northwoods
Footballguy
My 29 player team was below average this week with 161 points...I'll give 'em a C minus...lots of room for improvement.
The one variable from a fantasy team perspective that I have not seen here yet is the "luck" aspect. Just like in most games of chance, luck plays a big part. Like the lottery player that plays the same numbers each week that thinks they have a better chance to win this week since their numbers have not hit yet. Think back to the year that Brady was hurt in game 1 and out for the season. There were probably teams that lost or could have won their league without the injury. Some site offered a free 1 week contest where you pick your team for the week and highest score wins. If I had picked Chad Henne, I would have scored much higher than I did, but I think we would have all agreed just three weeks ago that he is not the guy to have. I had him in one of my leagues, then thought better of it and dropped him before the season started (Of course I did the same with McFadden last year - DOH!). When it comes to odds, there are 2 very important aspects to look at: 1. What is most likely to get me to the top 250 for the last 3 weeks. 2. Which will get me the most points in the final 3 weeks. With all players healthy, I think it is easy to pick which is the best team on paper for those last 3 weeks, but that would again go back to luck in hopes that all of your players stay healthy. Having a bigger team is like being diversified in your stock portfolio. Invest in a powerhouse such as Enron and you are screwed. Invest in 5 different companies and you are most likely to hit your goal. Now that we are 1 week into the contest, my gut tells me that I should have taken the best 18 players I could have. That way I would roll the dice that they stay healthy and put up big points in the end of the season. After all, I you just need to survive your bye weeks, not win them.'northwoods said:My 29 player team was below average this week with 161 points...I'll give 'em a C minus...lots of room for improvement.
Brady will have exactly the same number of dud weeks in weeks 2-17 as he would have if he had had a dud week in week 1.'butcher boy said:To use the Brady example, a lot of people thought I meant that since Brady had a good week 1 then that means he has to have a dud week to compensate. That's not really it. I think Brady will have one or more dud weeks in the future, not because of his week 1 performance, but because he (and every other stud) does every season and if he doesn't then he'll end up with a season that smashes every record in the book which I don't think anyone agrees will happen.
IMO, thats pretty much the agrument for small rosters. However, it's not all just surviving injuries. YOu also need those stud players to sort of alternate their "dud" weeks. Too many bad games in a single week will kill your team, even if they're all healthy.Now that we are 1 week into the contest, my gut tells me that I should have taken the best 18 players I could have. That way I would roll the dice that they stay healthy and put up big points in the end of the season. After all, I you just need to survive your bye weeks, not win them.
You also need them to actually be studs. Half of them will not be.IMO, thats pretty much the agrument for small rosters. However, it's not all just surviving injuries. YOu also need those stud players to sort of alternate their "dud" weeks. Too many bad games in a single week will kill your team, even if they're all healthy.Now that we are 1 week into the contest, my gut tells me that I should have taken the best 18 players I could have. That way I would roll the dice that they stay healthy and put up big points in the end of the season. After all, I you just need to survive your bye weeks, not win them.
True, but this argument goes both ways. When you select a larger roster, you also need to select the "right" low cost players. Half of them will probably be wrong.You also need them to actually be studs. Half of them will not be.IMO, thats pretty much the agrument for small rosters. However, it's not all just surviving injuries. YOu also need those stud players to sort of alternate their "dud" weeks. Too many bad games in a single week will kill your team, even if they're all healthy.Now that we are 1 week into the contest, my gut tells me that I should have taken the best 18 players I could have. That way I would roll the dice that they stay healthy and put up big points in the end of the season. After all, I you just need to survive your bye weeks, not win them.
Keep following this thread and you'll get lots of helpful advice that will help you (and lots of others!) build a better team every year!Hey guys, thanks for the insight on the big week 1 performance and how that limits a player for the rest of the season. I thought I found a gem in Cam Newton in the 15th round of my fantasy football league. Looks like I need to send him to the waiver wire instead. You guys ROCK!![]()
More than half of the low cost players will not do much for you; that's why they're low cost. But you get more chances to have someone doing good for you with low-cost players. So if you go from an 18-team roster with 2QB, 4RB, 6 WR, 2TE, 2K, 2D to a 30-person roster with 3QB, 7RB, 10WR, 4TE, 3K, 3D, you get huge upgrades each week in the number of players who might make a difference for you, and the number of cheap players who might wind up being studs. You only need to hit on one or two Brandon Lloyd 2010 type players to make your roster as strong as an 18-player roster.True, but this argument goes both ways. When you select a larger roster, you also need to select the "right" low cost players. Half of them will probably be wrong.You also need them to actually be studs. Half of them will not be.
I don't disagree with the math (assuming it's right, I didn't check it), but intuitively I disagree with the conclusion. It's probably my intuition that's off, but if it isn't then I'd guess the disconnect is that this week's stats aren't representative of what we'll actually see over the course of the year. Again, I haven't done anything to back this up quanitatively but I'm guessing some of the highest scoring players this week (e.g. Tom Brady) are disproportionately more highly owned by small rosters than by large rosters, skewing this analysis in their favor.OTOH it may also be something like: On any given week, a certain number of "studs" (e.g. expensive preseason players) are expected to put up big numbers. Also, a certain number of cheaper players will also step up and put up some big numbers. However, which players these are will vary from week to week. So while on average, the top scorer for any given week might be more likely to be an 18-man roster, it's not as likely to be the same 18-man roster two or three weeks in a row that consistently puts up big scores, since they only have one set of "studs". A larger roster has more players available, so if one week the $8 WR blows up and the next week the $6 RB blows up, or whatever, the larger roster is more likely to have both of those players, and therefore put up a big score (even if it's not the top score) several weeks in a row. So each week we'll see a small roster at the top of the standings but over cumulative three-week totals we'll see larger rosters at the top. Not sure if that makes any sense, I'm a little swamped at work this week and just throwing stuff out there. Like I said, if anything, it's probably my intuition that's wrong but I'm not sure.I'm going to respectfully disagree with you. If a single small roster has a greater chance of breaking 200 in any given week compared to a large roster, then (assuming there is independence between weeks) it has a greater chance of breaking 600 over 3 weeks.
This is simple probability. If a team has a 5.75% chance of breaking 200, then the chance it does it over 3 weeks is (5.75%)^3 = .0166% Chance.
Same with a team that has 5.29%. (5.29%)^3 = .0148% Chance.
Of course, we actually don't care about a team scoring 200+ for 3 consecutive weeks, we care about a team scoring 600+ over 3 weeks. So again if we assume independence amongst weeks, we can actually simply multiply the AvgScore and Variance by 3 to get an expected AvgScore and Variance for a 3 week period. Then we can use the Normal Distribution to calculate the chance of getting 600+.
Size Rosters AvScore StDev Exp 3 week 3 wk StDev 18 3568 165.77 21.72 497.31 37.62014354 0.317%19 1393 166.54 20.99 499.62 36.35574645 0.288%20 1059 167.74 20.95 503.22 36.28646442 0.383%21 836 168.41 20.28 505.23 35.12599038 0.349%22 766 168.26 19.37 504.78 33.54982414 0.227%23 641 168.27 19.68 504.81 34.08675989 0.261%24 547 169.84 20.15 509.52 34.90082377 0.476%25 396 169.99 19.17 509.97 33.20341398 0.335%26 415 170.43 17.76 511.29 30.76122234 0.196%27 296 169.97 19.01 509.91 32.92628585 0.311%28 269 169.93 17.56 509.79 30.41481218 0.151%29 214 171.67 17.51 515.01 30.32820964 0.254%30 376 171.56 17.58 514.68 30.4494532 0.254%However, you do bring up a good point, that perhaps these are out of whack due to a smaller roster more likely having Brady/Rodgers/Brees as their QB1. So it'll be interesting to see how this changes week to week. I know we tracked AvgScore by Roster for each week and over rolling 3 week periods last season, but I don't think we ever did it for St.Dev.
Oh don't get me wrong, I completely understood what you were saying. Just pointing out that it works both ways. Yes you get more chances has hitting those two Brandon Lloyd type of players, but you still need to hit them. Not trying to say that the chances of hitting on all your studs in a 18 man team = chances of hitting 2 brandon lloyds on a 30 man team. Just saying, that you need to hit your marks in this contest regardless of which size roster you get.More than half of the low cost players will not do much for you; that's why they're low cost. But you get more chances to have someone doing good for you with low-cost players. So if you go from an 18-team roster with 2QB, 4RB, 6 WR, 2TE, 2K, 2D to a 30-person roster with 3QB, 7RB, 10WR, 4TE, 3K, 3D, you get huge upgrades each week in the number of players who might make a difference for you, and the number of cheap players who might wind up being studs. You only need to hit on one or two Brandon Lloyd 2010 type players to make your roster as strong as an 18-player roster.True, but this argument goes both ways. When you select a larger roster, you also need to select the "right" low cost players. Half of them will probably be wrong.You also need them to actually be studs. Half of them will not be.
I took a quick look at the rosters holding Tom Brady and actually there seems to be pretty evenly spread out across Roster size. About 8 or 9% of rosters held him regardless of size. This makes sense since I'd think regardless of going 18 man or 30 man roster, QB strategy is probably very similar, 2-3 QB's with a Stud.I don't disagree with the math (assuming it's right, I didn't check it), but intuitively I disagree with the conclusion. It's probably my intuition that's off, but if it isn't then I'd guess the disconnect is that this week's stats aren't representative of what we'll actually see over the course of the year. Again, I haven't done anything to back this up quanitatively but I'm guessing some of the highest scoring players this week (e.g. Tom Brady) are disproportionately more highly owned by small rosters than by large rosters, skewing this analysis in their favor.
OTOH it may also be something like: On any given week, a certain number of "studs" (e.g. expensive preseason players) are expected to put up big numbers. Also, a certain number of cheaper players will also step up and put up some big numbers. However, which players these are will vary from week to week. So while on average, the top scorer for any given week might be more likely to be an 18-man roster, it's not as likely to be the same 18-man roster two or three weeks in a row that consistently puts up big scores, since they only have one set of "studs". A larger roster has more players available, so if one week the $8 WR blows up and the next week the $6 RB blows up, or whatever, the larger roster is more likely to have both of those players, and therefore put up a big score (even if it's not the top score) several weeks in a row. So each week we'll see a small roster at the top of the standings but over cumulative three-week totals we'll see larger rosters at the top. Not sure if that makes any sense, I'm a little swamped at work this week and just throwing stuff out there. Like I said, if anything, it's probably my intuition that's wrong but I'm not sure.
While a 3 week total could tell us something....it also doesn't account for the changes that occur to a players value due to injuries and over/under performance. There are a couple of low cost players whose role will change and they will be starting quality fantasy players by year's end. That is almost never the case in the first 3 weeks of the season (exceptions are like Warner the year he was $5 and Foster last year). A 3 week summary for teams in weeks 1-3 isn't going yield the same results as 3 week summary in weeks 14-16. Not only is it harder to survive bye weeks and injuries for a small roster, you also aren't able to capitalize on as many of these changes in player value, limiting your overall team value in the championship weeks. A few years ago, it wasn't Fitzgerald or Randy Moss that was a difference maker, but Antonio Bryant that carried teams to the top. I think he was like $7 that year (ETA: he was actually only $2...scored 41 pts in week 14).I took a quick look at the rosters holding Tom Brady and actually there seems to be pretty evenly spread out across Roster size. About 8 or 9% of rosters held him regardless of size. This makes sense since I'd think regardless of going 18 man or 30 man roster, QB strategy is probably very similar, 2-3 QB's with a Stud.I don't disagree with the math (assuming it's right, I didn't check it), but intuitively I disagree with the conclusion. It's probably my intuition that's off, but if it isn't then I'd guess the disconnect is that this week's stats aren't representative of what we'll actually see over the course of the year. Again, I haven't done anything to back this up quanitatively but I'm guessing some of the highest scoring players this week (e.g. Tom Brady) are disproportionately more highly owned by small rosters than by large rosters, skewing this analysis in their favor.
OTOH it may also be something like: On any given week, a certain number of "studs" (e.g. expensive preseason players) are expected to put up big numbers. Also, a certain number of cheaper players will also step up and put up some big numbers. However, which players these are will vary from week to week. So while on average, the top scorer for any given week might be more likely to be an 18-man roster, it's not as likely to be the same 18-man roster two or three weeks in a row that consistently puts up big scores, since they only have one set of "studs". A larger roster has more players available, so if one week the $8 WR blows up and the next week the $6 RB blows up, or whatever, the larger roster is more likely to have both of those players, and therefore put up a big score (even if it's not the top score) several weeks in a row. So each week we'll see a small roster at the top of the standings but over cumulative three-week totals we'll see larger rosters at the top. Not sure if that makes any sense, I'm a little swamped at work this week and just throwing stuff out there. Like I said, if anything, it's probably my intuition that's wrong but I'm not sure.
Wes Welker on the other had had a much wider array of being held, with smaller rosters more likely to hold him than larger rosters. Also smaller rosters made up a majority of the teams that had both Brady and Welker.
On your second point, I mostly agree. But what I think you're overlooking is that yes a larger roster is more likely to have both the $8 WR and $6RB that blows up, but he's also less likely to have the $30 WR that blows up. And that that $30 WR is also probably more likely to blow up than the two lower cost players. I'd also think that that $30 WR ceiling for the week >>>> $8 WR ceiling for the week.
I'm looking forward to see 3-week rolling totals with StDev to if it is like most are saying, that it just so happened that this week 2 high priced players blew up and no smaller cost player really did.
What makes this contest so great and also so hard to narrow down answers to questions is that there are so many dimensions. It's not simply a large roster vs small roster debate. It can be further broken down into how many at each position. And then down again into how they spread out that money across a position. If you decide to go with 9 WR's, are you better with 2-3 top studs and a bunch of low cost guys, or 4-5 mid-tier wrs and a some low cost guys?
I took a quick look at the rosters holding Tom Brady and actually there seems to be pretty evenly spread out across Roster size. About 8 or 9% of rosters held him regardless of size. This makes sense since I'd think regardless of going 18 man or 30 man roster, QB strategy is probably very similar, 2-3 QB's with a Stud.
Size w/Brady Total Pct.18 421 3568 11.8%19 146 1393 10.5%20 104 1059 9.8%21 72 836 8.6%22 57 766 7.4%23 54 641 8.4%24 41 547 7.5%25 33 396 8.3%26 33 415 8.0%27 28 296 9.5%28 19 269 7.1%29 15 214 7.0%30 33 376 8.8%
Yeah, I'd expect a higher % of the 18 man teams to have either Brady, Rodgers or Brees. When you are spending that kind of money on top players, you usually wouldn't look for a bargain #1 with Rivers or Stafford.I took a quick look at the rosters holding Tom Brady and actually there seems to be pretty evenly spread out across Roster size. About 8 or 9% of rosters held him regardless of size. This makes sense since I'd think regardless of going 18 man or 30 man roster, QB strategy is probably very similar, 2-3 QB's with a Stud.Code:Size w/Brady Total Pct.18 421 3568 11.8%19 146 1393 10.5%20 104 1059 9.8%21 72 836 8.6%22 57 766 7.4%23 54 641 8.4%24 41 547 7.5%25 33 396 8.3%26 33 415 8.0%27 28 296 9.5%28 19 269 7.1%29 15 214 7.0%30 33 376 8.8%
Very true. With a rolling 3 week summary, we should be able to capture the impact of the things you mention. I won't deny that the impact is there, however, my guess is that it isn't as high as most would believe. As we move through the season, not only do we get to see which cheap players break out and become solid contributers (ie. Brandon Lloyd), but we also get to see which "Studs" are stud-like and which turn to be duds. As the season goes on, the small roster teams will be made up of more of the stud players that panned out, while the larger rosters will tend to have the cheaper players that broke. While Bryant is a very good example of a cheap player carrying a team to the top, week 1 of this year could very easily of happened in week 14 and those with Brady/Welker combo would be carried to the top.While a 3 week total could tell us something....it also doesn't account for the changes that occur to a players value due to injuries and over/under performance. There are a couple of low cost players whose role will change and they will be starting quality fantasy players by year's end. That is almost never the case in the first 3 weeks of the season (exceptions are like Warner the year he was $5 and Foster last year). A 3 week summary for teams in weeks 1-3 isn't going yield the same results as 3 week summary in weeks 14-16. Not only is it harder to survive bye weeks and injuries for a small roster, you also aren't able to capitalize on as many of these changes in player value, limiting your overall team value in the championship weeks. A few years ago, it wasn't Fitzgerald or Randy Moss that was a difference maker, but Antonio Bryant that carried teams to the top. I think he was like $7 that year (ETA: he was actually only $2...scored 41 pts in week 14).
Some of the larger rosters will also have the stud players that panned out. The guy who won last year was a 25 man team but he had Rodgers and Adnre Johnson and Jason Witten. The "small vs large rosters" debate is often portrayed as "studs vs cheap players" but that's not accurate.'Modog814 said:As we move through the season, not only do we get to see which cheap players break out and become solid contributers (ie. Brandon Lloyd), but we also get to see which "Studs" are stud-like and which turn to be duds. As the season goes on, the small roster teams will be made up of more of the stud players that panned out, while the larger rosters will tend to have the cheaper players that broke.
Sure, and they'd be at the top of the standings for week 14. But if Brady, Welker, and their other players don't do that for three consecutive weeks, they'll probably have a hard time matching the cumulative scores put up by the larger rosters that have more player scores to draw from each week (especially those large rosters that have Brady and/or Welker - sure, that combo is more likely to appear on a small roster, but that doesn't mean there are no large rosters with that combo).You start 10 players every week. When you only have 18 players on your roster, that means you need players to put up big scores more than once in the playoffs. A 30 man roster could theoretically have 10 different players blow up every week in the playoffs. Of course that's unlikely to happen, but the point is that small rosters are somewhat handcuffed by their size. I think that's where my intuition was leading me earlier - it might be likely that over a three week span, the top scorer each week will be a small roster, but it won't be the same small roster three weeks in a row. The small rosters probably need to keep relying on most of the same players, while a larger roster is more insulated against the down weeks. The guy who won the whole thing last year had only one player count all three weeks in the playoffs.Lower mean/higher variance is a potential benefit in a single week; higher mean/lower variance is a benefit over a long period of time. I'm not sure where a three-week span falls in that spectrum. Part of the problem is that we don't know precisely what the differences in mean and variance are between small and large rosters, so it's nearly impossible to quantify an advantage one way or the other.While Bryant is a very good example of a cheap player carrying a team to the top, week 1 of this year could very easily of happened in week 14 and those with Brady/Welker combo would be carried to the top.
Guys with small rosters can pick the wrong studs just as easily. Happens in the first round of every redraft that has ever existed. And once you get to Week 10, 11, 12, you are talking about teams that chose right, teams that picked the right cheap players, and teams that, come playoff time, have 3 TE, K, and D to choose a starter from (so to speak). Those teams with small rosters are going to get a string of good weeks in a row, to have a chance.'Modog814 said:As the season goes on, the small roster teams will be made up of more of the stud players that panned out, while the larger rosters will tend to have the cheaper players that broke.
This isn't true. It's not the time line that matters, it's the difference in mean/variance that matters. IF scores are distributed normally (I'm not sure if they are, but I'd think it was a pretty safe assumption), then time doesn't matter.Lower mean/higher variance is a potential benefit in a single week; higher mean/lower variance is a benefit over a long period of time. I'm not sure where a three-week span falls in that spectrum. Part of the problem is that we don't know precisely what the differences in mean and variance are between small and large rosters, so it's nearly impossible to quantify an advantage one way or the other.
Of course they can. (I just noticed I left a word out of the post you quoted, so I added it in bold.)What I mean to say it when you get to weeks 10 and on, you're pretty much left with teams that either a) hit big on their studs, b) hit big on their cheap players or c) both. Regardless of roster size. So the bolded applies to everybody not just smaller rosters. To win this thing, you're pretty much need to have 6 or 7 good weeks in a row.Guys with small rosters can pick the wrong studs just as easily. Happens in the first round of every redraft that has ever existed. And once you get to Week 10, 11, 12, you are talking about teams that chose right, teams that picked the right cheap players, and teams that, come playoff time, have 3 TE, K, and D to choose a starter from (so to speak). Those teams with small rosters are going to get a string of good weeks in a row, to have a chance.'Modog814 said:As the season goes on, the small roster teams will be made up of more of the stud players that panned out, while the larger rosters will tend to have the cheaper players that broke out.
It is being redone on a different website. The link is in the first post of the thread.ETA - it is being setup by Organized Chaos and it will be free this year.What was that website last year that tracked your teams. Cost like $5? FantasyStarr or something? Sorry if posted already but I dug through a few pages and didn't find it and doing a google search for FantasyStarr or Fantasy Starr doesn't yield many safe for work hits...
Well, let's be realistic. An 18-, or 19-man roster isn't making it through the season with 3 TE, K and D. 20-man is the smallest you could try and that would be pushing it. Just for gits and shiggles here are stats from last year's playoffs:And what's to say a smaller roster can't have 3 TE, K and D?
Size Count Avg StDev18 53 483.225 46.42419 28 473.236 43.82720 22 508.705 39.25621 16 507.241 38.15922 21 525.712 41.59723 19 512.647 28.64824 16 493.059 34.98825 19 521.826 44.78326 13 494.177 47.42427 8 489.325 38.10628 12 513.754 35.17029 5 539.820 45.92930 19 527.468 33.426
I agree with this. I was mixing up concepts in my head as I typed - when I said higher mean is better over time, what I was thinking was if a team actually experienced a higher mean over a three-week period, then they would win over a team with a lower mean, regardless of their week-to-week variance. That's both obvious and meaningless. As I said, I'm swamped over here.This isn't true. It's not the time line that matters, it's the difference in mean/variance that matters. IF scores are distributed normally (I'm not sure if they are, but I'd think it was a pretty safe assumption), then time doesn't matter.Lower mean/higher variance is a potential benefit in a single week; higher mean/lower variance is a benefit over a long period of time. I'm not sure where a three-week span falls in that spectrum. Part of the problem is that we don't know precisely what the differences in mean and variance are between small and large rosters, so it's nearly impossible to quantify an advantage one way or the other.
Assume for a second that the week 1 scores are an accurate reflection of the truth. Than any team that is more likely to score 200 points in a given week, is more likely to score 600 in any given 3 weeks, and is more likely to score 800 in any given 4 weeks.
Time has no impact, assuming that weeks are independent, which I think we all agree that they pretty much are. Over any given period, a random 30 man team is expected to beat a random 18 man team. However, (again if these stats are accurate), over any given period, some 18 man has a higher chance of beating every 30 man team, than any 30 man team has of beating every 18 man team.
It's the difference in Mean and Variance that matter. If over the season we see that the means drift apart (which I believe we saw last year) then any advantage is shrunk, if they drift together, the advantage widens. Same with Variance, if variance drifts together, the advantage is shrunk, if they drift apart, the advantage is widened. I don't think we looked at variance last year (maybe we did?).
As I said earlier, I feel like, intuitively, there's something that this math is missing. Maybe it's that the mean and variance from week 1 aren't really representative of what we should expect throughout the season. Maybe 200/week is too arbitrarily high a cutoff; based on the week 1 numbers, 18-man teams are more likely to score 600 over three weeks, but that advantage should disappear if you lower that cutoff to something like 590. Maybe it has something to do with the makeup of teams that actually survive to week 14 being different than the makeup of all entries in week 1. Maybe it's a bad assumption that weeks are independent. Maybe it's a bad assumption that scores in the finals are normally distributed. Maybe we're not accounting for some phenomenon of teams being "covered" by larger rosters (e.g. the 18-man Brady-Rice-Welker owner has less of a chance of winning if there's also a 25-man Brady-Rice-Welker owner in the finals). Maybe it's just the fact that larger rosters have won the past two years that's clouding my judgment. Or maybe my intuition is just way off, and small rosters really do possess a significant advantage in the finals. I just can't shake the feeling that they don't.Yes, it'd be unrealistic. But it's certainly realistic for an 18 man roster to decide to go to 21 so he can get an extra cheap K, D, TE. I'd still consider 21 as a small roster. That's interesting about the playoff stats. But kind of meaningless. It's like saying I flipped a coin 10 times and got 7 heads, so head is 70% likely to come up. I'd be way more interested to see the average score and St dev of those teams that made it just prior to the top 250 (I guess that was top 500 if I recall correctly). So up to week 13. And then again for those top 250 seperated out up to week 13. I'd just need average total score, and St. Dev of those total scores and we can back out what the average per week mean and variance is. I'll see if I can put it together if I get around to it, but if someone has the info more easily accessible that'd be great.Well, let's be realistic. An 18-, or 19-man roster isn't making it through the season with 3 TE, K and D. 20-man is the smallest you could try and that would be pushing it. Just for gits and shiggles here are stats from last year's playoffs:And what's to say a smaller roster can't have 3 TE, K and D?Code:Size Count Avg StDev18 53 483.225 46.42419 28 473.236 43.82720 22 508.705 39.25621 16 507.241 38.15922 21 525.712 41.59723 19 512.647 28.64824 16 493.059 34.98825 19 521.826 44.78326 13 494.177 47.42427 8 489.325 38.10628 12 513.754 35.17029 5 539.820 45.92930 19 527.468 33.426
Yeah, feel like I've read a lot of, "If my 20 man roster had made it past week 9...."I agree with this. I was mixing up concepts in my head as I typed - when I said higher mean is better over time, what I was thinking was if a team actually experienced a higher mean over a three-week period, then they would win over a team with a lower mean, regardless of their week-to-week variance. That's both obvious and meaningless. As I said, I'm swamped over here.This isn't true. It's not the time line that matters, it's the difference in mean/variance that matters. IF scores are distributed normally (I'm not sure if they are, but I'd think it was a pretty safe assumption), then time doesn't matter.Lower mean/higher variance is a potential benefit in a single week; higher mean/lower variance is a benefit over a long period of time. I'm not sure where a three-week span falls in that spectrum. Part of the problem is that we don't know precisely what the differences in mean and variance are between small and large rosters, so it's nearly impossible to quantify an advantage one way or the other.
Assume for a second that the week 1 scores are an accurate reflection of the truth. Than any team that is more likely to score 200 points in a given week, is more likely to score 600 in any given 3 weeks, and is more likely to score 800 in any given 4 weeks.
Time has no impact, assuming that weeks are independent, which I think we all agree that they pretty much are. Over any given period, a random 30 man team is expected to beat a random 18 man team. However, (again if these stats are accurate), over any given period, some 18 man has a higher chance of beating every 30 man team, than any 30 man team has of beating every 18 man team.
It's the difference in Mean and Variance that matter. If over the season we see that the means drift apart (which I believe we saw last year) then any advantage is shrunk, if they drift together, the advantage widens. Same with Variance, if variance drifts together, the advantage is shrunk, if they drift apart, the advantage is widened. I don't think we looked at variance last year (maybe we did?).As I said earlier, I feel like, intuitively, there's something that this math is missing. Maybe it's that the mean and variance from week 1 aren't really representative of what we should expect throughout the season. Maybe 200/week is too arbitrarily high a cutoff; based on the week 1 numbers, 18-man teams are more likely to score 600 over three weeks, but that advantage should disappear if you lower that cutoff to something like 590. Maybe it has something to do with the makeup of teams that actually survive to week 14 being different than the makeup of all entries in week 1. Maybe it's a bad assumption that weeks are independent. Maybe it's a bad assumption that scores in the finals are normally distributed. Maybe we're not accounting for some phenomenon of teams being "covered" by larger rosters (e.g. the 18-man Brady-Rice-Welker owner has less of a chance of winning if there's also a 25-man Brady-Rice-Welker owner in the finals). Maybe it's just the fact that larger rosters have won the past two years that's clouding my judgment. Or maybe my intuition is just way off, and small rosters really do possess a significant advantage in the finals. I just can't shake the feeling that they don't.
In the past, I've mostly avoided the issue; my argument has typically been something like: even if small rosters have a measurable advantage in the finals, it's not enough to overcome their demonstrable disadvantage in the regular season. If the whole contest boils down to luck and and I need to catch lightning in a bottle one way or another, I'd rather try to get lucky for three weeks in December than for thirteen weeks from September to November.
No problem. Math concepts are very easy to get mixed up.I agree with this. I was mixing up concepts in my head as I typed - when I said higher mean is better over time, what I was thinking was if a team actually experienced a higher mean over a three-week period, then they would win over a team with a lower mean, regardless of their week-to-week variance. That's both obvious and meaningless. As I said, I'm swamped over here.![]()
Very possible. In fact, I'd say the chances are low that they are representative of what we should expect throughout the season. I'd expect the difference in means to widen, but I'm not exactly sure about the variances.As I said earlier, I feel like, intuitively, there's something that this math is missing. Maybe it's that the mean and variance from week 1 aren't really representative of what we should expect throughout the season.
You're correct that lowering the cutoff would shrink the advantage and eventual become an advantage for the higher mean/lower variance group. However, I think 200 is a fairly good cut off since the winner generally needs 600 points over a 3 week period.Maybe 200/week is too arbitrarily high a cutoff; based on the week 1 numbers, 18-man teams are more likely to score 600 over three weeks, but that advantage should disappear if you lower that cutoff to something like 590.
I think this goes back to your thought that maybe week 1 isn't representative. I'm looking forward to see the avg scores and st dev. of surviving teams each week.Maybe it has something to do with the makeup of teams that actually survive to week 14 being different than the makeup of all entries in week 1.
See argument in previous pages about Week 1 having no effect on a players rest of the season.Maybe it's a bad assumption that weeks are independent.
It's possible that scores aren't normally distributed, but I'd actually be very surprised if they weren't. Week 1 scores look pretty normal. The bolded is basically the question. Is there an advantage? If so, how big? Is it enough to warrant taking a smaller roster?Maybe it's a bad assumption that scores in the finals are normally distributed. Maybe we're not accounting for some phenomenon of teams being "covered" by larger rosters (e.g. the 18-man Brady-Rice-Welker owner has less of a chance of winning if there's also a 25-man Brady-Rice-Welker owner in the finals). Maybe it's just the fact that larger rosters have won the past two years that's clouding my judgment. Or maybe my intuition is just way off, and small rosters really do possess a significant advantage in the finals. I just can't shake the feeling that they don't.
In the past, I've mostly avoided the issue; my argument has typically been something like: even if small rosters have a measurable advantage in the finals, it's not enough to overcome their demonstrable disadvantage in the regular season. If the whole contest boils down to luck and and I need to catch lightning in a bottle one way or another, I'd rather try to get lucky for three weeks in December than for thirteen weeks from September to November.
Sure. I think it's a poor lineup decision, though, to be carrying a third K and D if you only have 12 QB/RB/WR.Yes, it'd be unrealistic. But it's certainly realistic for an 18 man roster to decide to go to 21 so he can get an extra cheap K, D, TE. I'd still consider 21 as a small roster.
Sure, but so is making inferences about what will happen in the playoffs based on last week's results. All of the analyses we do here are severely flawed for one reason or another. But anyway, I wasn't posting those playoff stats to make a point, they were just easy to pull and post, so I did.That's interesting about the playoff stats. But kind of meaningless. It's like saying I flipped a coin 10 times and got 7 heads, so head is 70% likely to come up.
I don't have that info anymore. Maybe at some point I'll be less busy and more bored and I'll recreate last year's DB for the hell of it. I'm curious why you'd be interested to see this, though. You want to take the final 500, and compare the 250 that made the finals to the 250 that didn't? What exactly would you be looking to see?I'd be way more interested to see the average score and St dev of those teams that made it just prior to the top 250 (I guess that was top 500 if I recall correctly). So up to week 13. And then again for those top 250 seperated out up to week 13. I'd just need average total score, and St. Dev of those total scores and we can back out what the average per week mean and variance is. I'll see if I can put it together if I get around to it, but if someone has the info more easily accessible that'd be great.
IIRC that argument didn't address whether or not weeks are independent. It just assumed that they are, and then concluded that week 1 has no effect on the rest of the season. But it's not clear that they really are; these aren't theoretical flips of a fair coin, these are NFL players.See argument in previous pages about Week 1 having no effect on a players rest of the season.Maybe it's a bad assumption that weeks are independent.
I agree they probably are. I was just spitballing a list of all the things that could possibly be wrong with our analysis.It's possible that scores aren't normally distributed, but I'd actually be very surprised if they weren't. Week 1 scores look pretty normal.
I don't think it is. But that's what I'm trying to work through here - I'll be convinced if we come up with a sufficiently strong quantitative case for that advantage, but I don't think we've done that yet.Is there an advantage? If so, how big? Is it enough to warrant taking a smaller roster?
checking the first post seems almost beyond obvious, yet here I am.It is being redone on a different website. The link is in the first post of the thread.ETA - it is being setup by Organized Chaos and it will be free this year.What was that website last year that tracked your teams. Cost like $5? FantasyStarr or something? Sorry if posted already but I dug through a few pages and didn't find it and doing a google search for FantasyStarr or Fantasy Starr doesn't yield many safe for work hits...

The way I think about is with regard to dynamic player values. If you could reprice players prior to week 14, a lot of values would change drastically from pre-season amounts. Circumstances change over the course of the season. The thing is that the pre-season studs are already priced as studs, so there is not as much surplus there relative to a larger roster that has hit on some of their value plays. Not that larger rosters have a monopoly on value plays, but a larger roster usually has more opportunities for players to "blow up".As I said earlier, I feel like, intuitively, there's something that this math is missing. Maybe it's that the mean and variance from week 1 aren't really representative of what we should expect throughout the season. Maybe 200/week is too arbitrarily high a cutoff; based on the week 1 numbers, 18-man teams are more likely to score 600 over three weeks, but that advantage should disappear if you lower that cutoff to something like 590. Maybe it has something to do with the makeup of teams that actually survive to week 14 being different than the makeup of all entries in week 1. Maybe it's a bad assumption that weeks are independent. Maybe it's a bad assumption that scores in the finals are normally distributed. Maybe we're not accounting for some phenomenon of teams being "covered" by larger rosters (e.g. the 18-man Brady-Rice-Welker owner has less of a chance of winning if there's also a 25-man Brady-Rice-Welker owner in the finals). Maybe it's just the fact that larger rosters have won the past two years that's clouding my judgment. Or maybe my intuition is just way off, and small rosters really do possess a significant advantage in the finals. I just can't shake the feeling that they don't.
I don't know about others, but I know I was only using the independence argument to combat the idea that there is negative correlation. I think it is close to independent, but the regressions on the QB data you shared seemed to indicate slight positive correlation.IIRC that argument didn't address whether or not weeks are independent. It just assumed that they are, and then concluded that week 1 has no effect on the rest of the season. But it's not clear that they really are; these aren't theoretical flips of a fair coin, these are NFL players.See argument in previous pages about Week 1 having no effect on a players rest of the season.Maybe it's a bad assumption that weeks are independent.
More or less poor than having 12 QB/RB/WR and 6 TE/PK/DT?Sure. I think it's a poor lineup decision, though, to be carrying a third K and D if you only have 12 QB/RB/WR.Yes, it'd be unrealistic. But it's certainly realistic for an 18 man roster to decide to go to 21 so he can get an extra cheap K, D, TE. I'd still consider 21 as a small roster.
Kind of but not really. One I'm using the past (week 1) to try and help us predict the future. The other, you're using the past to help predict the results of the data you're using to predict. Either way, you're correct, both are flawed. And yes I knew you weren't really making any point, but you posted it, so I put my 2 cents in.Sure, but so is making inferences about what will happen in the playoffs based on last week's results. All of the analyses we do here are severely flawed for one reason or another. But anyway, I wasn't posting those playoff stats to make a point, they were just easy to pull and post, so I did.That's interesting about the playoff stats. But kind of meaningless. It's like saying I flipped a coin 10 times and got 7 heads, so head is 70% likely to come up.
Not for the sake of comparing those who do make the top 250 to those who didn't. But I wanted a) see how well end of season data (mean and variance) does to a 1 week sample, and b) to see what it said the chances of each roster size had of winning the thing was and c) to see if that data had any predictive value as to what would happen in the final 3 weeks. The top 500 was just to see if it made any difference, since it'd increase the sample size. There were only like 5 27 man teams that made the top 250. So that data could be more easily skewed by 1 really good team.I don't have that info anymore. Maybe at some point I'll be less busy and more bored and I'll recreate last year's DB for the hell of it. I'm curious why you'd be interested to see this, though. You want to take the final 500, and compare the 250 that made the finals to the 250 that didn't? What exactly would you be looking to see?I'd be way more interested to see the average score and St dev of those teams that made it just prior to the top 250 (I guess that was top 500 if I recall correctly). So up to week 13. And then again for those top 250 seperated out up to week 13. I'd just need average total score, and St. Dev of those total scores and we can back out what the average per week mean and variance is. I'll see if I can put it together if I get around to it, but if someone has the info more easily accessible that'd be great.
Interesting...care to explain any thoughts on why you'd think they weren't independent? I believe i already posted on why I think they aren't quite independent, but are close enough to consider them independent. We're both working on the same question. Personally I believe there is an advantage (not proven but that's my gut instinct), and that it may be large enough to make worth it to take a smaller roster on an expected value basis.IIRC that argument didn't address whether or not weeks are independent. It just assumed that they are, and then concluded that week 1 has no effect on the rest of the season. But it's not clear that they really are; these aren't theoretical flips of a fair coin, these are NFL players.
I don't think it is. But that's what I'm trying to work through here - I'll be convinced if we come up with a sufficiently strong quantitative case for that advantage, but I don't think we've done that yet.Is there an advantage? If so, how big? Is it enough to warrant taking a smaller roster?
SUMMARY OUTPUT Regression Statistics Multiple R 0.142599208 R Square 0.020334534 Adjusted R Square 0.017567118 Standard Error 8.964148867 Observations 356 ANOVA df SS MS F Significance F Regression 1 590.4427718 590.4427718 7.347839983 0.007041416 Residual 354 28446.01158 80.3559649 Total 355 29036.45435 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%Intercept 18.53064565 1.257871419 14.73174871 1.20486E-38 16.05680525 21.00448606 16.05680525 21.00448606X Variable 1 0.143171617 0.052817408 2.710689946 0.007041416 0.039296264 0.247046971 0.039296264 0.247046971
What were your independent and dependent variables out of curiosity? Just passing yards for week T-1 and week T?This is some very interesting output. The r-squared indicates that it is not explaining much of the variation (2%), but the 2.7 t-stat indicates that the relationship is statistically significant.Out of curiousity, I looked at last years QB Fantasy Points on a game by game basis, and ran a regression on week to week output. I excluded any week where a QB scored less than 5 points in either of the input or output week (to try and get rid of those injury games).The results seem to indicate that there is no real dependence of the games week to week. Correlation of .1426 and R^2 of .02Regression output in case interested:
Code:SUMMARY OUTPUT Regression Statistics Multiple R 0.142599208 R Square 0.020334534 Adjusted R Square 0.017567118 Standard Error 8.964148867 Observations 356 ANOVA df SS MS F Significance F Regression 1 590.4427718 590.4427718 7.347839983 0.007041416 Residual 354 28446.01158 80.3559649 Total 355 29036.45435 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%Intercept 18.53064565 1.257871419 14.73174871 1.20486E-38 16.05680525 21.00448606 16.05680525 21.00448606X Variable 1 0.143171617 0.052817408 2.710689946 0.007041416 0.039296264 0.247046971 0.039296264 0.247046971
Staged.I'm pretty sure NASA put a man on the moon with far less analysis than one can find here on any given day concerning optimal roster size and uniqueness. Just sayin'
Fantasy Points (by Contest rules) for week T-1 and Week T.What were your independent and dependent variables out of curiosity? Just passing yards for week T-1 and week T?This is some very interesting output. The r-squared indicates that it is not explaining much of the variation (2%), but the 2.7 t-stat indicates that the relationship is statistically significant.Out of curiousity, I looked at last years QB Fantasy Points on a game by game basis, and ran a regression on week to week output. I excluded any week where a QB scored less than 5 points in either of the input or output week (to try and get rid of those injury games).The results seem to indicate that there is no real dependence of the games week to week. Correlation of .1426 and R^2 of .02Regression output in case interested:
Code:SUMMARY OUTPUT Regression Statistics Multiple R 0.142599208 R Square 0.020334534 Adjusted R Square 0.017567118 Standard Error 8.964148867 Observations 356 ANOVA df SS MS F Significance F Regression 1 590.4427718 590.4427718 7.347839983 0.007041416 Residual 354 28446.01158 80.3559649 Total 355 29036.45435 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%Intercept 18.53064565 1.257871419 14.73174871 1.20486E-38 16.05680525 21.00448606 16.05680525 21.00448606X Variable 1 0.143171617 0.052817408 2.710689946 0.007041416 0.039296264 0.247046971 0.039296264 0.247046971
Trying to replicate your results, and then doing the same for yards, has been enlightening. The conclusions appear to be the same as looking at the data from multiple years and determining the effect of week 1 on rest-of-season performance. In each of these cases, we get a positive relationship that is statistically significant at a 95% level. But the data is so scattered that the estimated impact can explain less than 10% of the variation.So I think we could say that week to week performance for QBs is either effectively independent or slightly positively correlated.Fantasy Points (by Contest rules) for week T-1 and Week T.What were your independent and dependent variables out of curiosity? Just passing yards for week T-1 and week T?This is some very interesting output. The r-squared indicates that it is not explaining much of the variation (2%), but the 2.7 t-stat indicates that the relationship is statistically significant.Out of curiousity, I looked at last years QB Fantasy Points on a game by game basis, and ran a regression on week to week output. I excluded any week where a QB scored less than 5 points in either of the input or output week (to try and get rid of those injury games).
The results seem to indicate that there is no real dependence of the games week to week. Correlation of .1426 and R^2 of .02
Regression output in case interested:
SUMMARY OUTPUT Regression Statistics Multiple R 0.142599208 R Square 0.020334534 Adjusted R Square 0.017567118 Standard Error 8.964148867 Observations 356 ANOVA df SS MS F Significance F Regression 1 590.4427718 590.4427718 7.347839983 0.007041416 Residual 354 28446.01158 80.3559649 Total 355 29036.45435 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%Intercept 18.53064565 1.257871419 14.73174871 1.20486E-38 16.05680525 21.00448606 16.05680525 21.00448606X Variable 1 0.143171617 0.052817408 2.710689946 0.007041416 0.039296264 0.247046971 0.039296264 0.247046971
I agree, rostering $110 worth of players would be about the worst thing possible.-QGSUBSCRIBER CONTEST WORST PICKS POSSIBLEQB PEYTON MANNING $26RB Ryan Grant $21RB Brandon Jackson $3RB Jeremiah Johnson $3WR Donnie Avery $10WR Mark CLayton $6TE John Carlson $2TE Tony Moeaki $9TE Chris Cooley $12TE Mike Hoomananewowieuowiwoeirwoieurwoier $2K Nate Kaeding $7DEF PIT $9
I'm not making a statistical argument here, but a personal insight. Since I think my odds of winning are pretty low, most of the fun is just enjoying the contest.So in my case, I'd rather still be in the running as long as possible. Just my $.02 thoughIf the whole contest boils down to luck and and I need to catch lightning in a bottle one way or another, I'd rather try to get lucky for three weeks in December than for thirteen weeks from September to November.

I have Pittsburgh's defense, so I think that is a pretty good pick.'QuizGuy66 said:I agree, rostering $110 worth of players would be about the worst thing possible.-QG'Crazy Tony said:SUBSCRIBER CONTEST WORST PICKS POSSIBLEQB PEYTON MANNING $26RB Ryan Grant $21RB Brandon Jackson $3RB Jeremiah Johnson $3WR Donnie Avery $10WR Mark CLayton $6TE John Carlson $2TE Tony Moeaki $9TE Chris Cooley $12TE Mike Hoomananewowieuowiwoeirwoieurwoier $2K Nate Kaeding $7DEF PIT $9
You do not need to be lucky for 13 weeks, you need to be above average (not sure how the cut off works) or you need to be better than the cut off group. In other words, since no one was eliminated in week 1, you could have the worst score of all time and still advance. Just like the two guys being chased by a bear.. guy stops to put his running shoes on and the other guy says, "you fool, you will never outrun the bear", to which the guy replied, "I do not have to outrun the bear, I have to outrun you". I think there is an argument that you need more luck in the last 3 weeks than in the first 13.'BaBastage said:I'm not making a statistical argument here, but a personal insight. Since I think my odds of winning are pretty low, most of the fun is just enjoying the contest.So in my case, I'd rather still be in the running as long as possible. Just my $.02 though'Ignoratio Elenchi said:If the whole contest boils down to luck and and I need to catch lightning in a bottle one way or another, I'd rather try to get lucky for three weeks in December than for thirteen weeks from September to November.![]()
I like this analogy. For each of the first 13 weeks you don't have to be the fastest, just fast enough. But in the last 3 weeks, theres only 1 bear, but you've got to outrun everybody. But I don't know that you can say you don't need to be lucky for 13 weeks. You definitely can't be unlucky. There's 10,000+ entries in here. Even if you want to be aggressive and say that only 5000 have a shot at getting to the Top 250, you still only have a 5% chance of getting there yourself. This is like Fantasy Football and Poker luck/skill debate. I think most will admit you need both, but how much of each? Personally, this contest, I believe is more luck than skill. All you can do is pick the best players, select the most effective breakdown of your team. But after Week 1 kicks off, you're in the hands of the players you selected. Skill will get you to that "top 5000 that have a shot", luck will get you to the Top 250. And very good luck will get you to the Top 1.You do not need to be lucky for 13 weeks, you need to be above average (not sure how the cut off works) or you need to be better than the cut off group. In other words, since no one was eliminated in week 1, you could have the worst score of all time and still advance. Just like the two guys being chased by a bear.. guy stops to put his running shoes on and the other guy says, "you fool, you will never outrun the bear", to which the guy replied, "I do not have to outrun the bear, I have to outrun you". I think there is an argument that you need more luck in the last 3 weeks than in the first 13.'BaBastage said:I'm not making a statistical argument here, but a personal insight. Since I think my odds of winning are pretty low, most of the fun is just enjoying the contest.So in my case, I'd rather still be in the running as long as possible. Just my $.02 though'Ignoratio Elenchi said:If the whole contest boils down to luck and and I need to catch lightning in a bottle one way or another, I'd rather try to get lucky for three weeks in December than for thirteen weeks from September to November.![]()
Broncos just told Jeremiah Johnson that he'll be activated off practice squad for Sunday's game. Maybe he gets the start and does well.Not good news for Moreno. Just saying.'QuizGuy66 said:I agree, rostering $110 worth of players would be about the worst thing possible.-QG'Crazy Tony said:SUBSCRIBER CONTEST WORST PICKS POSSIBLEQB PEYTON MANNING $26RB Ryan Grant $21RB Brandon Jackson $3RB Jeremiah Johnson $3WR Donnie Avery $10WR Mark CLayton $6TE John Carlson $2TE Tony Moeaki $9TE Chris Cooley $12TE Mike Hoomananewowieuowiwoeirwoieurwoier $2K Nate Kaeding $7DEF PIT $9