I approximated the odds for the games from having watched the TAB odds on NRL on Fox over last few weeks. I also took into account the idea that some teams are backed more heavily than others, and that sometimes the odds aren't always an exact representation of the chances of one team winning. I tried to approximate how often a team would beat another team as well and compare that to the odds - mainly using the percentage of people who tip teams on Oztips as compared to the odds on offer from the TAB, and how correct they have been in the last few weeks.
The only bias you might find is that I had trouble trying to work out the percentages for us to beat the Broncs or Dragons. I think in the end I came up with us beating the Drags 72% of the time and the Broncs 60-something. Some might say that is lenient, others harsh. I think if you look at it we would beat the Drags 7 out of 10, and probably the Broncs too, given their team and the home ground.
Anyway, I got to the figures using the method I explained above. Yeah it was an approximation that could have been out (and I stated in the original post that towards the end I was more thorough too) but the minute innacuraccies of one match don't really change the percentages that much anyway once you get to the end of all the figuring, unless your approximations are waaaay out.
So, once I had the figures for each match, I then did some tree diagrams to work out the percentages of each outcome.
Example: For the Dogs outcomes it was a tree diagram that started with Dogs Win or Dogs Loss against Melbourne, and then branched out from both those with Dogs lose and Dogs win v Cowboys. No I did not take into account draws
.
So, for the Dogs there were 4 tree diagram outcomes :
W v Melb and W v Cows
W v Melb and L v Cows
L v Melb and W v Cows
L v Melb and L v Cows
All these outcomes had different percentages of occuring according to the percentages of each individual game.
Of course these tree diagrams needed to be worked out for every team and/or every scenario. That meant working out exactly where we would finish given certain outcomes. So, using the Ladder Predictor i went through all possible outcomes, and where that would leave us in the table (hence the confusing 'criteria' for us if we lose both. Trust me that is right, I went over it and they are the criteria that affect us).
Depending on what i was trying to figure out I might take one of the results from a tree diagram, or I might take more than one.
eg continuing with the Dogs example, for us to come third there is only one possible scenario - It has to be the Dogs results = L v Melb and W v Cows (of course mutliplied by the chances of us winning both our games, which came from a tree diagram of its own).
But when I needed to know the possibility of the Dogs winning
any one game (which was needed in the case of us only winning one) there are two results possible from that tree diagram - W v Melb and L v Cows, or L v Melb and W v Cows. That's why the tree diagrams are important - even though they might not be needed in some instances (I could easily work out the Dogs results without a tree diagram) once you get on to more involved problems (eg Warriors results and Dogs results combined) they allow you to ensure that you don't miss anything.
Once I had worked out what needed to eventuate for certain outcomes to occur it was really just a matter of creating the necessary tree diagrams to work out the chances of each outcome occuring. I then went back and double-checked the figures to ensure that all tree diagram results were accounted for properly and that no data was missing or unaccounted for.
I am open to suggestions to improvements. That doesn't mean I'll go through it all again!! (though if you make a suggestion my compulsion for maths will probably have me doing it)
