Jump to content

Chances of Canada making the Hex


Recommended Posts

I'm curious about how you arrived at 17.5%. Did you have a methodology?

To have a chance at advancing, I think everyone would agree that we've got to win our last three. Assuming that we've got a 50% chance of winning (as opposed to getting a draw or a loss) each game, we've got a 12.5% chance of coming away with 10 points. I also think giving us a 50% shot at winning against both Guatemala and Honduras on the road is optimistic, so realistically I'd put 12.5% as an upper boundary of our chances.


quote:Originally posted by Canadienfan

I'd give us about 17.5% chance of making the hex. what says you?

Link to comment
Share on other sites

quote:Assuming that we've got a 50% chance of winning (as opposed to getting a draw or a loss) each game,

Because in a game you can get three results (win, loss, draw), we really have a 33% chance of winning each game ... divide that by 4, you get 8.25% ...

So really the upper bounds are 8.25% ... if that makes any sense at all. :D

Link to comment
Share on other sites

Remember the thread where I geekily calculated Canada's chance of reaching the WYC quarterfinals of being 53.3%? (or 50/50 depending on which method you chose)


There I assumed that the probability of a tie is 25%, based on the historical average for England top-flight matches. In addition, the home team wins approximately 50% of the time, and the away team wins the other 25%.

I would try to figure this one out, but it's way too complicated since there are a surprising number of scenarios where Canada can qualify. And since the matches aren't on neutral ground, I wouldn't assign even probabilities of winning to both teams.

But my quickie analysis is this:

If Canada wins its next three matches, it has a good chance of making it to the next round, but there are some scenarios where we would still be eliminated. If Canada wins two of the three matches, we have a slight chance of still making it to the next round. As an approximation, I will assume that Canada will advance if we win the next three matches.

Since we play two away matches and one at home, the probability is 50% * 25% * 25% = 3.1%.

or an alternative analysis is that Canada either WILL qualify for the next round OR they WILL NOT qualify for the next round. Therefore the probability is 50/50. :)

Link to comment
Share on other sites

OK, now look what you've made me do... :)

Ignoring the scores, there are 3 possible results for each match (home win, draw, away win), and 6 more matches in this round. So there are 3^6 = 729 possible scenarios. Canada qualifies directly in 56 of the scenarios, is tied for a spot in 45 scenarios, and eliminated in 628 scenarios.

Assigning probabilities to each scenario using the 50% home / 25% draw / 25% away weightings, and having Canada win half of the tiebreaker scenarios, then Canada has a 8.36% chance of advancing.

This analysis does not take into account how crappy we were against Guatemala and the second half of Costa Rica.

Link to comment
Share on other sites


Ok, my scenario included the assumption that Canada had a 50% chance of winning each game, therefore the probability of drawing or losing would total the other 50% in my scenario. A very optimistic scenario.

I don't know why you're dividing by four Jarrek. In your case if we had a 33% chance of winning each game, then the probability of winning all three is 0.33 X 0.33 X 0.33 = 0.359 or 3.6%.

Now talking probabilities with an actuary scares me, so I'll defer to sstachko. If he says it's too complicated then, I'll take his word. BTW, I knew you wouldn't be able to resist!

But yeah, like all those FIRE YALLOP and FIREBOMB the CSA threads indicate, our chances don't look so good. Who needs all the vitriol when you've got statistics. :)


quote:Originally posted by sstackho

OK, now look what you've made me do... :)

Link to comment
Share on other sites

Keeping up with the silly analysis:

If we get three wins, we have a 98.4% chance of advancing.

If we get two wins and a tie, we have a 45.9% chance of advancing.

If we get two wins and a loss, we have a 10.5% chance of advancing.

If we get one win and two ties, we have a 1.2% chance of advancing.

Link to comment
Share on other sites

So if we win each game we'd advance? ;)

Gosh you guys overanalyze all the time. :-) What are the odds if Radzinski pulls

something (other than his socks)? What are the odds if Onstad can't play and Lars is in goal?

What are the odds if Wanchope, Ruiz, Pavon, and that Honduran guy gets food poisoning on

each of their games against Canada? What are the odds if the ref gets sick and is replaced

by Peter Pendergrast? DON'T ANSWER THIS!

This is just to show you that POSSIBILITIES are indeed ENDLESS. :-)

Link to comment
Share on other sites

Really enjoyed reading some of your guy's post's! Figuring out our odds is kinda fun just cause there are so many possibilities, a good waste of time between games anyways. A few more points to add here on the idea that each game is 50-50 odds or even 33-33-33 is true i guess for each individual game but continuing to get the same result again and again (say 3 wins in a row)is new odds all over again.

Link to comment
Share on other sites

Just skimming but if the odds (x) and the numbers (y) are added together, with our sum being multiplied by our performance (z) gives us our answer to the equation.

If (z)= 0 then it doesn't matter about the rest. I have hope but I think that we're not going based on our performance (z).

Cheer for Canada to get there and buy a 6/49. Either one would be a present surprise if it happened.

Link to comment
Share on other sites

Overall probability of qualifying has been tweaked to 8.28%.

Here are the conditional probabilities, based on our result away to Honduras.

If we beat Honduras, this increases to 26.60%.

If we draw with Honduras, it sinks to 5.47%.

If we lose to Honduras, it plunges to a dismal 0.52%.

Conditional probalities on the result of Costa Rica v Guatemala (i.e. who should we be cheering for?)

If CR beat Guatemala, our chances of qualification decline to 7.70%.

A CR - Guatemala draw tweak our chances to 8.71%.

If Guatemala beat CR, our chances of qualification increase to 9.00%.

In other words, that match doesn't have a huge impact on us, but a Guatemala victory looks a bit better overall. However, if we win our next three games, the only scenario in which we could be eliminated involves a Guatemala win over CR. In addition, a Canada loss means elimination unless CR win. In other words, a Guatemala win slightly helps us if we draw or lose one of our last two matches.

Conditional on both our result and the result of Costa Rica v Guatemala

Canada win, CR win = 23.31%

Canada win, CR draw = 28.97%

Canada win, CR loss = 31.18%

Canada draw, CR win = 5.60%

Canada draw, CR draw = 5.86%

Canada draw, CR lose = 4.82%

Canada lose, CR win = 1.04%

Canada lose, CR draw = eliminated

Canada lose, CR lose = eliminated

Or alternatively, the odds are fifty-fifty.

Link to comment
Share on other sites

Thanks for the clarification. Your results are what I expected. We need to win and we need Guatemala to go free and clear. The good news, Guatemala ( moreso than anyone else) has had a ton preparation friendlies prior to WCQ which should help them. Also, If they can clinch a spot before their final game, they might rest players for that final home game. Which will be a big boost for Canada's chances.

Link to comment
Share on other sites

  • 3 weeks later...

I feel like bumping this thread back up.

Guatemala qualify if they win, unless Canada also win. Then Canada has the chance to tie Guatemala for second place in the group.

It's a bit of a tough call as to what we want to happen in the CR-Guat match. I post the qualifying odds above, which imply we want a Guat win. However, if we manage to qualify, it will most likely be at the expense of Honduras - who Guatemala play in the midweek match. So perhaps we want a hungry Guatemala in that match - although I wouldn't expect them to ever lie down for their rivals, even if the match means little to them.

But on the other hand, there is only one scenario in which Canada would be eliminated even if we win all three matches - and that involves a Guatemala win on Saturday. In addition, should Canada lose, we are mathematically eliminated if Costa Rica doesn't win.

Anyway, who cares. We know what we have to do. We have to win. We're not eliminated with a draw, but the chances become even slimmer.

Link to comment
Share on other sites

Without any statistical analysis, the best result seems to be a tie between Ticos and Guatemala. That way, everyone would be alive after the fourth game. That, coupled with a Canuck win, would make the race ever so exciting.

Then, a Guatemala win over Honduras would be the ideal scenario making sure that the last match away in Guatemala will no longer be a do or die scenario and Guatemala could rest some of its key players for the next round, in November.

Link to comment
Share on other sites

Any result that improves the gap between us and 2nd place is a step in the right direction.By beating Honduras we'll be no worse than 2 pts.out with 2 games to play.Quite a bit better than our current situation.

A subsequent win over Costa Rica would give us 2nd place out right unless Honduras beat Guatemala.

With 2 straight wins we would be at worst 1 point out of a hex qualification with 1 game to play.

Link to comment
Share on other sites

quote:Originally posted by jeffymac1971

Canada's chances of going to the hex are just as good as Paris Hilton declaring herself a born again christian....:D

Don't laugh--anything is possible. Like someone once said--"ya gotta sin to be saved"...

Maybe there's still hope for me and Paris and CANADA afterall.


Link to comment
Share on other sites


This topic is now archived and is closed to further replies.

  • Create New...