Apr 01 2019 05:36 PM
Hi guys,
Have got quite a challenging problem.
I'm trying to build a model that produces the probability of horses winning a race.
There are 4 "speedmaps" (i.e. scenarios of how the race might play out) and each scenario has a percentage of how likely it is to happen. There are 3 horses in the race.
So,
Speedmap 1 (happens 40% of the time)
Horse A wins 70%
Horse B wins 25%
Horse C wins 5%
Speedmap 2 (happens 30% of the time)
Horse A wins 30%
Horse B wins 50%
Horse C wins 20%
Speedmap 3 (happens 20% of the time)
Horse A wins 10%
Horse B wins 20%
Horse C wins 70%
Speedmap 4 (happens 10% of the time)
Horse A wins 80%
Horse B wins 10%
Horse C wins 10%
I manually worked out that for this race, the probability of each horse winning is: A = 47%, B=30%, C=23%
How do I build a model in excel where I can input any values in and the probability of the horses winning is spat out?
Would appreciate any help/discussion!!
Thanks!
Apr 03 2019 08:15 AM
I think you need to give more information. What values are you entering? You can generate a random number between 1 and 10 and assign values of - 10,20,20,30,30,30,40,40,40,40 -. That would tell you which "Speed map" to use. So, I'm guessing, you get 3 friends to each select a horse. Then run the random number generator. Then that will show which horse won?
Apr 03 2019 09:33 AM
To get the figures you show either calculate the probability for each horse individually
= SUMPRODUCT( HorseA, Likelihood )
= SUMPRODUCT( HorseB, Likelihood )
= SUMPRODUCT( HorseC, Likelihood )
or as a single calculation
= MMULT( speedmaps, TRANSPOSE(Likelihood) )
[committed with CSE]
where 'Likelihood' is the probability for each speedmap.