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The perfect auction (1 Viewer)

mingusrude

Footballguy
My league has been doing an auction draft for a few years, and being a little bit of a nerd, I realized that figuring out who to draft/buy is really an applied "Knapsack problem", which is a combinatorial optimization problem. Wikipedia has a pretty good entry on these types of problems.

Essentially, if you trust your projections and your auction values going in, you can figure out a mathematically ideal roster, and just target those players. So what I've done is written a program in some stats software that will maximize the projected points you can score in a season with a given budget. I feed in an excel sheet of players, projections, and my auction values, and it spits out a roster. Its pretty neat. Here is an example just based on ESPN's suggested auction values and projected stats (and standard ESPN roster and scoring settings):

Perfect "Balanced" Roster ($200 spread across all 16 spots)
Projected Score 109.8 pts/game
Matthew Stafford
Tony Romo
Adrian Peterson
Reggie Bush
Eddie Lacy
BenJarvus Green-Ellis
Calvin Johnson
Mike Wallace
Torrey Smith
Danario Alexander
Steve Johnson
Rob Gronkowski
Tony Gonzalez
49ers D
Seahawks D
Stephen Gostkowski

Perfect Top-Heavy 3RB Roster ($193 spent on starters, $1 on each bench spot)
Projected Score 113.5 pts/game
Staters:
Matt Ryan
Adrian Peterson
Arian Foster
Eddie Lacy
Mike Wallace
Jordy Nelson
Rob Gronkowski
49ers D
Stephen Gostkowski

Perfect Top-Heavy 3WR Roster (ESPN has a flex position. $193 spent on starters, $1 on each bench spot)
Projected Score 113.5 pts/game (yes, exactly the same as the 3RB roster)
Staters:
Matt Ryan
Reggie Bush
Adrian Peterson
Mike Wallace
Randall Cobb
Calvin Johnson
Rob Gronkowski
49ers
Stephen Gostkowski

Perfect Top-Heavy 2TE Roster ($193 spent on starters, $1 on each bench spot)
Projected Score 112.7 pts/game
Staters:
Matt Ryan
Reggie Bush
Adrian Peterson
Torrey Smith
Calvin Johnson
Rob Gronkowski
Jimmy Graham
49ers
Stephen Gostkowski

A couple observations.
  • Adrian Peterson shows up on every roster above, even the "balanced" one with a strong bench
  • Calvin Johnson shows up on all but the 3-RB top-heavy roster
  • Gronkowski is a great value at TE
  • Mike Wallace and Torrey Smith show up multiple times (and probably represent good values at their prices
Its not a perfect method. And it assumes that ESPN's suggested prices will be what these guys go for (which is not a terrible assumption; see the concept of Anchoring). But seems to be a good way to identify players who are good values and to get an idea of what a well-constructed team looks like. If anyone's interested I'll follow up with a little how-to guide.


 
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kutta

Footballguy
So it looks like we need to get AP, Calvin, and Gronk on our teams. Basically, the number 1 RB, the number 1 WR, and the number 1 (or 2) TE. That's not really giving us a lot of insight...

 

MarcO

Footballguy
big waste of time. There is NO way to predict how an auction draft will go and therefore no way to project the prices going in. You can only use these to predict how others will value the player compared to other players in the same tier. If B Marshall goes for $40, it's a good bet that D. Thomas will go for around the same amount - However, throw the projected numbers out the window when you have a the last of a top 5 QB on the board - or the last of a top 10 RB or a team desperately trying to fill a need. I paid $80 for matt Ryan (compared to the $60 or so that it took to get Brees / Rodgers) cause i got caught with him being the only top 10 QB left on the board and another team in the same boat. but I got good value on other positions - so I felt i could afford it.

The key is quickly being able to gauge the prices during the draft and adjusting accordingly. Take advantage of the value where you can and then if you have to overpay for a need it doesn't hurt as much.

 
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mingusrude

Footballguy
So what running this analysis did for me is convince me that even if I want a "balanced" roster, I should go top heavy and go after the studs. You're not going to benefit much from having three number-two WRs, for example. The value is not in the middle area, but at the top. In the past, I've struggled with mediocre, but what felt like well-balanced teams. So, the takeaways are at a strategic rather than specific-player level. An advantage of the auction is that you can have 2 or 3 first round picks on your team if you're willing to pay. This suggests that you should pay up.

 

kutta

Footballguy
big waste of time. There is NO way to predict how an auction draft will go and therefore no way to project the prices going in. You can only use these to predict how others will value the player compared to other players in the same tier. If B Marshall goes for $40, it's a good bet that D. Thomas will go for around the same amount - However, throw the projected numbers out the window when you have a the last of a top 5 QB on the board - or the last of a top 10 RB or a team desperately trying to fill a need. I paid $80 for matt Ryan (compared to the $60 or so that it took to get Brees / Rodgers) cause i got caught with him being the only top 10 QB left on the board and another team in the same boat. but I got good value on other positions - so I felt i could afford it.

The key is quickly being able to gauge the prices during the draft and adjusting accordingly. Take advantage of the value where you can and then if you have to overpay for a need it doesn't hurt as much.
If your cap is $200, $80 is waaaaaay too much to be spending on Ryan in just about any situation.

 

Warrior

Footballguy
So what running this analysis did for me is convince me that even if I want a "balanced" roster, I should go top heavy and go after the studs. You're not going to benefit much from having three number-two WRs, for example. The value is not in the middle area, but at the top. In the past, I've struggled with mediocre, but what felt like well-balanced teams. So, the takeaways are at a strategic rather than specific-player level. An advantage of the auction is that you can have 2 or 3 first round picks on your team if you're willing to pay. This suggests that you should pay up.
This is flawed logic because you're assuming that each player will earn their projected # of points. In reality, players get injured and you need solid bench players to fill in. Your calculations just assume that you'll plug in your best starting lineup and let it ride all year. Common sense would tell you that the best way to build a roster under this scenario (of no injuries) is to spend as much $ as possible on your starting lineup and only $1 each per bench player.

That's not how it works in reality.

 

mingusrude

Footballguy
Your calculations just assume that you'll plug in your best starting lineup and let it ride all year.
No. Even in the balanced projected roster above, in which $200 is spread evenly over all spots (starter and bench), it still spits out Peterson, Johnson, Gronk. The total amount spent on the starters is $164 out of $200, with the rest on the bench. That's $18 average per starter, $4 average per bench spot. And that maximizes the projected points across 16 roster spots.

The upshot is even if you're playing it safe and keeping in mind that in the NFL injuries happen, you shouldn't be spending a ton on your bench.

 
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Run It Up

Footballguy
I doubt a lot of things about these projections, not the least being that you somehow landed both Graham and Gronk in a 2TE league as well as ADP, Megatron and Bush.

 

SaintsInDome2006

Footballguy
My league has been doing an auction draft for a few years, and being a little bit of a nerd, I realized that figuring out who to draft/buy is really an applied "Knapsack problem", which is a combinatorial optimization problem. Wikipedia has a pretty good entry on these types of problems.

Essentially, if you trust your projections and your auction values going in, you can figure out a mathematically ideal roster, and just target those players. So what I've done is written a program in some stats software that will maximize the projected points you can score in a season with a given budget. I feed in an excel sheet of players, projections, and my auction values, and it spits out a roster. Its pretty neat. Here is an example just based on ESPN's suggested auction values and projected stats (and standard ESPN roster and scoring settings):

(1) Perfect "Balanced" Roster ($200 spread across all 16 spots)
Projected Score 109.8 pts/game
Matthew Stafford
Tony Romo
Adrian Peterson
Reggie Bush
Eddie Lacy
BenJarvus Green-Ellis
Calvin Johnson
Mike Wallace
Torrey Smith
Danario Alexander
Steve Johnson
Rob Gronkowski
Tony Gonzalez
49ers D
Seahawks D
Stephen Gostkowski

(2) Perfect Top-Heavy 3RB Roster ($193 spent on starters, $1 on each bench spot)
Projected Score 113.5 pts/game
Staters:
Matt Ryan
Adrian Peterson
Arian Foster
Eddie Lacy
Mike Wallace
Jordy Nelson
Rob Gronkowski
49ers D
Stephen Gostkowski

(3) Perfect Top-Heavy 3WR Roster (ESPN has a flex position. $193 spent on starters, $1 on each bench spot)
Projected Score 113.5 pts/game (yes, exactly the same as the 3RB roster)
Staters:
Matt Ryan
Reggie Bush
Adrian Peterson
Mike Wallace
Randall Cobb
Calvin Johnson
Rob Gronkowski
49ers
Stephen Gostkowski

(4) Perfect Top-Heavy 2TE Roster ($193 spent on starters, $1 on each bench spot)
Projected Score 112.7 pts/game
Staters:
Matt Ryan
Reggie Bush
Adrian Peterson
Torrey Smith
Calvin Johnson
Rob Gronkowski
Jimmy Graham
49ers
Stephen Gostkowski

A couple observations.
  • Adrian Peterson shows up on every roster above, even the "balanced" one with a strong bench
  • Calvin Johnson shows up on all but the 3-RB top-heavy roster
  • Gronkowski is a great value at TE
  • Mike Wallace and Torrey Smith show up multiple times (and probably represent good values at their prices
Its not a perfect method. And it assumes that ESPN's suggested prices will be what these guys go for (which is not a terrible assumption; see the concept of Anchoring). But seems to be a good way to identify players who are good values and to get an idea of what a well-constructed team looks like. If anyone's interested I'll follow up with a little how-to guide.
I think this merits more discussion. Any more thoughts on this?

I've added numbers next to each of the options in the OP. Any ideas on which is most optimal?

Auction values can fluctuate greatly. Hometown fans can inflate the price of local favorites. Some owners get jammed after getting outbid or over-waiting. And some leagues can have rules or owners who can tweak or inflate or deflate certain positions or players.

Ok, having said that:

Option 2 - Anyone see the value in investing heavily in 2-4 top tier or near top tier RB's and waiting for sleeper value at WR, TE & QB? Because auction is one way in which you can indeed get more than one top 10 player. And there is a fun element because you then have to switch gears and do extremely well on sleepers or picking right on the WW.

One way to view it is that you may have say X% of your salary cap to spend on premium players.

If that number is 60%, is that a lot? That could be one player, that could be four players, let's presume as above some will be at above value and some will be at less than value, so perhaps it evens out.

If 40% is considered a lot for one premium player, then you can get at most two, right? I doubt Peterson and Foster like the above would be possible but (again depending on how things go) maybe a Martin + Charles/McCoy/Forte could be?

I think Jimmy Graham may indeed be worth it this year, so I would consider him with many of the usual but limited non-RB suspects found in a 1st round draft.

Even if the OP is based on ESPN estimates, in a real auction with a 14-20 player roster I really wonder if you could get Peterson + Foster + Ryan + Gronk + Wallace etc. as above. I doubt it.

But I think it would be worthwhile to find a reliable auction $ estimate somewhere that we could use to build a more likely outcome.

 
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massraider

Footballguy
Anyone with Peterson and Foster isn't getting any other studs.

Those guys will be nominated within the first ten picks, by someone that wants to control the auction later.

 
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GregR

Footballguy
My league has been doing an auction draft for a few years, and being a little bit of a nerd, I realized that figuring out who to draft/buy is really an applied "Knapsack problem", which is a combinatorial optimization problem. Wikipedia has a pretty good entry on these types of problems.

Essentially, if you trust your projections and your auction values going in, you can figure out a mathematically ideal roster, and just target those players. So what I've done is written a program in some stats software that will maximize the projected points you can score in a season with a given budget. I feed in an excel sheet of players, projections, and my auction values, and it spits out a roster. Its pretty neat. Here is an example just based on ESPN's suggested auction values and projected stats (and standard ESPN roster and scoring settings):
If the players don't go for the auction prices you estimated, then you haven't optimized your team.

That's the beauty of auctions. You don't have to lock in a list of players. If you lock in a list, you may pass on the actual good values waiting for a player you think will be a good value, but who ends up going for more than you thought.

To optimize a team, you need to know a price that every player is worth based on your projection. Then as the auction progresses, be willing to bid on any starter at a position of need who is still at a price that he's a value. Once he's no longer a value you stop bidding.

It's also worth to add you have to pay attention to trends as you do this. If you notice, say, that every RB is going for more than he should, you will at some point also have to overpay for a RB just to have a quality starter. But in that case, you should aim to overpay less than everyone else, and then use that money to pick up good values at other positions.

 
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SaintsInDome2006

Footballguy
massraider said:
Anyone with Peterson and Foster isn't getting any other studs.

Those guys will be nominated within the first ten picks, by someone that wants to control the auction later.
There you go.

Really there's a total amount of virtual cap cash available ... and then the big names drum out a good deal of the reserve for 2-3 teams.

 

SaintsInDome2006

Footballguy
Greg Russell said:
My league has been doing an auction draft for a few years, and being a little bit of a nerd, I realized that figuring out who to draft/buy is really an applied "Knapsack problem", which is a combinatorial optimization problem. Wikipedia has a pretty good entry on these types of problems.

Essentially, if you trust your projections and your auction values going in, you can figure out a mathematically ideal roster, and just target those players. So what I've done is written a program in some stats software that will maximize the projected points you can score in a season with a given budget. I feed in an excel sheet of players, projections, and my auction values, and it spits out a roster. Its pretty neat. Here is an example just based on ESPN's suggested auction values and projected stats (and standard ESPN roster and scoring settings):
If the players don't go for the auction prices you estimated, then you haven't optimized your team.

That's the beauty of auctions. You don't have to lock in a list of players. If you lock in a list, you may pass on the actual good values waiting for a player you think will be a good value, but who ends up going for more than you thought.

To optimize a team, you need to know a price that every player is worth based on your projection. Then as the auction progresses, be willing to bid on any starter at a position of need who is still at a price that he's a value. Once he's no longer a value you stop bidding.

It's also worth to add you have to pay attention to trends as you do this. If you notice, say, that every RB is going for more than he should, you will at some point also have to overpay for a RB just to have a quality starter. But in that case, you should aim to overpay less than everyone else, and then use that money to pick up good values at other positions.
I guess this is the problem with Option 2. If you bid heavy and early on certain studs you miss the values.

The difference could be in getting several premium players instead of just say 2.

 

silentcoach

Footballguy
I like this thread--numbers.

You may want to tier the numbers so you can maximize your team. I know peterson is number 1 but maybe you can say the top 6 rbs are essentially just as valuable to any one team, and see if rb 6 enables you to save money to increase value at another position. Keep doing this across positions and you can have a maximized starting and bench team.

There is no need to restrict yourself to Peterson and Calvin because you are paying for what they are worth, and not taking into account that they may not produce at their values. With the method I described, you still get wiggle room and you may be able to have better players across the board.

Tier them up however you'd like.

 
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Chaos Commish

Footballguy
massraider said:
Anyone with Peterson and Foster isn't getting any other studs.

Those guys will be nominated within the first ten picks, by someone that wants to control the auction later.
There you go.

Really there's a total amount of virtual cap cash available ... and then the big names drum out a good deal of the reserve for 2-3 teams.
You never know. Auction values present themselves after the auction starts. I did an auction last weekend with a group of degenerate gamblers in their 6th year. My fourth. Live auction in Vegas. $500 entry. Solid group. Deeeep league with 10 IDPs, starting 2qbs, and using three flex starters in addition to 2rb, 3wr. $300 budget. This format generally favors the balanced approach. It drives prices down.

I have Brees and Brady.

AFoster, TRichardson, DWilson

Dez, Shorts, MWilliams,

Witten...

I was broke and built my D on $1 players, but it made sense, and I'm liking this team.

 

Ghost Rider

Footballguy
big waste of time. There is NO way to predict how an auction draft will go and therefore no way to project the prices going in. You can only use these to predict how others will value the player compared to other players in the same tier. If B Marshall goes for $40, it's a good bet that D. Thomas will go for around the same amount - However, throw the projected numbers out the window when you have a the last of a top 5 QB on the board - or the last of a top 10 RB or a team desperately trying to fill a need. I paid $80 for matt Ryan (compared to the $60 or so that it took to get Brees / Rodgers) cause i got caught with him being the only top 10 QB left on the board and another team in the same boat. but I got good value on other positions - so I felt i could afford it.

The key is quickly being able to gauge the prices during the draft and adjusting accordingly. Take advantage of the value where you can and then if you have to overpay for a need it doesn't hurt as much.
Agreed. In an auction I did the other day, Trent Richardson went for as much as Doug Martin and for only $2 less than Adrian Peterson because he was the last of the 1st round-tier RBs to be put up for bid, so many of the owners who had missed out on the other top RBs saw Richardson as their last chance to grab one of them, so the bidding went high, while AP went for only low 50s cause he was put up first or second. Now, had Richardson been the first RB put up, he probably goes for 8-10 bucks cheaper. In an auction, it's all a matter of WHEN a player is put up for bid.

 
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SaintsInDome2006

Footballguy
I like this thread--numbers.

You may want to tier the numbers so you can maximize your team. I know peterson is number 1 but maybe you can say the top 6 rbs are essentially just as valuable to any one team, and see if rb 6 enables you to save money to increase value at another position. Keep doing this across positions and you can have a maximized starting and bench team.

There is no need to restrict yourself to Peterson and Calvin because you are paying for what they are worth, and not taking into account that they may not produce at their values. With the method I described, you still get wiggle room and you may be able to have better players across the board.

Tier them up however you'd like.
This is what I was thinking.

Foster and Peterson may just be in their own tier in terms of price. (And Calvin).

Martin is a wild card, I wonder where his value goes in auctions this year. I'm guessing high like Peterson and Foster, where he should be.

But however you rank them (consider the RBs at near, or with a shot at finishing 3-5 and that may number 8-12 players) I'd like to devote as much as 60-80% of my $$$ spent on RB. So then: Spiller, Richardson, Charles, Forte, Lynch, Rice, Morris, McCoy (not in that order, it's a tier, but I do like some better than others). And I will put Graham in this tier because (to me) he really could be that good this year.

I believe I can do very well at mid tier guys & sleepers at WR & TE & QB, and I actually enjoy that.

 

Chaos Commish

Footballguy
big waste of time. There is NO way to predict how an auction draft will go and therefore no way to project the prices going in. You can only use these to predict how others will value the player compared to other players in the same tier. If B Marshall goes for $40, it's a good bet that D. Thomas will go for around the same amount - However, throw the projected numbers out the window when you have a the last of a top 5 QB on the board - or the last of a top 10 RB or a team desperately trying to fill a need. I paid $80 for matt Ryan (compared to the $60 or so that it took to get Brees / Rodgers) cause i got caught with him being the only top 10 QB left on the board and another team in the same boat. but I got good value on other positions - so I felt i could afford it.

The key is quickly being able to gauge the prices during the draft and adjusting accordingly. Take advantage of the value where you can and then if you have to overpay for a need it doesn't hurt as much.
Agreed. In an auction I did the other day, Trent Richardson went for as much as Doug Martin and for only $2 less than Adrian Peterson because he was the last of the 1st round-tier RBs to be put up for bid, so many of the owners who had missed out on the other top RBs saw Richardson as their last chance to grab one of them, so the bidding went high, while AP went for only low 50s cause he was put up first or second. Now, had Richardson been the first RB put up, he probably goes for 8-10 bucks cheaper. In an auction, it's all a matter of WHEN a player is put up for bid.
This isn't an issue with Mingusrude's applied combinatorial optimization knapsack (more on that later). I love the thinking, btw. This is just being one of the knuckleheads screwed by the end of a perceived tier. That's just being bad at the task at hand. Be on your toes and avoid those bidding wars. I generally try to do that via the nomination process. More importantly understand two sets of tiers -- perceived tiers and your tiers. Overlay them and strategy emerges. Your's may match perceived. Sometimes mine do, but usually they don't. It isn't the end of your tiers that create bidding wars. It's the end of perceived tiers. If you agree with a tier, move early even if you have to nominate to do so. If you don't agree with a tier, maybe nominate your outlier to own that tier before the war, or wait for the war to end and take that position when prices normalize/fall. However you figure it out, don't be one of the desperados overbidding because the last guy of a perceived tier is up for sale. Instead try to set up those wars early in the process to drain accounts.

In the auction I mentioned above Sproles was clearly the end of tier. 6 guys nominated someone else for whatever reasons. I nominated him when it came to me, happy with my spending in his tier. He went for the same money as Richardson/Lynch and for more than Jackson, etc. PPR so the guy may be okay, but he only owns him because he mismanaged the tier. If he really wanted Sproles, he could have $10-$12 by nominating him earlier. Then some other back would have ended the tier at a silly price.

 

Bayhawks

Footballguy
  • Gronkowski is a great value at TE
I'm guessing this assumes Gronk won't miss the first 6 or so games?
Doesn't seem like a bad guess since there's no real reason to expect him to miss that many.
Assumption =/= guess.

Dictionary.com is your friend
Yes, yes it is:

http://dictionary.reference.com/browse/assumption?s=t

Synonyms: presupposition; hypothesis, conjecture, guess, postulate, theory.

But, now that I've finished educating you on what the word assumption means, there has been no negative news about Gronkowski since his surgery. Therefore, it is best to assume (or GUESS) that he is on the normal rehab/recovery timetable, which has been widely reported as having him ready around week one, not after week 6. Assuming (or guessing) that he will miss between 1/4-1/2 of the season would be foolish, based on the information we have available.

 

Bayhawks

Footballguy
So what running this analysis did for me is convince me that even if I want a "balanced" roster, I should go top heavy and go after the studs. You're not going to benefit much from having three number-two WRs, for example. The value is not in the middle area, but at the top. In the past, I've struggled with mediocre, but what felt like well-balanced teams. So, the takeaways are at a strategic rather than specific-player level. An advantage of the auction is that you can have 2 or 3 first round picks on your team if you're willing to pay. This suggests that you should pay up.
This is flawed logic because you're assuming that each player will earn their projected # of points. In reality, players get injured and you need solid bench players to fill in. Your calculations just assume that you'll plug in your best starting lineup and let it ride all year. Common sense would tell you that the best way to build a roster under this scenario (of no injuries) is to spend as much $ as possible on your starting lineup and only $1 each per bench player.

That's not how it works in reality.
In my experience, there's no "one way" to do an auction. I've seen teams spend virtually all their cap on their starters, and have no/little bench depth and win it all, and I've seen teams do the same thing and end up dead last. I've seen teams build balanced rosters and win it all, and I've seen teams with balanced squads miss the playoffs. Bottom line is, you have to hit on some players. You have to get some value: A QB for the average price (or below) who puts up stats of a top QB, a cheap RB who grabs a starting job. A WR who isn't expensive but makes the leap to WR1 status.

 

TALL hobbit

Footballguy
So what running this analysis did for me is convince me that even if I want a "balanced" roster, I should go top heavy and go after the studs. You're not going to benefit much from having three number-two WRs, for example. The value is not in the middle area, but at the top. In the past, I've struggled with mediocre, but what felt like well-balanced teams. So, the takeaways are at a strategic rather than specific-player level. An advantage of the auction is that you can have 2 or 3 first round picks on your team if you're willing to pay. This suggests that you should pay up.
This is flawed logic because you're assuming that each player will earn their projected # of points. In reality, players get injured and you need solid bench players to fill in. Your calculations just assume that you'll plug in your best starting lineup and let it ride all year. Common sense would tell you that the best way to build a roster under this scenario (of no injuries) is to spend as much $ as possible on your starting lineup and only $1 each per bench player.

That's not how it works in reality.
Warrior - what % of your budget do you usually hold back for your bench spots?

This is going to be my first year participating in an auction draft - and I'm trying to balance having adequate depth while making sure I don't take too much money away from my starters.

 

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