# Calculating a distribution from a gameline

I am trying to learn some statistics and I was given a task.

Above you can see a game line for basketball match between Milano and Olympiacos teams. What I know is this:

• I can calculate probability from coefficient using this formula: p = 1 / (c(1+m)) where m=0.025, 0.05, 0.075, ...

• Coefficient in Spread near -3.5 (1.90) means probability p1=0.5 for Milano team to win a match by 4 or more points(marked as -4, -5, -6,...)

• Coefficient near +3.5 (1.90) means a probability(p2 = 1- p1 = 0.5) for Milano team to win by 3, 2 or 1 point or to lose the game(marked as -3, -2, -1, 1, 2, 3, ...)

• Field Total contains total points of the game

• Coefficient near O 165.5 means a probability(p_o=0.488) for both teams to get a total of 166 or more points
• Coefficient near U 165.5 means a probability(p_u=1-p_o=0.512) for both teams to get a total of 165 or less points.
• In the same way coefficients in Money Line column means probabilities for one or another team to win the match.

I need to calculate the distribution of Spreads using which I could calculate the probability of Milano team winning by any amount of points.

I do not want you to give me the solution, I just want to know, where do I even start with this?

I want to write a python app which would take these coefficients as an input and give me a table with distributions as an output later, but I need to figure out the maths...

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• You don't have enough information to calculate the distribution based on this snapshot. Usually statisticians estimate distribution parameters on the basis of a sample of observations (which maybe games in your situation). – Alexey Burnakov Sep 12 at 13:49
• @Alexey Burnakov So basically I need to get historical data of the games of these two teams and then find the right distribution? – milka1117 2 days ago
• I would say you need in-game dynamics for multiple games. – Alexey Burnakov 2 days ago