First of all, we still need to list the expected rate of return formula (Kelly value formula) as follows:
1) parameter a: average probability (AP, the negative average probability of the main win and draw is expressed as APH, APD and APA respectively, which is the average value of the negative probability of the win and draw judged by each company accurately corresponding to the odds of the European compensation system of each company.
2) Parameter B: Odds (main wins, flat losses are represented as OH, OD and OA respectively).
3) parameter c: expectED rate of return (Kelly value) (EH, the main winning average negative Kelly value is expressed as EH, ed and EA respectively).
EH=OH * APH
ED=OD* APD
EA=OA* APA
4) Parameter D: Possibility (the negative probability of the main victory is expressed as PH, PD and PA respectively).
PH= 1.0/OH * R
PD= 1.0/OD * R
PA= 1.0/OA * R
5) parameter e: return rate r
R= 1.0/（ 1.0/OH+ 1.0/OD/+ 1.0/OA）
Then we analyze the data of Cagliari by quoting the data recorded by TIP-EX from Messner in Serie A on 1 1 2, 2006:
Singbet 2.000 2.900 3.900 45 3 1 23 0.85 0.92 1.00 9 1
Ladbrokes 2. 100 2.800 3.500 43 32 26 0.89 0.89 0.90 89
(The first set of three digits represents the odds, the second set of three digits represents the probability of occurrence (%), the third set of three digits represents the Kelly value, and the last column represents the European compensation return rate of the company. )
Now let's assume that there is only one company in the market, SINGBET, so the average probability of the market is its own probability, and its main victory Kelly value is calculated as follows:
EH=OH * APH = OH * PH = OH * （ 1.0/OH）* R = R
That is to say, Kelly value is its return rate at this time. Now let's assume that there is another company LADBROKES in the market, and let's see what happens. At this time, APH is equal to the PH of the two companies divided by 2, that is
APH= （45+43）/2=44（%）
APD= （3 1+32）/2=3 1.5（%）
APA= （23+26）/2=24.5（%）
Then we calculate the Kelly values of SINGBET respectively:
EH= 2.0 * 44% =0.88
ED=2.9 * 3 1.5%=0.9 135
EA=3.9 * 24.5%=0.9555
And calculate the Kelly value of LADBROKES company:
EH=2. 1 * 44% =0.92
ED=2.8 * 3 1.5%=0.882
EA=3.50 *24.5%=0.858