft via rockers.
The Ballot 2LTS was presented in 1925. So it is highly probable that it was when working on the 2LS replacement, leading to the 2LTS, that Louis Germain studied the eventuality of a Desmo system, the one described in the patent. In addition: – the Desmo system described in the patent is shown on a single overhead camshaft engine with V-shape valves (but here the angle is 77°), so you see the relation with the 2LTS studies (and Ernest Henry never designed a single overhead camshaft engine), – the date of the patent is end 1924/end 1925, exactly the period when Louis Germain was chief-engineer at Ballot (at that time Ernest Henry had left Ballot already for at leat 3 years) and exactly the period when the 2LTS was being studied.
– Ernest Henry, as great as he was, never designed a Desmo engine.
– So none of the Peugeot and Ballot racing cars did have a Desmo engine.
– The only Desmo impact in all this is solely a study (no physical application, other than in possible prototype form)
made by Louis Germain, when studying the Ballot 2LS replacement.

Used references:
“The Classic Twin-can Engine” by Griffith Borgeson, chapter six : “Ballot” p. 73-86
“Ballot’s Production Car Era” by Griffith Borgeson in “Automobile Quarterly” n° 21/2 (1983)
“Les 2 litres et 8 cylindres Ballot” by Paul Frère in “L’automobile historique” n° 7 (Mars/Avril 2001)