5th round fixture

[Punk Blade]

I'm going back to my original answer which is before the draw is made it is 1 in 120 simply because that is number of combinations of balls that are available. The moment the first ball is drawn that all changes. The chances of them coming out in any of the rounds before the draw is made 1 in 940 that is because there are 8 attempts to get 1 set of balls. That is the same for any combination of two balls. If however you asking the probability of United drawing Wednesday AND Man City drawing Man Utd for instance then by your argument it would still be 1 in 15 but obviously you the chances of this are much less.

Ps can we pack in now? Think we've bored everyone silly enough!!

We can pack in if you answer me one thing.

If there are 940 possible outcomes (it was 960 before l, but we can forgive that 20 for this purpose) and one of those is SUFC against SWFC in either order somewhere in the draw, and 14 other outcomes would be SUFC against the other 14 balls in either order somewhere in the draw, name me ONE of the other 925 (or 945, whichever number you prefer) possible outcomes. Just one.

 

[MobileBlade]

We can pack in if you answer me one thing.

If there are 940 possible outcomes (it was 960 before l, but we can forgive that 20 for this purpose) and one of those is SUFC against SWFC in either order somewhere in the draw, and 14 other outcomes would be SUFC against the other 14 balls in either order somewhere in the draw, name me ONE of the other 925 (or 945, whichever number you prefer) possible outcomes. Just one.

Personally I would prefer any of the others for us. Hate it when we play them. Its not a normal game.

 

[Punk Blade]

Personally I would prefer any of the others for us. Hate it when we play them. Its not a normal game.

So you would rather have any of the other 14 balls, or any of the other 945 mystery outcomes that you are unable or unwilling to exaplin what they are?

 

[BettingBlade]

Sky Bet are currently offering odds of 28/1 for us to be drawn at home to the pigs and vice versa.

Us to draw any specific team is at 14/1

The odds of any team to come out of the hat first are at 14/1. Same with last out of the hat.

For the purposes of the original question of what are the odds of us drawing Wednesday, it is 14/1. Can we just shut the fuck up about it now?

 

[ZoneManWilf]

I'm going back to my original answer which is before the draw is made it is 1 in 120

Forget the number crunching for a sec and take a step back.

In a draw where we're concentrating on the probability of one team drawing one of the 15 other teams, does it 'feel' that 1/120 is the correct answer?

It is a given that we have to draw one of the 15.

If the probability of drawing one specific team is 1/120 what is the probability of drawing the others?

If it's also 1/120, then aren't there 105/120 cases where we don't have a 5th round tie?

Maybe we'll get a bye!

I think you're confusing yourself with what happens in each particular round and not considering the draw as a whole. I agree that the probabilities start to change when the balls start to be drawn.

But as it stands right now before the draw starts, we have 1/15 chance if drawing the pigs, just like any other if the teams in the draw. Anything else simply doesn't add up.

Ps everyone saying this thread is boring is wrong

 

[Sean Thornton]

“I agree that the probabilities start to change when the balls start to be drawn”

^ this......

 

[Punk Blade]

Anyone of the 14 being drawn out first DOES give us information we weren’t aware of before that first drawn ball. It tells us that as either Sheffield team could be drawn second the likelihood of a derby is lessened until the second ball is drawn.

If the first ball out is neither Sheffield club, then we lose one possible outcome of a Sheffield derby, that being the first tie. However, from this point on for any of the other remaining seven ties to be a Sheffield derby we don't need both of the first two balls to be others - we only need the second ball to be an other as the first ball is already drawn.

The probabilities of any of ties two to eight being a Sheffield derby increase slightly as they are now only dependent on the drawing of 15 balls, not 16, however this is offset by the probability of the first tie being a Sheffield derby now being zero. Ties two to eight become 1/105 each, so overall the probabilty of a Sheffield derby is the sum: 7/105. Which is still 1/15.

After two balls are drawn and the first tie is known, that is when the probabilty starts to change. The longwinded way will give you 7/91, or 1/13. As two balls have gone there are now 13 possible balls to be drawn against SUFC, one of which is Wednesday, so 1/13 at that stage is as simple as 1/15 before any balls have been drawn. After ball three it remains 1/13. After ball four (assuming neither team has been drawn yet) it becomes 1/11. The probability will increase after every round that neither team is drawn (or odds shorten for gambling parlance), and if after seven ties neither team has been drawn it becomes 1/1.

 

[Worksop II]

“I agree that the probabilities start to change when the balls start to be drawn”

^ this......

When they start to be drawn ... or when 1 has been drawn ?

 

[Punk Blade]

Forget the number crunching for a sec and take a step back.

In a draw where we're concentrating on the probability of one team drawing one of the 15 other teams, does it 'feel' that 1/120 is the correct answer?

It is a given that we have to draw one of the 15.

If the probability of drawing one specific team is 1/120 what is the probability of drawing the others?

If it's also 1/120, then aren't there 105/120 cases where we don't have a 5th round tie?

Maybe we'll get a bye!

I think you're confusing yourself with what happens in each particular round and not considering the draw as a whole. I agree that the probabilities start to change when the balls start to be drawn.

But as it stands right now before the draw starts, we have 1/15 chance if drawing the pigs, just like any other if the teams in the draw. Anything else simply doesn't add up.

Ps everyone saying this thread is boring is wrong

Deserved a like anyway, but the last line made me smile!

 

[Cheets]

“I agree that the probabilities start to change when the balls start to be drawn”

^ this......

The best way I can think to explain it is, we're concerned with pairs of teams. If Liverpool are drawn first they still haven't been paired up with anyone.
Can anyone out there explain this more eloquently than I can? Please....?

 

[Punk Blade]

The best way I can think to explain it is, we're concerned with pairs of teams. If Liverpool are drawn first they still haven't been paired up with anyone.
Can anyone out there explain this more eloquently than I can? Please....?

I had a go, but I can't help but lean on numbers to illustrate. I think your explanation that it is about pairs works perfectly and complements my explanation - it will only change with each known pair.

 

[Sean Thornton]

If the first ball out is neither Sheffield club, then we lose one possible outcome of a Sheffield derby, that being the first tie. However, from this point on for any of the other remaining seven ties to be a Sheffield derby we don't need both of the first two balls to be others - we only need the second ball to be an other as the first ball is already drawn.

The probabilities of any of ties two to eight being a Sheffield derby increase slightly as they are now only dependent on the drawing of 15 balls, not 16, however this is offset by the probability of the first tie being a Sheffield derby now being zero. Ties two to eight become 1/105 each, so overall the probabilty of a Sheffield derby is the sum: 7/105. Which is still 1/15.

After two balls are drawn and the first tie is known, that is when the probabilty starts to change. The longwinded way will give you 7/91, or 1/13. As two balls have gone there are now 13 possible balls to be drawn against SUFC, one of which is Wednesday, so 1/13 at that stage is as simple as 1/15 before any balls have been drawn. After ball three it remains 1/13. After ball four (assuming neither team has been drawn yet) it becomes 1/11. The probability will increase after every round that neither team is drawn (or odds shorten for gambling parlance), and if after seven ties neither team has been drawn it becomes 1/1.

My initial question was purely linked to the first ball being drawn. Possibility/probability or whatever, if any of the 14 are drawn out, because of the chance that either Sheffield team could be the second team drawn - so at the point only the home ball has been drawn - the odds must lengthen at that point. Two chances for a local side has been stated at 2/15, so why don’t the odds change on a derby at that instant because the chances of 1/15 is dependent on the second team drawn.

Further draws don’t affect that point.

 

[Sean Thornton]

When they start to be drawn ... or when 1 has been drawn ?

Let me see. What have l been saying? Start, first ball? Possible whoosh?

 

[Cheets]

My initial question was purely linked to the first ball being drawn. Possibility/probability or whatever, if any of the 14 are drawn out, because of the chance that either Sheffield team could be the second team drawn - so at the point only the home ball has been drawn - the odds must lengthen at that point. Two chances for a local side has been stated at 2/15, so why don’t the odds change on a derby at that instant because the chances of 1/15 is dependent on the second team drawn.

Further draws don’t affect that point.

As stated by myself and others, they don't lengthen or shorten until the second ball has been drawn out. I've done my best to explain why. I give up now.

 

[Alf Tuppers Shorts]

Yes, ties are to be played Tues, Weds and Thursday, so if either us or Norwich play on the Thursday night then I presume our league game against Norwich will be put back to Sun 8 March.

Nailed on Norwich then
Play them twice

 

[Sean Thornton]

The best way I can think to explain it is, we're concerned with pairs of teams. If Liverpool are drawn first they still haven't been paired up with anyone.
Can anyone out there explain this more eloquently than I can? Please....?

If Liverpool aren’t paired with anyone at that point both teams could be the second ball. With that possibility the odds can’t be 1/15 on a derby because either could be drawn to face Liverpool. 1/14 resets when the third ball is drawn. If the odds on the second ball become 2/15 ( both teams possible) there has to be a change in odds, when Liverpool are drawn.

 

[Punk Blade]

My initial question was purely linked to the first ball being drawn. Possibility/probability or whatever, if any of the 14 are drawn out, because of the chance that either Sheffield team could be the second team drawn - so at the point only the home ball has been drawn - the odds must lengthen at that point. Two chances for a local side has been stated at 2/15, so why don’t the odds change on a derby at that instant because the chances of 1/15 is dependent on the second team drawn.

Further draws don’t affect that point.

You’re falling into the trap of focusing on the first tie. The probability of a Sheffield team coming out second is 2/15, yes. But that isn’t the only way of avoiding a Sheffield derby, so 2/15 isn’t the answer for no derby. You would have to add up all the probabilities of not getting a Sheffield derby if ball two were to be another team. At the point of only one ball having been drawn they would add up to 14/15, of which your 2/15 for ball two being Sheffield is a part.

 

[Salmonfarm]

Only did up to A level maths, and I've only done the first 3 'draws' to prove the point but here is it written down. Every time the fraction becomes 1/120. Therefore, as there are 8 draws this becomes 1/15. (B is blades, p is pigs and o is other). Shows how the probabilities change after each ball is pulled.

 

[Sean Thornton]

As stated by myself and others, they don't lengthen or shorten until the second ball has been drawn out. I've done my best to explain why. I give up now.

Well as I’ve explained, if I had 15/1 on a derby, and Liverpool or any other of the 14 were drawn out first, I wouldn’t lump on at that price before the second ball was drawn. For obvious reasons.

 

[Corazon]

I think this turned into the most boring thread I’ve ever read

Personally I think its been one of the most entertaining ….

 

[Sean Thornton]

You’re falling into the trap of focusing on the first tie. The probability of a Sheffield team coming out second is 2/15, yes. But that isn’t the only way of avoiding a Sheffield derby, so 2/15 isn’t the answer for no derby. You would have to add up all the probabilities of not getting a Sheffield derby if ball two were to be another team. At the point of only one ball having been drawn they would add up to 14/15, of which your 2/15 for ball two being Sheffield is a part.

I’ve only concentrated on the first tie all along. At that point any of the 14 clubs being drawn first - and for what I’ve been saying only at that point - the odds aren’t 15/1. The rest of the draw isn’t part of what I’ve been saying. Liverpool being drawn first means that at that moment in time, there can’t be a derby draw. So how can the odds not change at that point?

 

[BushBlade]

I think this turned into the most boring thread I’ve ever read

Did you read the Ched one? That was just people saying the same thing over and over again for three years.

 

[Punk Blade]

I’ve only concentrated on the first tie all along. At that point any of the 14 clubs being drawn first - and for what I’ve been saying only at that point - the odds aren’t 15/1. The rest of the draw isn’t part of what I’ve been saying. Liverpool being drawn first means that at that moment in time, there can’t be a derby draw. So how can the odds not change at that point?

Because the probability of a derby hasn’t changed, even though it can’t be tie one. I explained that further up. The probability of there being a derby draw has to consider the entire remainder of the draw, not just the next ball.

If you want to focus on tie one, then the probability of tie one being a derby becomes zero if the first ball if Liverpool. The probability of a derby at all must consider the other seven ties. Tie one hasn’t been determined yet so the probability doesn’t change until ball two is drawn.

 

[BushBlade]

I’ve only concentrated on the first tie all along. At that point any of the 14 clubs being drawn first - and for what I’ve been saying only at that point - the odds aren’t 15/1. The rest of the draw isn’t part of what I’ve been saying. Liverpool being drawn first means that at that moment in time, there can’t be a derby draw. So how can the odds not change at that point?

They do. But a basic probability calculation looks at the probability of an event occurring before the start of something. In simple terms, it’s the odds pre-match. You’re introducing in play betting, which is obviously more complex as it’s fluid. That’s why bookies use computers to calculate those shifting odds and not people like me who can appreciate the concept but have no idea how to express it mathematically.

 

[Sean Thornton]

Because the probability of a derby hasn’t changed, even though it can’t be tie one. I explained that further up. The probability of there being a derby draw has to consider the entire remainder of the draw, not just the next ball.

If you want to focus on tie one, then the probability of tie one being a derby becomes zero if the first ball if Liverpool. The probability of a derby at all must consider the other seven ties. Tie one hasn’t been determined yet so the probability doesn’t change until ball two is drawn.

Say you have 15/1 on a derby draw. Liverpool are drawn first. Would you seriously have another 15/1 bet in that case because “probability doesn’t change”, even when there are two chances to scupper that and your first bet? Or would you wait for the second ball and if neither were drawn out, have that bet then??

 

[Sean Thornton]

They do. But a basic probability calculation looks at the probability of an event occurring before the start of something. In simple terms, it’s the odds pre-match. You’re introducing in play betting, which is obviously more complex as it’s fluid. That’s why bookies use computers to calculate those shifting odds and not people like me who can appreciate the concept but have no idea how to express it mathematically.

Neither can I, which is why l tried to keep it simple. Yes, it’s in play betting, but as you say, the odds do change. I’ve not used probability but an actual fact.

 

[Bergen Blade]

Would it make it easier for people to agree on the formula if we reduce the number of teams? Say we've moved on to the semi final:


Three possible outcomes for the Blades surely, one of which is SW. 1/3 or 33%.

If Liverpool are drawn first? There are still three possible outcomes for us. Liverpool, SW or Oxford. 1/3 chance of each being the opposition.

 

[BushBlade]

Would it make it easier for people to agree on the formula if we reduce the number of teams? Say we've moved on to the semi final:
View attachment 69541

Three possible outcomes for the Blades surely, one of which is SW. 1/3 or 33%.

If Liverpool are drawn first? There are still three possible outcomes for us. Liverpool, SW or Oxford. 1/3 chance of each being the opposition.

What happens though if the draw is being done by Alex Scott and Peter Shilton? Do we have to factor in his big hands?

 

[Greenwich Blade]

Would it make it easier for people to agree on the formula if we reduce the number of teams? Say we've moved on to the semi final:
View attachment 69541

Three possible outcomes for the Blades surely, one of which is SW. 1/3 or 33%.

If Liverpool are drawn first? There are still three possible outcomes for us. Liverpool, SW or Oxford. 1/3 chance of each being the opposition.

I'll just take Oxford United please. Thanks!

 

[Punk Blade]

Say you have 15/1 on a derby draw. Liverpool are drawn first. Would you seriously have another 15/1 bet in that case because “probability doesn’t change”, even when there are two chances to scupper that and your first bet? Or would you wait for the second ball and if neither were drawn out, have that bet then??

If I were considering only 2/15 to lose the bet I would have to assume 13/15 to win. Which would be wrong.