Probability Calculator

**wildwestarena** · 01-26-2016, 01:33 AM

Hello Forum,

I have a unique request. I am trying to figure out how to set up an excel spreadsheet to help me enter rodeos. I ride saddle broncs professionally and would like to figure out a good way to determine which rodeos to enter and what days to enter them for.

For example: Rodeo A costs $200 to enter, it pays $5000 to win it, $4000 for 2nd, $3000 for 3rd, there are going to be 50 contestants where statistically an 82 (out of 100 possible) score wins the rodeo and a score of 80 wins third. The rodeo is 300 miles from my house so it will cost me around $300 in travel expenses.

Rodeo B costs $50 to enter, it pays $800 to win it and $500 for 2nd, there will only be 12 contestants where statistically a 77 point score wins it and a 67 gets second. The rodeo is 40 miles from my house so it will cost me around $10 in travel expenses.

Rodeo C costs $150 to enter, it pays $1000 to win it, $800 for 2nd, $600 for 3rd, $400 for 4th, and $200 for 5th, there will be 75 contestants where statistically a 90 point score wins it and an 82 wins 5th. The rodeo is 100 miles from my house and will cost me $80 in travel expenses.

I can only enter one of these rodeos, which would be the best bang for my buck, keep in mind a 77 score is a lot easier to achieve than a 90.

I want to be able to set this up for the 500+ rodeos there are in a year to determine which 75 rodeos would be best to attend. There are also some other variables we could discuss later. One variable is different bucking horses are easier to achieve higher scores. Some rodeos are typically won with higher scores but that's because the bucking horses are better and it is easier to achieve a higher score. Also, most rodeos are more than one day but you only enter for one day and compete against people during the rest of the days, i.e. a Friday-Saturday rodeo usually has lower scores on the friday then on saturday or vice versa. Some rodeos are Friday-Saturday-Sunday and they only want their good horses out one day so they will put them up saturday so you have a better chance getting a higher score on saturday so if you're up saturday, by default, you will outscore 2/3 of your opponents. These added variables can be discussed after developing a basic spreadsheet, though.

Thank you so much for your time.

**mrice** · 01-26-2016, 03:59 PM

A common way to deal with such optimisation problems is to create a scoring function which combines the variables in such a way as to generate a single number which can then be used to sort.

Looking at your challenge, it would appear that there are some factors which are multiplicative such as chances of gaining a winning position. Others are additive/subtractive - the value of the transport costs should be subtracted from each of the prizes to give an overall profit and this simplifies the calculation. Factors that positively influence the outcome should be additive/multiplicative while those which make it less attractive should be subtractive or used to divide.

Splitting the calculation by day (so the two days of a multi-day event are separate lines) would avoid extra complexity.

My advice would be to include a number of weighting factors which you can manually adjust to see if the ranking produced looks sensible.

I hope that is useful. I must admit that I seeing a question from a rodeo rider from a city called Great Falls did bring a smile to my face.

**shg** · 01-26-2016, 04:17 PM

seeing a question from a rodeo rider from a city called Great Falls did bring a smile to my face

My laugh for the day, thank you

**xladept** · 01-26-2016, 10:33 PM

Good point mrice!

**MrShorty** · 01-26-2016, 10:55 PM

If you are up to the programming challenge, another strategy is a "Monte Carlo" strategy. In essence, you have the spreadsheet "play through" the rodeo season many times. You have the spreadsheet compute your score and the scores of your competitors based on probabilities that you give it. You do this for each chosen event, and you end up with one possible outcome. Repeat this process thousands of times and see what patterns develop.

The hardest part of this sort of thing is coming up with the "play through the season once" algorithm. Once you have that entered into the spreadsheet, then performing the simulation thousands of times is as "simple" as copying and pasting the algorithm into new rows/columns. I link to a few Monte Carlo tutorials in this post: http://www.excelforum.com/excel-form...ml#post4289914 If you decide to pursue this route, it would probably be beneficial to review the simpler examples given and work up to the more complex algorithm needed here.