To Hedge, or Not to Hedge (1 Viewer)

[Dinsy Ejotuz]

This is kind of a fun one (at least I thought so when I realized my choices):

I'm in four semifinals this coming week. Here are my viable starting options at QB for each, (with Dodd's projection):

League I: Rivers (18.3)

League II: Rivers (18.7) or Roethlisberger (18.3)

League III: McNabb (19.9) or Campbell (19.9)

League IV: McNabb (19.9) or Rivers (18.3)

Assume that you're a coin flip to win in each of the four leagues.

Would you go with the 'best' QB in each situation - which would leave you with Rivers (x2) and McNabb (x2)

or

Would you hedge and go with Rivers, Roethlisberger, Campbell and McNabb?

or

Would you choose another option?

Why did you make the choice you did?

 

[LadyBeBop]

Voted other.

I need to see your complete team first before I decide.

Leaning towards....Rivers, Rivers, Campbell, McNabb.

 

[gonzobill5]

I'd say put Rivers in every lineup you can. The guy just doesn't have bad games. However McNabb and Campbell offer good upside, and I can see why you wouldn't want all your eggs in one basket. From a purely fantasy perspective, I'd go Rivers, Rivers, McNabb, Rivers. The Giants have been just awful on defense, and Campbell has been on fire, but I just don't trust him enough to put him into a playoff lineup.

From a more mathematical perspective I'd look at it this way. You say each game is a coin flip. So you should be happy if you win 2 or more of the 4.

Let's assume you need about 18 points from your QB, so if the guy performs under his projection you lose and over his projection you win. Assume he's just as likely to outperform it as he is to underperform. Here are your options from riskiest to safest.

If you start Rivers in three leagues you could end up winning 0, 1, 3, or 4 games. The probabilities of each outcome is 25%, so your expected number of wins would be exactly 2. (st. dev 1.58)

If you start Rivers in two and McNabb in two, you could end up winning 0, 2, or 4 games. The probabilities are 25%, 50%, and 25% respectively. Your expected number of wins would again be 2. (st dev 1.41)

If you start two Rivers and two other guys, you could win 0, 1, 2, 3, or 4 games. The probabilities are 12.5%, 25%, 25%, 25%, and 12.5% respectively. Again, you'd expect to win 2 games. (st. dev 1.22)

If you start 4 different guys, you could win 0, 1,2 ,3, or 4 games. The probabilities are 6.25%, 25%, 37.5%, 25%, and 6.25%. No surprise, you can expect to win 2 games. (st. dev = 1)

After looking at that, I'd have a hard time not starting 2 McNabb and 2 Rivers. It's 75% likely that I'd win 2 or more.

PS: thanks for providing me with a lesson plan for my stat class tomorrow.

 

[Dinsy Ejotuz]

I'd say put Rivers in every lineup you can. The guy just doesn't have bad games. However McNabb and Campbell offer good upside, and I can see why you wouldn't want all your eggs in one basket. From a purely fantasy perspective, I'd go Rivers, Rivers, McNabb, Rivers. The Giants have been just awful on defense, and Campbell has been on fire, but I just don't trust him enough to put him into a playoff lineup.From a more mathematical perspective I'd look at it this way. You say each game is a coin flip. So you should be happy if you win 2 or more of the 4. Let's assume you need about 18 points from your QB, so if the guy performs under his projection you lose and over his projection you win. Assume he's just as likely to outperform it as he is to underperform. Here are your options from riskiest to safest.If you start Rivers in three leagues you could end up winning 0, 1, 3, or 4 games. The probabilities of each outcome is 25%, so your expected number of wins would be exactly 2. (st. dev 1.58)If you start Rivers in two and McNabb in two, you could end up winning 0, 2, or 4 games. The probabilities are 25%, 50%, and 25% respectively. Your expected number of wins would again be 2. (st dev 1.41)If you start two Rivers and two other guys, you could win 0, 1, 2, 3, or 4 games. The probabilities are 12.5%, 25%, 25%, 25%, and 12.5% respectively. Again, you'd expect to win 2 games. (st. dev 1.22)If you start 4 different guys, you could win 0, 1,2 ,3, or 4 games. The probabilities are 6.25%, 25%, 37.5%, 25%, and 6.25%. No surprise, you can expect to win 2 games. (st. dev = 1)After looking at that, I'd have a hard time not starting 2 McNabb and 2 Rivers. It's 75% likely that I'd win 2 or more.PS: thanks for providing me with a lesson plan for my stat class tomorrow.

Great post - this is exactly the conversation I was hoping to kick off...

 

[ratbast]

I voted for your first vote but I would not connect these decisions at all, in fact I would purposefully ignore any connection from league to league.

I would probably only consider Rivers and McNabb based on how i rank them but I would decide on a per league basis.

The problem you are presenting is an additional variable in a game that has so many already. You play to win the game! (not "hedge your bets")

 

[BassNBrew]

Rivers

Rivers

Campbell

Mcnabb

 

[broncofan13000]

Rivers x3 and mcnabb. I would just go with imo the best fantasy starter in each league and not look at them together. One shouldn't affect what I do in another. Unless the assumption is all qbs have the same chance for success/failure where hedging would make sense just to be safe. But I don't see them as equal.

 

[PosterNutBag]

Rivers x3 and mcnabb.

I'd do the same.

x3

 

[Doug Drinen]

I'd say put Rivers in every lineup you can. The guy just doesn't have bad games. However McNabb and Campbell offer good upside, and I can see why you wouldn't want all your eggs in one basket. From a purely fantasy perspective, I'd go Rivers, Rivers, McNabb, Rivers. The Giants have been just awful on defense, and Campbell has been on fire, but I just don't trust him enough to put him into a playoff lineup.From a more mathematical perspective I'd look at it this way. You say each game is a coin flip. So you should be happy if you win 2 or more of the 4. Let's assume you need about 18 points from your QB, so if the guy performs under his projection you lose and over his projection you win. Assume he's just as likely to outperform it as he is to underperform. Here are your options from riskiest to safest.If you start Rivers in three leagues you could end up winning 0, 1, 3, or 4 games. The probabilities of each outcome is 25%, so your expected number of wins would be exactly 2. (st. dev 1.58)If you start Rivers in two and McNabb in two, you could end up winning 0, 2, or 4 games. The probabilities are 25%, 50%, and 25% respectively. Your expected number of wins would again be 2. (st dev 1.41)If you start two Rivers and two other guys, you could win 0, 1, 2, 3, or 4 games. The probabilities are 12.5%, 25%, 25%, 25%, and 12.5% respectively. Again, you'd expect to win 2 games. (st. dev 1.22)If you start 4 different guys, you could win 0, 1,2 ,3, or 4 games. The probabilities are 6.25%, 25%, 37.5%, 25%, and 6.25%. No surprise, you can expect to win 2 games. (st. dev = 1)After looking at that, I'd have a hard time not starting 2 McNabb and 2 Rivers. It's 75% likely that I'd win 2 or more.PS: thanks for providing me with a lesson plan for my stat class tomorrow.

Great post - this is exactly the conversation I was hoping to kick off...

This is a cool thread. And I agree that gonzobil5's post is a solid breakdown of the math involved (and a great example for a stat class!). In my mind, though, it simply reinforces that the answer to your question doesn't depend on any of that stuff; it depends on your own personal risk tolerance. gonzobil looked at his breakdown and chose 2 Rivers + 2 McNabb because that maximizes your chance of winning two or more. But somebody else could look at the same breakdown and say, "I'd start four different guys because that gives me a 94% chance of still being alive next week." IOW, as phrased, I don't think math has much to say about your question. You have to know the marginal enjoyment that you'd get from winning 1 game instead of 0, 2 games instead of 1, and so on. And that's something only you can answer.

 

[Dinsy Ejotuz]

In my mind, though, it simply reinforces that the answer to your question doesn't depend on any of that stuff; it depends on your own personal risk tolerance. IOW, as phrased, I don't think math has much to say about your question. You have to know the marginal enjoyment that you'd get from winning 1 game instead of 0, 2 games instead of 1, and so on. And that's something only you can answer.

Agreed... as witnessed by the fact that I hadn't considered the "enjoyment" factor at all, but rather the "fear" factor of not wanting one bad week by Rivers (previously in three lineups) to kill off three teams. That's what got me thinking about this in the first place. With that in mind, I'm leaning towards all four QBs - especially since these are dynasty leagues and there's a lot of overlap in the rest of my starting lineups. In this example, I'd rather have a 93% of chance of still being alive and a 69% chance of two or more wins than have a 25% chance of losing all four and a 75% chance of winning two or more.

 

[Thorpe]

Are you facing any of these 4 QBs in any of your leagues?

 

[gonzobill5]

Are you facing any of these 4 QBs in any of your leagues?

Ooh, i hadn't considered that, but it could change everything! Doug is right, my final answer wasn't the "correct" answer. It came from my interpretation that I'd like to maximize the chance that I win 2 or more, minimize variability, all while keeping the likelihood that I go 4-0 very high. Someone more risk averse might think differently.ETA: Just so I'm clear, I think this advice is only as good as the assumptions that I made, which are likely not true. I believe that some players are more likely to meet or exceed their projections than others (surely some disagree). It's also not true that you will win just because that one player beats his projection or lose otherwise. I also believe some players are more likely to greatly exceed their projections than others.

 

[PolishNorbi]

.....After looking at that, I'd have a hard time not starting 2 McNabb and 2 Rivers. It's 75% likely that I'd win 2 or more......

Are you not also 75% likely to lose 2 or more?

 

[PolishNorbi]

Another thing is are all the leagues equal in money?

 

[gonzobill5]

.....After looking at that, I'd have a hard time not starting 2 McNabb and 2 Rivers. It's 75% likely that I'd win 2 or more......

Are you not also 75% likely to lose 2 or more?

Why so pessimistic?

 

[daveR]

I voted 1 game each. It just sounds like more fun than hanging it all on two of 'em.

Too bad they don't all start on different days...

 

[PolishNorbi]

.....After looking at that, I'd have a hard time not starting 2 McNabb and 2 Rivers. It's 75% likely that I'd win 2 or more......

Are you not also 75% likely to lose 2 or more?

Why so pessimistic?

Realist maybe?For me it all comes down to money and what is/how much at stake. Let's say I got two leagues where I can win $5,000 (more than all my investments) I would not use Rivers in both.