Deterministic is by far the best of the winners out of Giulio's Jewel (Speightstown), a three-time winner who died in 2022. Her other foals include the multiple winner Frills (Candy Ride), the winner Nu Pi Lambda (City Zip) and the unraced Seeking Mo Jewel (Nyquist), dam of Imperial Honor (Honor A. P.), third in the Grade 1 American Pharoah Stakes in the US.

Second dam Acadiana (Tiznow) was placed and has two winners, among them Duff One (Harlan's Holiday), a winner placed at Grade 2 level.

Third dam Amelia (Dixieland Band), a Listed winner and a half-sister to the sprinter Bertolini and to Alchemilla, produced seven winners. They include Asakusa Genki (Stormy Atlantic), a Group 3 winner in Japan, Rabbit Run (Tapit), a Group 2 winner in Japan, the multiple graded winner Rainha Da Bateria (Broken Vow), who was also Grade 1-placed, Kindergarden Kid (Dynaformer), a graded winner placed at Grade 1 level, and the graded winner Assateague (Stormy Atlantic), dam of the stakes winner Explorationist (Pioneerof the Nile).

The family also includes He's Had Enough (Tapit), second in the Grade 1 Breeders' Cup Juvenile in 2012 and now a sire, and the sire Bayern (Offlee Wild), a dual Grade 1 winner.

The youngest registered foal of Giulio's Jewel, Morana (Frosted), won on her debut at Turfway Park in March 2026.