The baton stick passed in a relay race symbolizes a written message passed in a capsule by courier in the far old days.
And the Estonians and Finns call the relay race in sports exactly as 'running with message': teatejooks, viestijuoksu (where teade[Spoiler (click to open)]https://new-etymology.livejournal.com/163846.html, viesti is 'information, message', Rus. весть [vest']).
Interestingly, the Estonians also still call any train and bus stations as jaam[Spoiler (click to open)]https://eesti-keel.livejournal.com/184187.html - which is a very old archaic name for stations where horses where changed, in the mailing transportation within Russia (Tartaria).
And passing messages in a capsule seems to have been learnt from the ETs. Here is a proof of this (Frederick Valentich' message sent to us in a capsule found on the Soviet-Chinese border in 1982, four years after his plane disappearance near Australia) : https://www.facebook.com/kalju.patustaja/posts/178042329660061