I just saw this thread...I'll add my two cents. I appreciate your contributions, BP.
I think it is justified to vary the weight of your bets. No question about it. With the spectrum of opportunities that we analyze, if we have any (justifiable) confidence in what we are doing, we have to. A few examples with hypothetical bet amounts:
1. I like a game, been following the team a little, expect a good effort tonight, blah, blah. My est. of prob. of a cover (P(cover)) around 53%; maybe I throw a $100 on it. Let's say $100 is a 1 unit bet.
2. I like an NFL or NBA side, I've had conversations with respected cappers about this play, there is some consensus, I get some reduced juice...P(cover) around 53.5%; 2 Unit bet.
3. I like an NBA or NFL total, similar consensus from some cappers, I shop and make sure I'm getting the best of it...P(cover) around 54%; 3 Unit bet.
4. CBB Side or total from respected capping service I may use, if I can fill my order without losing best number (not likely with totals) ...P(cover) around 54.5%; 4 Unit bet
5. CFB side from my model, with agreement from respected associates ... P(cover) around 55%; 5 unit bet
6. CFB total from my model....P(Cover) around 100%....OK around 55.5%; 6 unit bet
7. RAS release....P(cover) around 56%; 7 unit bet (of course as we've discussed and seen, RAS releases move extremely quickly so I may not be able to fill my order, but I would take that much at his release number).
8. WNBA, Arena Football, WFC, Tennis, Mispriced props, NASCAR (I don't bet, but fits the example), Golf and any other obscure sport where you either have the selections of a competent capper or find exceptional value you should and must bet more if possible.
The "trick" is to assess the P(cover) as accurately as possible. That is impossible for a novice but if you have been betting, capping, and/or using services for an extended period of time, you should have a decent estimate of expected long-term performance.
With your experience, I'm sure you are well aware of this. If your question was more directed at should an individual capper release selections with weightings that vary from 1-10, my knee jerk response is no because he likely is doing his own work and, therefore, his mortal lock probably isn't too much better than his standard selection. Many cappers release higher rated plays in the hopes of reversing a bad record. If they are down 40 units on 1 or 2 star selections, they might try to get it all back with a 50 star lock. That said, it would be justifiable for a capper to release a range of units if he did this consistently over time and it was clear to all that he wasn't chasing, especially if he gave write-ups to support the strength of the selection. It would be up to the consumer to determine if a multiple weighted selection usually outperforms single weights for this capper and bet size accordingly.
I bet in a range of approx. 1-10 units for the reasons given above. I've been doing it a very long time and have had good success.
It bares repeating that I'm not suggesting you bet 4 times as much on Jim Feist's (or anyone else's) 4 star release as their 1 star release unless YOU are confident (we know they are) it will hit a couple % higher over the LONG TERM. It is imperative that you determine, as best you can, the Probability a selection will cover. For example, let's say you have a local bookie that gives a free half point on every selection. (I used to know guys that did such things, they are defunct of course). Do your homework, learn the push percentages etc., and evaluate your advantage. You simply must bet more when your advantage is greater. Don't run from this; you must estimate your advantage or you are giving away tremendous value.
If I were posting selections on this or any other board, I think I would be forced to limit the range of my weights from 1-3 or possibly 1-4, otherwise the critics will scream that I am gaming the system. If I were posting my bets for someone to follow I would post in a 1-10 range because that is what I do. The goal is to make money. I'd rather hit 50% of my bets but win my higher weights, than hit 55% of my bets a make less money.
As far as the mathematical demonstration, I don't have time for that. It should be obvious that betting more when your advantage is greater will yield better results. Honestly, if you have no idea how to evaluate when you have a greater P(cover) then you are in trouble. Of course you must manage your bankroll wisely. A 10 unit bet for me isn't 10% of my bankroll, not by a long shot. It's a function of how much I'm targeting to earn in a year, how many units I expect to win, and what my pain tolerance is. To each their own.
Best of luck.