Implied Probability  How does the bookmaker distributes his margin?
You often see the odds proportional calculation: odds = payout rate / (implied) probability > (implied) probability = payout rate / odds.
This leads to equal bookmaker margins (= (1 / payout rate)  1) and different risk buffers (= 1 / odds  (implied) probability) for all outcomes.
An example: odds 1.2 / 5.0 > payout rate = 1.2 * 5.0 / (1.2 + 5.0) = 6 / 6.2 = 0.96774 > (implied) probabilities 0.80645 / 0.19355 > expected values (= probability * odds) 0.96774 / 0.96774 > margins 0.03333 / 0.03333 & risk buffers 0.02688 / 0.00645.
Impact of an 2% probability error:
A) +2% / 2% > expected values: 0.99174 / 0.86774
B) 2% / +2% > expected values: 0.94374 / 1.06774
> Tipsters who constantly finds this kind of error would make a nice profit 6.774%.
I never liked this because i don't understand why the bookmaker would use that much higher / lower risk buffers for smaller / bigger odds.
Of course he'll get much more wagers on lower odds, but since odds are being calculated with the inverse of probability, the potential damage of a faulty probability assumption corresponds with the odds.
Alternatively the equal risk buffer method: odds = 1 / (probability + (whole market margin / number of outcomes)) > probability = (1 / odds)  (whole market margin / number of outcomes).
This leads to different bookmaker margins and equal risk buffers for every outcome.
In the example: odds 1.2 / 5.0 > whole market margin = (1 / 0.96774)  1 = 0.03333 > (implied) probabilities 0.81667 / 0.18333 > expected values (= probability * odds) 0.98 / 0.91667 > margins 0.02 / 0.08333 > risk buffers 0.01667 / 0.01667.
Impact of an 2% probability error:
A) +2% / 2% > expected values: 1.00400 / 0.81667
B) 2% / +2% > expected values: 0.95600 / 1.01667
> Even a tipster who finds such error repeatedly won't get rich.
So, if i would be a bookmaker, i wouldn't use the odds proportional calculation but the equal risk buffer method.
Statistics suggests that bookmakers use rather the latter. Betting on all pinnacle sports closing odds leads to smaller losses with lower odds and far greater losses with bigger odds.
Even laws of market economy suggests that the larger the turnover (> lower odds vs higher odds) the smaller the margin.
Practical use: Over the years i saw a few betting colleagues mourning that although they beat the pinnacle sports closing line by 5% or more they still were in the reds and how unlucky they felt.
For me the reason wasn't a lack of luck but the explanation above. Beating a @6+ pinnacle sports closing line even by 5% just equals a probability difference < 0.8% and that's just not enough even for low margins / risk buffers pinnacle sports.
