What would be cool is if there were a lot of options when setting up the tournament, such as whether you want to have an RP or BE entrance fee. If you chose RP stakes for your tournament, then the tournament prizes would be granted in RP and/or RP exclusive rewards. If you chose BE stakes, then the tournament prizes would be BE.
The prize structure could be set up like this:
1 RP of prize = 1 Tourney Credit; Tourney Credits can be "cashed out" converted back 1:1 for RP, or they can be used to purchase tournament exclusive rewards. Tournament exclusive rewards could include special skins, ward skins, borders, etc. Example: Triumphant Ryze skin for 1,500 Tourney Credits + a "Triumph Token" from finishing as the #1 team or top 5 solo players in an elimination tournament. Less prestigious but still exclusive prizes would be available for Tourney Credits without the "Triumph Token" requirement.
10,000 BE of prize = 1 Hextech Gem(?) up to a maximum of 3 gems
Ie., 1st place 5 players = 50% prize pool/5 -30,000 BE +3 gems if sufficient prize pool;
2nd place 5 players = 25% prize pool/5 -20,000 BE +2 gems if sufficient prize pool;
3rd place 5 players = 15% prize pool/5 -10,000 BE +1 gem if sufficient prize pool;
Runner-up 10 players = 10% prize pool/10 as BE only
For the total 1st through 3rd place prizes, a maximum total of 300,000 BE would be converted to a maximum total of 30 gems distributed to participants. For the pool to get that large, it would need to be a large tournament or have very high entry fees.
For all winners, 1 BE of remaining prize after gems deduction = 1 BE direct reward pay-out
To prevent manipulation of the system (abuse to convert BE to gems or RP to tourney credits without real competition), a minimum number of tournament participants should be required to host a prized tournament, especially for private tournaments. If the minimum number of participants is not met by the planned tournament starting time, then all stakes would be refunded to their owners and the tournament would be canceled.
There could even be an option for a mixed stake pool, where an (less) RP and (more) BE stake amount could be set and the players could choose their preferred option (probably the BE option for most) and prizes would be drawn from the mixed pool. Ie., if 80/100 players choose to stake 10,000 BE and 20/100 stake 500 RP, then the prize pool would contain 800,000 BE and 10,000 RP from which to draw prizes from, so the #1 team might receive 50% of the pool divided by their 5 players for 1 Triumph Token, 1,000 Tourney Credits, 3 gems, and 50,000 BE per 1st place winner.
Essentially, when a person is setting up a tournament, they could set entry fees for RP and BE, and then they could mark whether the entry fee is AND/OR. They could also include a sponsor contribution to the prize pool from any source (ie., if Riot was sponsoring the tournament, they could contribute 5,000 RP and 30,000 BE directly to the pool if they so chose). It should also be possible to setup a tournament with no entree fee, but then the prize is either entirely contributed by the sponsor(s) or there is no in-game prize (ie., casual tournament with no reward beyond the fun of participating). If the fee is AND (ie., 500 RP + 0 BE for an RP-only fee) then the expected prizes (ie., 2,000 tourney credits + 1 Triumph Token for each 1st prize team member) from the expected total pool based on required number of participants (ie., 40 players) would be visible to entrants. If the fee is OR, then just the running totals (of both RP and BE) for the pool and number of filled/required participant slots would be visible to entrants.
That's how I would set it up personally - allowing the freedom for different stake types and different prize structures. If a Rioter wants more feedback about the system I am imagining, please let me know and I can provide more details about the tourney credits, tournament structures, etc.