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Post 01 Oct 2015, 3:26 pm

Possibly relevant to the tiebreaker discussion:

The odds of exactly 5 heads in 10 coin flips are 24.6%. So if we ignore category ties and assume two teams that are dead even in each category, that's the chance that the tiebreaker comes into play. Or in other words, the team with the tiebreaker would be expected to win 62.3% of the time.

Category ties would of course lower this percentage, but it's hard to say by how much, as it depends on the odds of a given category ending in a tie, which varies greatly from category to category even assuming that the teams are dead even.
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Post 01 Oct 2015, 4:16 pm

Sharur wrote:Possibly relevant to the tiebreaker discussion:

The odds of exactly 5 heads in 10 coin flips are 24.6%. So if we ignore category ties and assume two teams that are dead even in each category, that's the chance that the tiebreaker comes into play. Or in other words, the team with the tiebreaker would be expected to win 62.3% of the time.

Category ties would of course lower this percentage, but it's hard to say by how much, as it depends on the odds of a given category ending in a tie, which varies greatly from category to category even assuming that the teams are dead even.

In my rarely humble opinion, that is both relevant and helpful. That's a significant advantage.
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Post 01 Oct 2015, 5:19 pm

If the teams are tied going into the final day of the season, the teams get to submit just three players to the commissioner, who reveals the selections at once. Those three players are the only ones who can play on the final day.
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Post 02 Oct 2015, 1:59 am

Interesting stuff about the advantage of having a tiebreaker , Todd.
So basically you present an idealized situation where two equal teams each have a 50 percent chance of winning each category, so the chance that they tie will occur 24.6% of the time so the team holding the tiebreaker would win those and the remaining 75.4 % would be split equally ( 37.7% each), giving a team that hold a tiebreaker a 62.3% chance of winning.

I looked at a situation where a team had a 60 percent chance of winning each category and what would be the chance of getting 5 categories.
So P(X=5)=10!/5!(10-5!).6(exp5).4(exp5)=about 20%
So in that situation the advantage would go from 60 to 68%.

I also took a look at how our league did with category ties this year. There were 90 out of 1680 categories that tied; however, 30 of those ties came in match-ups where there were two ties so they canceled each other out so out of a total of 168 match-ups there were a total of about 60 ties that did not cancel out. That's about 35%. If you subtracted 35% from 24.6% that would yield a 58% chance that as between two equally matched teams the one holding the tiebreaker would win.
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Post 02 Oct 2015, 5:52 am

freeman3 wrote:Interesting stuff about the advantage of having a tiebreaker , Todd.
So basically you present an idealized situation where two equal teams each have a 50 percent chance of winning each category, so the chance that they tie will occur 24.6% of the time so the team holding the tiebreaker would win those and the remaining 75.4 % would be split equally ( 37.7% each), giving a team that hold a tiebreaker a 62.3% chance of winning.

I looked at a situation where a team had a 60 percent chance of winning each category and what would be the chance of getting 5 categories.
So P(X=5)=10!/5!(10-5!).6(exp5).4(exp5)=about 20%
So in that situation the advantage would go from 60 to 68%.

I also took a look at how our league did with category ties this year. There were 90 out of 1680 categories that tied; however, 30 of those ties came in match-ups where there were two ties so they canceled each other out so out of a total of 168 match-ups there were a total of about 60 ties that did not cancel out. That's about 35%. If you subtracted 35% from 24.6% that would yield a 58% chance that as between two equally matched teams the one holding the tiebreaker would win.


All of this drives me back to one simple conclusion: it is too powerful an advantage to know ahead of time who has the tiebreaker.
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Post 02 Oct 2015, 6:27 am

How does that advantage compare to MLB home-field advantage? The justification for using records is that having the tie-breaker represents that home-field bonus.

On the other hand, we certainly don't wish to model anything on how home-field advantage is determined for the World Series (blech)!

I'm ok with using another system, btw. I just don't know what it should look like.
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Post 03 Oct 2015, 6:16 pm

62% is definitely higher than MLB home field advantage. In fact it's higher than any other major sport (MLS doesn't count): http://freakonomics.com/2011/12/18/football-freakonomics-how-advantageous-is-home-field-advantage-and-why/

58% is pretty close to the NFL rate.

Here's the problem with changing the system, though: there's nothing we can do to alter that math in a way that only changes the tiebreaker. We could, for example, introduce additional categories, but that would obviously have a much larger impact. So someone will receive the advantage, whether or not you think it's too large. Given that, who do we want to have the advantage? I think it makes sense to have a substantial reward for having the overall better team, given the randomness inherent in one (or even two) week matchups.

I'm also not sure what Steve means by it being too much of an advantage to know in advance. It impacts your strategy during the playoff week, sure, but that's not something you can plan for from far away. No one builds their team to only win 5 categories from the outset.
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Post 03 Oct 2015, 9:43 pm

Sharur wrote:62% is definitely higher than MLB home field advantage. In fact it's higher than any other major sport (MLS doesn't count): http://freakonomics.com/2011/12/18/football-freakonomics-how-advantageous-is-home-field-advantage-and-why/

58% is pretty close to the NFL rate.

Here's the problem with changing the system, though: there's nothing we can do to alter that math in a way that only changes the tiebreaker. We could, for example, introduce additional categories, but that would obviously have a much larger impact. So someone will receive the advantage, whether or not you think it's too large. Given that, who do we want to have the advantage? I think it makes sense to have a substantial reward for having the overall better team, given the randomness inherent in one (or even two) week matchups.


So, let's say one team has a small edge over another in terms of season record, is that really worth that kind of advantage? It could be as little as half a game, which is not significant.

I'm also not sure what Steve means by it being too much of an advantage to know in advance. It impacts your strategy during the playoff week, sure, but that's not something you can plan for from far away. No one builds their team to only win 5 categories from the outset.


It allows you, going in, to aim for a draw. So, if you figure you can win 3/5 offensive categories and you have a day or two of good pitching, you bench all your pitchers and the game is over--maybe by Wednesday. In other words, it permits you to tailor your strategy in some situations--not always, but I think it is not insignificant.
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Post 04 Oct 2015, 7:34 am

Doctor Fate wrote:So, let's say one team has a small edge over another in terms of season record, is that really worth that kind of advantage? It could be as little as half a game, which is not significant.


Again, this is unavoidable. The advantage will exist whether we want it or not. The question is simply how to allocate it. And it makes more sense to me to use it as a reward for success in the regular season than to do it in a more random or arbitrary fashion.

That's why I've likened it to home-field advantage, even though it's larger than HFA usually is. HFA is still a big deal in any sport, and can be won by extremely slim margins, but someone's got to have it (barring playing at a neutral site like the Super Bowl, but we don't have that option).

Keep in mind also that the bye could be earned by the slimmest of margins as well, and the bye is worth FAR more than the tiebreaker.

Doctor Fate wrote:It allows you, going in, to aim for a draw.


It does, but so what? Aiming for a draw is only as valuable as its impact on your strategy. You're going to spend the whole season trying to build a team that can win at least 6 categories. Come playoff time, if you hold the tiebreaker, then lucky you, your job got easier, but you won't be able to overhaul your roster in response to the situation. And even to the extent it affects your start/sit decisions, the dynamic is not fundamentally different from how you might respond to being up 6-4.
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Post 04 Oct 2015, 1:51 pm

It looks like we're going to have the championship decided by a tiebreaker. I just lost in the play-offs in a Yahoo league based on regular-season record and I did not particularly like that (I had the better regular-season record.)

We already give the two-best teams byes--that's enough of a reward for having a good record. Giving them the tiebreaker is too much of an advantage. We don't have to have play-offs--we could take team with the best overall record, but that's kind of boring. Also, of course, the play- offs measure how the best teams do against each other, not the record they compile against weaker teams and against different schedules. I have never been in a fantasy league where is such a large advantage given to the two top regular season teams. We had this discussion about the tiebreaker and part of the issue is how difficult it would be to win the championship when you're in a league with Matt or Nick and you get the wild-card. You have to win three games and the other team has the tiebreaker in each. Pretty tough.

This is a keeper league. It's not just that Matt or Nick are good fantasy managers , but they come into every year right now with a significant advantage because of the players they have already acquired.

With regard to the strategy regarding the tiebreaker, however we do it teams are going to strategize. My feeling is that the fairest is based on winning a category, because every team can strategize how good they want to be in that category (starting with the draft). What's unfair about it? All I can say is that I can't see how anyone could complain they lost a tiebreaker because they were beaten that week in the tiebreaker category, but getting beat because someone holds the tiebreaker advantage just sucks. You should be beaten that week--losing that way does not feel like you really lost. Well, you didn't--you tied.

I have heard that people don't like using a category as a tiebreaker but I haven't seen (recently, I probably just forgot them)any arguments as to why it would be unfair. Let's say we went to saves and holds as the tiebreaker. Some categories there might be a concern that certain teams have built up an advantage , but I don't see that there is much of a concern about that in saves and holds. So teams would have a more or less equal opportunity to try and get an advantage in the tiebreaker category. That's what competition is about--competing at that time to see who is better.
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Post 04 Oct 2015, 4:13 pm

freeman3 wrote:We already give the two-best teams byes--that's enough of a reward for having a good record.


What about the other teams? The third best team might be a lot better than the 6th best.

freeman3 wrote:My feeling is that the fairest is based on winning a category


The problem isn't fairness. The problem is now we've arbitrarily privileged some category over all the others. Why would we want that, from a strategic standpoint? We have a lot of owners that try to focus on different things, and that includes some owners that punt SV/HD. That seems like a perfectly legitimate strategy to me that gets arbitrarily penalized if we use SV/HD as the tiebreaker, per your suggestion.

Or even just looking at the championship, we can see that the Sauce focused on pitching and the 'Jacks on hitting. Both of them have been dominant in those areas, and that's a large part of why they're tied. So we could have arbitrarily decided that one of pitching or hitting was more important in choosing that category, or, under the current system, we can award the title to the team that proved itself a little more throughout the course of the regular season.

Neither of these options is unfair per se, but the status quo seems far more reasonable to me.

I also don't follow your bit about your Yahoo league- it sounds like our system would have solved the problem in your league.

---

Another way of thinking about this: the solution to winning the tiebreaker, under the current system, is very simple: build a better team. It's the same thing you're trying to do in general, and it doesn't matter how you do it. I'd want any alternative system to be able to meet that same standard.
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Post 04 Oct 2015, 5:51 pm

Yes, it stinks to lose on the tiebreaker, but everything Todd says is right on. The tiebreaker is earned over the course of the whole season.

I just played a final in my Yahoo league in which I didn't hold the tiebreaker - incidentally also best regular season record. It didn't bother me at all that I needed to win at least 5-4-1. My opponent had had a better season than I had and it was only right that he get that advantage. It was well earned, and not insurmountable as I proved today with a nail-biting 5-4-1 win!
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Post 05 Oct 2015, 10:49 am

Okay, now THIS is a labor-intensive suggestion for a tie-breaker, but it might make sense. What about calculating the relative strength of each team (during the match only) in each of the categories? In other words, winning S/H by one would not be worth as much as winning SLG by 0.1. Each category would be expressed by a ratio and all the ratios summed.

Like I said, not easy. However, it seems to me it would have these advantages: 1) it would take into account total performance of the two teams; 2) it would not be easily manipulated.

No one likes losing a tie-breaker, but at least in this case you have to agree that you lost. It makes it clear.
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Post 05 Oct 2015, 11:37 am

That seems rife with problems.

How do you get equivalency between categories? I don't think straight percentages work - you'd have to do some kind of standard deviation. What if I want to punt a category? It's a legitimate strategy yet I'd be punished for it.

Is the tie-breaker we have really that awful? It's transparent and rewards past performance. Even if it does bring a greater advantage than home-field would in the real world, who cares? This is not a true baseball simulation nor is it meant to be.
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Post 05 Oct 2015, 1:17 pm

SLOTerp wrote:That seems rife with problems.

How do you get equivalency between categories? I don't think straight percentages work - you'd have to do some kind of standard deviation. What if I want to punt a category? It's a legitimate strategy yet I'd be punished for it.


I'm not sure that anyone in the finals really "punts" a category, but okay.

However, I would still say that this gives a better overall look at how the two performed during the week, which seems to me like a better tie-breaker than regular season record.

Can you imagine a Super Bowl decided on the basis of regular-season record? It just seems "fair" for the tie-breaker to be something occurring during the tie.

Is the tie-breaker we have really that awful? It's transparent and rewards past performance. Even if it does bring a greater advantage than home-field would in the real world, who cares? This is not a true baseball simulation nor is it meant to be.


It's not the end of the world.

However, if there is a way to make it more fair, I think we ought to look at it. We spend time every day for several months on this. It seems "wrong" to give such an edge, particularly when the regular season difference could be very minimal. Again, how about a situation where the two teams are separated by half a game? What if the second team had beaten the #1 team head-to-head?