double result - odds

[paparainbow]

lets say someone has priced the 3way full time final (%) and the 2way halftime final (%) how can we calculate the double result odds? mathematically speaking the outcomes are not independent, hence you cannot just multiply them. any good ideas?

[Ledu]

Re: double result - odds I'm not sure if I undertood your point but: example: 1X2 = odd = % 1 = 1,60 = 63% X = 3,30 = 30% 2 = 2,10 = 48% Double Chance: 1X = 93% = 1,08 2X = 78% = 1,28

[froment]

Re: double result - odds Ledu, I think you’ve got it wrong – he did not ask for double chance, but double result; that’s market HT home – FT home, and so on, you know. Paparainbow, as far as I know this field, you are right – these events are dependent, so you cannot just multiply them; probability of dependent events A and B is Probability (A and B) = Probability (A) * Probability (B if A fulfilled) This means, you lack data for calculation – you need to know probability of team A to win FT if team A has already won at HT; probability of draw FT if team A has already won HT, ..., probability of team B to win FT if team B has already won HT. Now, this 2-way HT result confuses me a bit – I don’t know which two ways exactly – DNB, or double chance, or what? Anyway, I will try to explain the missing data using the tree. There are three possible events at full time – 1, X or 2; let’s label probailities as FT1, FTX and FT2; and there are two possible events at half time – 1 or 2 (although I don’t know exactly what HT1 is – team A to win, or team A draw no bet, or Team A double chance, etc...; although it does not change the calculation); let’s label probabilities as HT1 and HT2. I also asume you have not built overround into your probabilities, i.e., their sum is 1. Obviously, there are six possible scenarios within second half: 1. Second half started after event 1 at half time, and ended as event 1 at full time – let’s label probability as HT1FT1. 2. Second half started after event 1 at half time, and ended as event X at full time – HT1FTX. 3. Second half started after event 1 at half time, and ended as event 2 at full time – HT1FT2. 4. Second half started after event 2 at half time, and ended as event 1 at full time – HT2FT1. 5. Second half started after event 2 at half time, and ended as event X at full time – HT2FTX. 6. Second half started after event 2 at half time, and ended as event 2 at full time – HT2FT2. Obviously, there are two scenarios that lead to full time event 1 – scenarios 1 and 4; those two events are mutually exclusive – match is either 1 either 2 at halftime, so its probability is sum of those two probabilities. Scenario 1 consists of two events: event 1 at halftime (probability HT1), and event 1 at fulltime IF event at halftime was 1 (probability HT1FT1); those two events are independent, so its probability is multiplication of the two probabilities (in fact, they are independent only from mathematical point of view; in reality, performance of a team within first half, or other occurences – cards, injuries, etc., may give them a boost or depression for second half, so they are not really independent; that in fact means, you cannot really decide probabilities HT1FT1, HT1FTX, etc., before halftime); the same applies for other scenarios. So, finally, we have this equation: FT1 = HT1 * HT1FT1 + HT2 * HT2FT1 In the same way: FTX = HT1 * HT1FTX + HT2 * HT2FTX, and FT2 = HT1 * HT1FT2 + HT2 * HT2FT2 In addition: HT1FT1 + HT1FTX + HT1FT2 = 1, and HT2FT1 + HT2FTX + HT2FT2 = 1 So, you have 5 equations, and 6 variables, and, as I said in the beginning, you’re lacking data to determine the probability you’re after... :\

[Ledu]

Re: double result - odds

Ledu' date=' I think you’ve got it wrong – he did not ask for double chance, but double result; that’s market HT home – FT home, and so on, you know.[/quote'] :spank :D

[paparainbow]

Re: double result - odds i can calculate the h/f by using a live model. i can calculate all the possible outcomes of 1st half and then all the possible final outcoume based on the initial score of 2nd half.. nevertheless this is not a formal mathemarical aproach, more likely a simulation. results are pretty decent and consistent with the bookies outthere. i want to expand my models to other sports, like, basketball, handball or rugby, where calculating exact scores is not the basic idea. This is y i am asking you if you have any ideas

[paparainbow]

Re: double result - odds ps:thanx for your replies