Algebra question I think

[RHB]

I think this is for the algebra guru's if it is at all possible.
I'm trying to estimate a race horse win prize money based on number of wins and total prize money won.
Winning prize money is approx. 60% of the prize money allocated to the race.
<table border="1" cellpadding="0" cellspacing="0"><tbody> <tr style="text-align: center; background-color: rgb(202, 202, 202); font-size: 8pt; font-weight: bold;"> <td> </td> <td>A</td> <td>B</td> <td>C</td> <td>D</td> <td>E</td></tr> <tr style="height: 17px;"> <td style="text-align: center; background-color: rgb(202, 202, 202); font-size: 8pt;">1</td> <td style="text-align: center; font-weight: bold;">Prizemoney</td> <td style="text-align: center; font-weight: bold;">Starts</td> <td style="text-align: center; font-weight: bold;">Wins</td> <td style="text-align: center; font-weight: bold;">Others</td> <td> </td></tr> <tr style="height: 17px;"> <td style="text-align: center; background-color: rgb(202, 202, 202); font-size: 8pt;">2</td> <td style="text-align: center;">100,000</td> <td style="text-align: center;">12</td> <td style="text-align: center;">2</td> <td style="text-align: center;">10</td> <td> </td></tr> <tr style="height: 17px;"> <td style="text-align: center; background-color: rgb(202, 202, 202); font-size: 8pt;">3</td> <td style="text-align: center;">77,000</td> <td style="text-align: center;">10</td> <td style="text-align: center;">3</td> <td style="text-align: center;">7</td> <td> </td></tr></tbody></table>As you can see I'm only interested in getting the winning $$'s and no other info.
So the win money is 60% of available money and the other placings etc would be 40% of available prize money I reckon.
Just tell me if it's not possible which it may be.
Thanks
Bob

 

[stefankemp]

There are two unknown variables: the amount of prize money available for each particular race, and the actual placings the horse achieved in the races marked as "other".

You can try to make some reasonable assumptions for these unknowns, but you will have to do some research. For example if a horse has some sort of "grading" or "class" that means he runs in certain types of races, you can work out what the average prize money is for those races.

You can also do some research on if a horse wins x% of his races, then what % does it tend to place?

And so forth. But I suspect this would be more effort than it's worth and the accuracy of your estimate at the end would still be spurious.

 

[RHB]

Thanks guys
Todd- You are somewhere near the mark I reckon and I may have to assume an average field size to get to the "others" number.
Using your formula gives what looks as though they could be realistic numbers.
I think you meant column E by the way.
But how did you arrive at the $41,667 as that seems about "right".

stefankemp-
The win and place percentages are freely available for each horse.
Avg prize-money for past races is a different kettle of fish.
And the "class" is what this exercise is all about as I'm trying to determine if a horse wins higher value races than his opposition, he could be the better animal.

 

[skull_eagle]

"how did you arrive at the $41,667 as that seems about?"

if 60% = $25,000
then 100% would = $41,667

I've been thinking about my calculations and I'm not that happy, there a probably lots of things wrong with it as I'm no mathematician but my main concern is it assumes that the horse always gets a pay out.

We may have to put in a another guesstimate of what % of "other" the horse did not receive any pay out at all possibly 20% or something.

Column E = (A2*0.4)/x*(D2-20%)

The other concern is that A2*0.4 is making the massive assumption that 40% of the winnings is coming from "other" and as there is theoretically no relation between "wins" and "other" this could be completely out.

There are lots of issues with this.

 

[RHB]

You're correct regarding the issues as I've just run it over real numbers.
Making the wrong assumption about average field size numbers if too low can give you a negative number. - Pity.
Here's a small sample.
<table border="1" cellpadding="0" cellspacing="0"><tbody> <tr style="text-align: center; background-color: rgb(202, 202, 202); font-size: 8pt; font-weight: bold;"> <td>
</td> <td>A</td> <td>B</td> <td>C</td> <td>D</td> <td>E</td> <td>F</td> <td>G</td></tr> <tr style="height: 17px;"> <td style="text-align: center; background-color: rgb(202, 202, 202); font-size: 8pt;">1</td> <td style="text-align: right; font-weight: bold;">Prizemoney</td> <td style="text-align: center; font-weight: bold;">Starts</td> <td style="text-align: center; font-weight: bold;">Wins</td> <td style="text-align: center; font-weight: bold;">Others</td> <td style="text-align: right; font-weight: bold;">Others $$</td> <td style="text-align: right; font-weight: bold;">Win $$</td> <td> </td></tr> <tr style="height: 17px;"> <td style="text-align: center; background-color: rgb(202, 202, 202); font-size: 8pt;">2</td> <td style="text-align: right;">104,693</td> <td style="text-align: center;">17</td> <td style="text-align: center;">3</td> <td style="text-align: center;">14</td> <td style="text-align: right;">73285</td> <td style="text-align: right;">31408</td> <td> </td></tr> <tr style="height: 17px;"> <td style="text-align: center; background-color: rgb(202, 202, 202); font-size: 8pt;">3</td> <td style="text-align: right;">137,895</td> <td style="text-align: center;">27</td> <td style="text-align: center;">6</td> <td style="text-align: center;">21</td> <td style="text-align: right;">144790</td> <td style="text-align: right;">-6895</td> <td> </td></tr> <tr style="height: 17px;"> <td style="text-align: center; background-color: rgb(202, 202, 202); font-size: 8pt;">4</td> <td style="text-align: right;">69038</td> <td style="text-align: center;">13</td> <td style="text-align: center;">3</td> <td style="text-align: center;">10</td> <td style="text-align: right;">34519</td> <td style="text-align: right;">34519</td> <td> </td></tr> <tr style="height: 17px;"> <td style="text-align: center; background-color: rgb(202, 202, 202); font-size: 8pt;">5</td> <td style="text-align: right;">140070</td> <td style="text-align: center;">30</td> <td style="text-align: center;">4</td> <td style="text-align: center;">26</td> <td style="text-align: right;">182091</td> <td style="text-align: right;">-42021</td></tr></tbody></table>
Column E has your formula and column D is A-D
Thanks for trying to help - I really appreciate it.
Might be time to forget about it I think.

 

[mtravis38]

Stefankemp, I'll chime in on this one, as a 16-year college Algebra Professor.

You don't have enough information to solve the problem as is. As other posters have alluded to, there are too many variables to solve without a system of equations, and you don't have enough info to make a system of equations.

 

[RHB]

Yes mtravis38
As I said back about post 6 or 8 if one of the pools was known the rest would be simple.
The number of starts,wins and placings is known but that is not enough.

 

[West Man]

I think you may be unable to get anything meaningful from the information you have. The 2 wins may have been in low value races, well below the average, and the majority of the winnings obtained by placing lower in higher value races. Or it could be the reverse. There just is not enough information to know.