Methodology- The Model
May 7th, 2010 by Bill Phipps in TheoreticalThe next step in our methodology is to input the projections into our pricing model. Since Robert created the model, I will simply describe it in general terms and defer to him to share as much or as little about it as he cares to.
The premise behind the model is that the more closely a category is contested the more valuable that statistic is relative to other stats. For example, imagine on August 1st that you had your choice of increasing your total in any category by 5, how would you choose which to add? To answer, you would need to look at the standings and see how valuable 5 extra Steals would be relative to 5 extra HR, or Saves, or Wins, etc etc. This is what our approach attempts to solve.
First, we look at the history of as many leagues as we can to see how each category historically disperses. To do this, we take the team totals in each of the categories and measure the standard deviation between the teams. This gives us a good approximation of how tightly clumped we can expect each category to be. After measuring all 10 categories, we then set about determining what each stat is worth relative to each other. To do this, we translate each statistic into a common currency. Just like currency markets can be measured against the U.S dollar, we express all of our terms into RBI. The final result might look something like : HR=3.7 rbi. SB =3.1 rbi Win = 7.7 rbi, and so on ( this is just an illustration and not actual conversion values). Having done this, we can now take a player’s projected season and convert it into one number, adjRBI. For example, a season of 20 hr, 80 rbi, 70 runs, 5 sb and a .267 batting avg in 530 ab might equal a total of 232 adjusted RBI. After we have done this calculation for the entire league, we now have 1 term, adjRBI, to describe the net production of every player.
The next step is to establish a baseline at each position. To determine this, we begin by looking at the total adjRBI production of the bottom few draftable players at each position. For example, in a 10 team league where 20 catchers start, we will look at the adjRBI for catchers 16-24 to get an idea of where to set the baseline. We also recognize that, over the course of a long season, players will emerge in the claims pool and add depth to each position. To account for this, we move each baseline up by various amounts to reflect this claim pool optionality ( I should mention that determining baseline production for pitchers is a tricky proposition worthy of a very long post and I will hold off on discussing it at this time). After determining the baseline at each position, we go back and subtract that baseline number from the adjRBI to create a Value RBI number, VRBI. The last step is to take the total VRBI in the league and divide them by the total auction dollars to create a divisor number. This divisor shows how many VRBI = 1 auction dollar. To find out how much a player is worth, I simply take his VRBI and divide by the divisor number.
After we end up with a dollar value for every player I will then begin a series of reality checks. I have historic records of the prices that players went for in past auctions and I know what their final seasons were worth. I also have a rough idea of the prices I expect them to be worth. I will check these numbers against my generated values to see how they compare. I then keep tinkering with systemic inputs and tweaking individual players until I have a pool of numbers I am satisfied with.
The usefulness of the model is not limited to player valuation. We have created a very helpful spreadsheet for auctioning. It tracks how much premium/discount is left in the pool and what percent of it is from hitting vs. pitching. When a player is purchased, all I have to do is enter the amount and a reference number for the team that owns him. The player’s stats are immediately transferred to that owner, and every value for the remaining players is recalculated based on the remaining pool. The data entry is kept to a minimum and the spreadsheet makes on the fly adjustments much more accurately than I ever could by myself.
The model is also particularly adept, intra-season, at identifying the dynamic shift of values between each category. We are constantly running our current league and check to see if the distribution is differing significantly from past leagues. Then we compare current league distribution to how we think teams are headed in various categories. Instead of obstinately sticking with static valuations we actually are quite dynamic and at the forefront of anticipating shifting player values throughout the year. This is particularly useful for making trade valuations.
I have seen many objections to models made in others posts around this blog, and I would like to anticipate and address some of those concerns.
1) Our model does not shift the relative value of one category to another during the auction. It would certainly be easy enough to program the model to constantly recalculate the values based on the projected distribution of stats for each team. However, I intentionally do not do this because I think the effect on the overall pool is drastically overstated. If I draft Ellsbury and Crawford, this does not materially change the value of Juan Pierre. He is likely still worth my pre-auction value to some owner. If I find the bidding on Pierre stalls 3.5 dollars below my fair value, I am not obligated to buy him. I can, if I choose, make changes in the relative value of SB to other offensive stats and bring my values back into line. Or, I can let some other owner buy him cheap. Or, I can simply buy him myself and trade stolen bases later in the season. Because trading is allowed, game theory suggests that teams with excess trade some of those values back into the pack. Similarly, teams lagging in these categories will provide a market place for those stats. I keep reading references to the effect of fluctuating values during an auction, due to projected distribution of stats. I would like to see some concrete analysis of this. What are some examples of this happening? How big can the effect be?
2) People have stated that the process of projecting seasons and modeling their value will collapse the prices of the star players towards the middle. This is certainly not true in our methodology. We have approached the baseline in a fashion that keeps star players valued at star prices. Entering the CR auction, I had Arod priced at 38.5 and 8 other players worth over 30. Does this strike anyone as too timid?
3) Chris Liss has said “if you look at what the goal of this is – picking off mistakes in valuation relative to the "market's" projections, isn't this a pretty unambitious system, more designed to finish in the top half of the league each year rather than win it? Won't one of the six "genius" drafters almost always cash in bigger than the guy making a small but riskless profit from the vig?” I think this objection is without merit. The players I purchase have the same element of volatility as any other team. In fact, I have put a great amount of effort factoring volatility into my player pricing. My goal is to assemble a team with an expected value of much greater than 260. After achieving that, there is nothing riskless about my team. It can still get as lucky or unlucky as any other owner's.
4) I believe a more reasonable objection to our approach is its reliance on historical data for the distribution of categories. How do we know that we have enough data, or that an oddball strategy won’t throw all of our inputs off? On the surface, this appears to be a problem. However, at least it is a problem that every owner is left with on auction day. We have looked at enough data that we are comfortable that our opening day values represent our very best guess, and I think it is a pretty good one. Plus, our methods allow us to make quick adjustments to offbeat strategies that would be much more difficult without a modeling tool.
Tags: draft prep, Model
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Very clearly explained Bill.
In the Cardrunner's League auction, Chone Figgins went for $23 fairly early in the auction. Other speed guys, like Ellsbury, went early for pretty much their full price.
In the middle rounds the bidding stopped on Ichiro, another speed play, at $22, and shortly thereafter Denard Span went for $16.
In the late rounds, Juan Pierre went for $16.
At these particular points in the auction, stolen bases were priced differently by the whole room. This happens because we individually have our own $260 budgets, and if we buy enough of an item we reduce down the price we're willing to pay for more of it. If Pierre were going for $3 less than his price and you had all the SB you wanted, you probably wouldn't pay it.
My original point on this was that it happens, and that it doesn't take big differences in valuation to make big differences in how our teams would be put together if we didn't make adjustments throughout the auction. My original example involved closers. If you have the top five closers valued at 24, 23, 22, 21, and 20, and the rest of the room has them priced at 23, 23, 21, 21, 20, a difference of a couple dollars from $100, if you didn't make adjustments you'd end up with two of these expensive guys and have spent two thirds of your pitching budget on closers. That's not something most teams want to do, though it is, of course an option, which will have it's own ramificatioins on the prices other teams pay for the remaining closers.
At that point in the beginning of our discussion I was still reacting to your statement that your model based your prices on projections and that everything spun off the mathematical formulas you had devised. But I think as we've gone along we've seen that that isn't so. As it turns out, and should have been apparent then, your methods are quite similar to those many of us use. You make the same intuitive adjustments to escape the straightjacket of mechanically regressed projections, and you sometimes decide not to buy players who are going for significantly less than you have them priced at, when you feel that's the right thing to do.
It seems like we're playing the same game.
Your approach doesn't seem that different from some other popular valuation systems. The problem with 'category spread' based systems is that the values they assign assume that you're going to be somewhere within the typical range of totals in each category. That may be a reasonable assumption once the season is underway, but prior to the draft is it a safe assumption? Does using this approach change the likelihood of that happening?
In many leagues, Runs and RBI end up clustered almost as closely as SBs. If I end up valuing them at say half the value of an SB, I'm going to end up with virtually no SBs, because everyone else will value the speed players more than I will. I also may end up with a surplus of high RBI players, which leaves me above the 'cluster' in that category.
Yes Alex, it is based on assumptions around historic clumping. On auction day, what assumptions would you rather make?
Also, as I touched on earlier, this approach allows for shifting values as the auction goes on. I prefer to do very little of that, though, since I have found that leagues generally approach something very close to historic spreads as the year goes on anyway. If one team is running away with a category it should be fairly easy for him to trade some of his excess into the pack for value.
As the season progresses we will take into account the specific clumping of the league we are in and shift our values, but until the very end these shifts are rarely dramatic. This makes sense because it is almost impossible to maintain any winning chances while tanking more than one category. This keeps things reasonably tight across the board. There is certainly room for flukish endings where a run is worth more than a SB, but I don't think that can be anticipated by anyone until the final couple weeks of a season.
We built this in a vacuum, but I have always assumed that other similar models are out there. There are a lot of details to hammer out once you take this approach (correct baselines that account for value of the claims, turning projections into values when a player is worth more than their mean like injured players or players with skewed upside).
If you have found a different approach that works better I would love to hear about it in detail. I would be very curious to hear how another approach to the relative value of categories works.
Robert – I haven't found a better approach yet…but that doesn't mean that I don't think one exists. The other popular general approach is based on scarcity of each category and targeting certain levels in each category. I think that may be the correct approach, but the implementations of it that I've seen all seem to have made huge mistakes. One particular error is comparing players to 'replacement level' players instead of comparing them to some sort of 'average remaining available player'.
There is certainly room for improvement, and likely always will be. I think the next area we need to attack is player volatility. It impacts not only the value of players who can be replaced when they don't pan out, but also impacts winning chances above and beyone the expected return on player. I think the FBB model is similar to models in the financial world where the fundamental theory underlying them does not change but the battle for the best set of tweaks to take into account real world vs purely theoretical world is where the edge is.
Robert – I view player volatility more as part of projections than valuation…but agree that an edge can probably be gained by understanding it better. Every projection system which I've seen the details of uses some sort of weighted average of part performance (either by season or at bat). For example, they might weight each at bat at 99% of the weight of the subsequent at bat when projecting performance. But it seems as though projections for certain players who are very young, very old, coming off of injuries, showing statistical signs of possible injury, etc. should weight recent performance much more heavily.
I realize you're talking about player volatility in a different sense. At least I think you are. When I'm doing a very early draft in a relatively shallow league, I look for volatile players who will either be very valuable or potentially worthless…for example good pitchers coming off of injuries or hot prospects who may or may not make the team out of spring training, or guys fighting for a chance at being a team's closer. I figure the volatility is a strategic advantage, since I can always pick up someone mediocre to replace them if they don't pan out.
Another strategic consideration I look at is what I think of as 'playability'. If full season projections (taking park into account) for two marginal players are the same, I'd rather get the player with inferior skills but a favorable home park. Instead of usually being mediocre, he's going to be pretty good at home and really lousy on the road. That may mean that he's usable at home, where the other player isn't really usable anywhere.
ROBERT: "I would be very curious to hear how another approach to the relative value of categories works."
In the early 90s Les Leopold would run regression analysis using the stats of winning teams from many leagues as the input, and getting dollar values for each stat as the output. A homer might be worth 18 cents, an AB -3 cents, a win 22 cents. These are just illustrations, not real values. Thus you derived the category adjustments employed by winning teams, which tended to undervalue BA and SB, if I recall correctly.
In those days it was possible to get the final stats for a great many leagues from a stat service, which was meaningful because at that point we were all playing the same game, which was 4×4 Rotisserie.
About clumping: I don't really understand the need to make these tiny adjustments to player draft prices based on clumping. We know that there will be clumps, but we know that these will mostly be created by teams making strategic decisions to give up on a category or to go for it, which causes a ripple effect throughout the clumps.
Teams make these decisions because things haven't worked out the way they planned. They believed they had bought one type of balance/achievement on draft day, but because of injury or under or overperformance, they end up with a different type of balance/achievement.
The effect of these strategic decisions far overwhelms the utility of adjusting player prices on draft day.
On the other hand, since we know that meaningful clumping (that which can be most readily manipulated for strategic effect), is pretty much limited to Steals and Saves, it is an important component of player pricing to properly weight those two categories. What changes their value, however, aren't the clumps, but the ability of a player to spend his money elsewhere, either on draft day, or knowing that he can trade out of the commodity during the season, which reduces draft day demand.
In my pricing model my goal is to have a price reflect what people would have paid for those stats if they were buying the finished stat line, that is the actual value of the stats filtered by likely strategies that change their value. There is a hefty discount for Steals and Saves, just as there is in Art McGee's system, but the calculating is easier and I think the rationale is much clearer.
Knowing what a player is worth on draft day is important. Clumps take care of themselves as the season progresses.
By running stats on finished leagues we see exactly the range that they "worked themselves out". We not only have the average answer, but we have the range of answers. For instance, we have roughly seen SBs worth between 2.8 and 5.0 RBIs at season end and HR worth between 3.0 and 4.0 RBIs at season end. We can argue about what specific numbers to use for fair value, but not having seen anything outside of that it is hard to believe the fair value of either lies outside those ranges. What we use on auction day is our best guess, which is basically the mean of what we have witnessed with some small adjustments based on how the pool stacks up that year.
And as long as I'm taking the time to respond to some stuff, Peter, I think your conclusion that we are playing "the same game" is not quite accurate.
Bill and I are certainly willing to deal with information on a pure qualitative basis, but in every facet of our decision making we are constantly striving to quantify things even if we can only express something as a range or a rough estimate. It isn't that we think we could ever take the human element out, rather we want to always express our decisions in terms of probabilities and expected outcomes. We are both certainly trying to solve the same puzzle, but we are attempting it in clearly different ways.
I'm not sure I follow how your expression of decisions in terms of probabilities and expected outcomes differs from my expression of decisions in terms of probabilities and expected outcomes.
You and Bill put a range of probabilities to each outcome, but those are made up numbers. How do I know that they're made up numbers? Because there isn't enough data in the ML database to give you reasonable backup data to tell me whether Jason Heyward had a 10, 40 or 70 percent chance of surviving this year. In fact, we still don't know nearly a quarter of the way into the season. So where is the precision in that.
Or what are the probabilities for Lance Berkman? He's got a long history with surges and dings. Is his chance of hitting just 15 homers 10 percent? 30 percent? 60 percent? What about his chance of hitting 30 homers? You can make estimates based on what he's done in the past, and how he's done thus far this year, but those are guesses. They're gut. That's fine, that's the best we have, but it is far from precise. I think it's worth doing, I agree that something is better than nothing, but I think you should call it for what it is. A guesstimate.
I, on the other hand, put a range of probabilities through the blender and come up with a number that is part calculation and part guesswork, too. In fact, I quantify it. I publish a magazine full of these quantities. I publish prices and projections full of these quantities that people buy, and they tell me they win because of them. I tell them, and have told them, for 15 years, that some of the information is based on the math, and some of it is reading and parsing other data and qualitative information and making a call based on all of that.
When we got off to a bad start in this discussion it was because you made it sound like you had discovered a way to model baseball that was more accurate and rigorous than anyone else. But it isn't true, based on your own description. You collect a lot of qualitative information and a lot of quantitative information. You plug the quantitative information into your model, apply qualitative analysis so that the end results line up with what you think they should look like, and you have a system. You talk about your rigorous reality checks, and that may well be a virture. Your system may be more conservative in how it deviates from the baselines, or more selective in how it applies modifiers to them. Maybe your system identifies breakout guys in some way, we haven't talked about that yet. That may make you a great player. But that is the way every Tout started out, except maybe Liss. I don't see how there is any difference to this, except you seem to believe that doing what people have essentially been doing for more than 20 years is of some sort of extra importance.
I think we'd all like to see why you're so sure that's so? And why you won't even entertain the possibility that there are other approaches to these enduring problems.
Ps. In re the clumping question, You didn't address why deciding on August 1st (your example) that you need five extra in any category is a question that can or should be addressed on auction day.
Pps. In re the question of player values changing during the draft, I gave you (well, Bill) a specific example of how small differences make for big differences. This actually aligns with Bil's example of choosing not to pay $3 less for Pierre than you judged he was worth because you have that choice, but doesn't that mean that your market values are just guidelines? If you're not going to jump all over a 15-20 percent discount, why even bother making the list?
The answer, obviously, is because prices for resources during the auction fluctuate, both due to scarcity/abundance of resources and inflation/deflation based on the relative prices paid to expected prices. What is the probability of this? A certainty.
Peter, I think you're being rather unfair here.
They've noted they developed their model independently. If their methods are strong, its not surprising others came up with similar approaches. What they're saying is they've come up with better solutions to certain obstacles on the way (and some of those obstacles may have appeared insurmountable to the original practitioners- many of whom appear to have given up on modelling). The claim is that they've got a better light bulb, not that they've invented electricity.
I think whatever insight they have to offer is going to come in a discussion of details, not in general approach. Obviously though, they do have to start with the broad view.
I also think your characterization of Robert being unwilling to hear other ideas is unjustifiable. He's posted on a number of occasions that he would welcome hearing about other ideas and approaches. Perhaps to the extent that these ideas essentially constitute ' 'There's a lot of imprecision, take your best guess' he has been resistant to an extended back and forth, but where is that dialogue really supposed to go? I think the intention is more to focus the discussion on a refining of techniques for those who are interested in quantifying things as much as possible.
Sorry, but I don't think I'm being unfair. He asked for detail on the question of values changing during the auction, without offering any evidence that they don't change. I tried to continue the conversation and got no response. I thought we were discussing the issue, but we weren't.
He made category balance and clumping point number one in determining value (maybe not the most important, but clearly important), but when asked about the validity or importance of this in draft day pricing, he goes off onto a tangent about the variability of historic ratios between RBI and other categories. Not a word about clumping. Or an answer to my question about it's signficance on draft day pricing.
Finally, I think when you say that "If their methods are strong, it's not surprising others came up with similar approaches." The other approaches were developed 20 years ago and more. They've been published and adopted across the fantasy baseball world. I think it's unreasonable to say their model was developed independently, especially so until they show some of the better and innovative solutions they've discovered. I want to hear about the insurmountable, and how they mounted it.
Peter, that was not a tangent. As Bill explained in the post that we are commenting on our method involves translating all the categories into their relative tightness in relation to RBIs to give a constant currency.
Understood about the constant currency. I guess what I misunderstood is that you don't create the constant currency from the projected stats, but rather from the historical work you do deriving standard deviations in each category. Then, I guess, you apply the ratios to the projections. Is this correct?
What are the statistics used for the conversion of a category into RBI? I don't follow how the historical measuring of a category's spread leads to numbers that result in the ratios you cite.
And if the value of a SB can vary from 2.8 RBI to 5.0 RBI, how does that happen? Is that a function of the way individual leagues play out? Or year to year variation? And on what numbers are those ratios calculated? I know they're year end, but that they're not the total accumulation of each stat but rather some marginal part of it, right?
I find the discussion about changing values of the stats during the auction to be interesting.
I think if we look at the absolute cases and abstract from there, we can have a meaningful discussion. One absolute case is a league with no trading. I have played in several of these. You draft you team and wear it until the end of the season. In a league like this, maintaining a statistically balanced team is paramount. If you win SB by 80, you still only get the max points (10 or 12 or whatever number of players in your league.) So being aware that SBs are cheap or expensive and revaluing your team is important.
The other absolute would be a league with unlimited trading (very active owners). In this type of league, you would be able to optimally balance your team’s statistics with no cost. The optimal strategy in this league would be to buy the best value you can and trade around that later.
I personally feel that the second strategy is closer to optimal.
If you are in an environment where 2 parties trading is mutually beneficial at the expense of the remaining players, then everyone should trade frequently. I noted this in a comment I just put up on the trading thread Eric started.
Let’s consider the SB case that was brought up. Peter pointed out that:
In the Cardrunner's League auction, Chone Figgins went for $23 fairly early in the auction. Other speed guys, like Ellsbury, went early for pretty much their full price.
In the middle rounds the bidding stopped on Ichiro, another speed play, at $22, and shortly thereafter Denard Span went for $16.
In the late rounds, Juan Pierre went for $16
Suppose one player buys enough speed that they now expect to have 2x the average winning steals total at the end of the year. In a league with no trading, they have clearly blundered.
In a league with trading, what happens as we approach the end of June?
I think they are likely to have enough steals stockpiled to finish in the top 2 if they trade away all of their speed.
But what will the speed market look like?
I think the remaining 9 players will be clumped tighter than usual. This should actually cause an increase in the relative value of steals.
This should allow the player who drafted too much speed to disperse his value to the categories he needs help in without having to pay a premium. He has a commodity that helps the other players. In a league where trading is frequent, the stockpiling of talent in one category or another during the auction should not be harmful.
My conclusion has always been to draft the best value you can and worry about managing the categories later.
As to Peter’s argument that:
My original example involved closers. If you have the top five closers valued at 24, 23, 22, 21, and 20, and the rest of the room has them priced at 23, 23, 21, 21, 20, a difference of a couple dollars from $100, if you didn't make adjustments you'd end up with two of these expensive guys and have spent two thirds of your pitching budget on closers.
This just comes down to your ability to buy players undervalue. Just because you think a guy is 22, you aren't going to pay 22 if he is the first guy on the block. During the auction, if you start with a conservative approach of say only buying players that are 10% cheap, you will have time to observe what the perceived value of various positions and stats are by that group of players. This type of reactionary bidding is part of all the good players’ processes. No one has stated that this is a bad idea or they don’t evaluate on the fly.
The difference of opinion as to valuation is one thing that makes the game work. If we all agreed on prices, it would amount to the same thing as a dice rolling game.
I don't think it is clear that buying those players is good or bad. (Assuming you can trade)
If you are the guy with a higher value on saves (or whatever category), who will certainly own more of that type of player coming out of the auction. If you are right, you will have extra value. You will also be able to trade later. If you are wrong, you will have less value.
One thing I am sure of, very few people go home from auctions thinking they have a team that is worth less than the 260 they paid. They might admit so and so had a better auction, or that they could have done better…
Yes, REP, certainly if that works, go for it.
I think the idea of cornering the market is positively Huntsian, and it might be an excellent gambit. Or at least something to attempt. It will, at worst, learn us something, as they said on the Beverly Hillbilies. But I'm not sure it would work for winning, because your opponents are surely aware of how out there you are, and they're aware that once you make a trade that helps them, another trade will follow that will hurt them. So not making a deal may be the best strategy for any thinking team.
Assuming a league of not-idiots, I think you'll get hung out to dry, with lots of late action that helps other teams, but not you.
My conclusion is that you shouldn't pass up unbelieveable bargains in the draft, regardless of category, but if there are unbelievable bargains in your draft, you're playing in a simple league, go for it. Take their money, and then step up.
PETER, I think you missed my point.
I am not proposing setting out to corner the market. I am merely saying that you are unlikely to harm yourself in a league that has trading by buying the best value available. It should not matter that you may become unbalanced.
I was arguing that there should not be a need for signicant revaluing of stat to stat values during the action.
On a side note, there is no need to claim I am playing with simpletons just because I offer an opinion…..
Sorry, your second post and my funny post about the Hunt Bros. crossed in the night. I get your point, and was exagerrating to try to make mine. But maybe my larger point is getting lost.
"Evaluating on the fly" is revaluing based on perceived needs and available inventory, which I think is changing the values of the categories. It is absolutely true that trading mitigates the need to balance during the draft, but let me try to pose a thought experiment:
Every owner goes in with a price list. All the prices on the lists conform to that owner's valuations, so for one every steal is worth .18, for another each steal is worth .19, and for another each is worth .185, etc. This is true for all cats and all owners. If the owners buy off their price lists the player who has the highest price on steals is going to buy the most steals, the person with the highest price on hr is going to buy the most hr, so on and so on.
But that doesn't happen in any fantasy baseball auction. Some of that is because different owners work off different projections, and because we all try to buy underpriced players, but also because we often evaluate on the fly that it is preferable to pass on a second speed only guy like Pierre even if he's 15 percent cheap, and go for what we need, then to count on being able to make a trade later.
And I'm arguing that this evaluating on the fly constitutes a revaluing of the category. If the .19 cent steal guy drops out, the price of steals drops to .185, and when that guy's full the price to drops to .18. That's assuming we're all following our models and not freelancing.
Obviously this is way more schematic than the real world, but these are real numbers and values and these little differences make big differences in category accumulation. Unless we evaluate on the fly.
I'm sorry for the glib joke about joining a tougher league. That wasn't meant to be personal, at all, but rounded out the thought that if a player is able to buy up a lot of discounted players in his auction, he's not playing in a very tough league. I didn't mean to give offense.
But I'm not sure it would work for winning, because your opponents are surely aware of how out there you are, and they're aware that once you make a trade that helps them, another trade will follow that will hurt them. So not making a deal may be the best strategy for any thinking team.
That's an interesting point, Peter but I don't think I agree. Let's first be clear that we're going to rule out explicit collusion. The other teams haven't spoken and said 'hey don't trade for X's sbs and we'll be better off as a group." That would be cheating.
So what you're saying is that the teams will implicitly collude to get to the same spot. I don't think they will. I don't think its necessarily a full on Prisoner's Dilemma, but it's probably close. There's definitely a lot of value in buying sbs here if everyone else doesn't. And if everyone else does buy sbs, it might be correct to buy them anyway. It's like an arms race you can't afford to fall behind in, even if we'd all be better spending our money on other categories (like education.)
I also think the most realistic scenarios involve a major dumping of sbs instead of all of them. The less already sold, the more desperate the owner is to get rid of some, and the higher the discount the first bunch will be sold at. If no one takes them, his price is forced to go even lower. He MUST deal.
So basically if no one deals, we have a spot where whoever breaks the collusion first gets both the best price and either the possibility of being the only person acquiring them (huge benefit) or the possibility that others will be forced to follow behind at higher prices. I think this will actually lead to nearly everyone dealing for sbs.
However, I do agree with the idea that these trades will often involve some loss of value to whoever has the surplus, as you will often have to sell at a discount. Where implicit collusion will hold up is in the league's awareness that you must deal, and they can wait you out for a better price. I just don' t think they'll let you choke on it entirely, because too much is to be gained for them.
Where implicit collusion will hold up is in the league's awareness that you must deal, and they can wait you out for a better price. I just don' t think they'll let you choke on it entirely, because too much is to be gained for them.
Just seems like a hell of a gamble to take – to be at the whim of other owners who overvalue their players. I took Ryan Braun over Tim Lincecum in an innings cap league draft for that very reason. Even though I preferred Lincecum, I was concerned that everyone would wait on pitching, so if i took Lincecum, I'd be forced to go all hitting most of the next 8-10 rounds, and if pitchers were huge bargains as they often are, i'd be faced with either unbalancing my team or ignoring the bargains. So I went Braun because I knew top hitters would be scarce.
In the end, pitching wasn't overly discounted – at least more than usual – and I regret not manning up and taking Lincecum with No. 6 overall – even though Braun has been great. But at the time, I had no way of knowing that, and I didn't want to be at the mercy of the league needing to trade. There is almost always a serious vig if you need to trade unless you find the perfect fit. Even then, the timing must also be good. If you wait too long, then you need to make two trades to balance your team in the categories.
Yes, I agree with you there. And I also agree with the 'vig' point that even if you are right in some abstract sense about the value, you may have difficulty converting it into other categories at a fair exchange rate. You can definitely get squeezed and forced to discount. I just didn't agree with the extreme example Peter suggested, where they leave you entirely out to dry.
My extreme example was exageration to make the point that your imbalance costs you bargaining position. Of course a deal would get made once the price got low enough, but at that point you would probably be wishing you'd drafted a more balanced team.
Fair enough. I think we're mostly agreed then, it's just a matter of degree. How much value should you give up in the name of balance? The size of the league and expected liquidity of the trading markets obviously also to be considered.
I think an interesting difference of opinion here lies in the amount of trading that should occur. I posted this at the bottom of the trading thread and no one commented, so I am not sure who saw it.
Rep says:
05/11/2010 at 8:54 PM
I am a big advocate of trading.
In a zero sum environment (as this league is), if two players make a trade that benefits both of them, the rest of the league is harmed.
Think 4 player monopoly. If 2 guys trade to complete sets, the other 2 guys are suddenly way behind. It obviously isn't that stark in FBB, but the point is the same.
So, as Eric pointed out, if a team is performing well, and their gambles look to have paid off, it should benefit them to trade out of that volatility and into stable value. If a team is performing poorly, they will need to increase their relative volatility to improve their chances of winning the league.
By the 1st of July, with the stats that have been accummulated, many teams already have almost no chance to win.
In a more realistic outcome of the "unbalanced team", they will have one more speed merchant than they need. With that speed out of the pool, the remaining players will be slightly more bunched that usual.
As a result of the bunching, wouldn't one speed guy add more than the normal amount of expected points to one of those guys? And with trading being mutually beneficial, shouldn't several of those guys want to make trades with the guy with a little extra speed? Especially since they rate to have a greater impact that usual?
I don't think it is clear at all that the market becomes "depressed" in these environments. Maybe it does in a league where players trade seldomly, but I believe that strategy in clearly flawed.
Peter,
As a follow up to the thought experiment, I have these comments.
I think the average person preparing for a draft values players not statistics. They look at what each player is likely to do and value that without the benefit of a matrix of value.
In these cases, most people end up with differing values for categories within their own work.
So they give player X a $17 value and player Y a $18, but a lot of times that works out to bidding .19 for player X and .18 for player Y. How can you really tell what you are bidding for? If you had a value of each stat in mind, you can at least be consistant in your own valuations.
Consistancy is the fundamental reason why the projectors think they have edge. They believe (and I do too) that if you are consistant in your valuation technique, you will end up with better expected values at the end of the day.
If everyone had to go do some math and come back and bid for category specific stat lines, I think the auctions would find equilibriums very quickly. And the guys who are paying .19 would realize they can pay less… They might not agree, but they would adjust.
I wonder what would happen if you allowed a additinal slot on each team for a stat line instead of a player. Say auction off a hitter with 450abs .274ave 67 runs 12 hrs 75 rbis and 5 stls (or some other known result)
Perhaps one of the fundamental disconnects we're having in these discussions is who we play against. In the leagues I play in everyone knows the players and everyone knows their prices. Their pricing is pretty consistent and their are no bargains. None.
Once you get to that point, the winning advantage comes from other strategies. I think Mr. Liss's approach plays against the equilibrium, and while it isn't the right approach for everyone, if there are no bargains on draft day you have to either make better projections or find other ways to gain an edge.
I wonder what different decisions we'd make if we just had the statlines for players, and not their biographies and scouting reports.
That is an interesting way to frame it. I tend to disagree though. I think Pierres you have pointed out have to be considered bargains. (whether they are a result of money being tight or "revaluing of the pool")
When I have played in leagues full of smart people, I still have seen discrepancies in valuation. Do you think it is possible that you all value players similarly and implement the same not trading policy due to group think?
While I think the auction is the best place to gain expectancy, I think there are lots of other ways as well.
If you evaulate the teams after the auction and conclude the value was divided up as follows:
285 280 275 270 265 255 250 245 240 235,
then the team with the 285 value has about a 25% chance to win?
I've never found there to be much correlation between my after-draft analysis of the distribution across the categories and the way the league plays out. That's because that analysis was based on projections, which obviously don't foretell the striking blows of injury and utter incompetence that drive winning and failing fantasy teams. It is helpful, however, to see who bought and paid for what, to further develop trading strategies.
I have to admit, I've never tried to figure how much dollar value each team bought on draft day because that seemed another step removed and prone to even more error. Plus, it doesn't tell me anything about what teams did during their draft, the way totaling up their projected stats does (if I'm not using my projetions).
I think those of us who have played fhe game a long time and write about it regularly end up with similar prices because we all use similar methods to value players, and we have a feedback loop of people telling us all spring if our price on an individual player is much higher or lower than anyone else's. When you're making a price list, you want your optimistic prices to be $1 higher than the next guy's, because that helps you keep all your prices on a realistic scale.
I think the trading issues have to do with the things we talked about in the early season: Waiting to find out if busts are really busts, Whether a team off to a bad start can rebound . Etc. There is more trading as the leverage points are seen, and then a decline when the teams that are out of it choose not to help one leader at the expense of another.
In the leagues I play with so-called experts where that chivalry isn't valued, there is plenty of trading all season long. But not so much early on.
I'm not sure how you get a 25 percent chance. My back of the envelope calculation is 20 percent, and even though I get that by giving the 235 team no chance of winning, which I don't think is right, I would not go to war over the difference.
I used a stdev of 32.5 for all the teams for the season and ran a simulation. The ave winning score that resulted was slightly below the observed range in this type of league. This allows some room for profitable trading and waiver wire claims.
My results have the 235 team winning about 1.5%.
I knew the 235 team had some chance.
Since we were having this discussion earlier, what is the amount a team needs to have out of the auction to be an even prop against the field? If it's not too much trouble…
My teams almost always grade poorly when run through projections systems. In 2009, mixed Tout, the service they used had me dead last among 17 teams. I won the league by 20 points. The only thing I think that's good for is to see how well you executed according to your own valuations.
Chris, I believe that Rep has written a quick program to do a monte carlo simulation for team's winning chances given certain theoretical values and various standard deviations. When he speaks about value it is in theoretical sense.
Peter, I think that using Rep's methods will show that one team with a value of 312 versus a field of 254 value teams is about 50-50 to win. This is assuming the same standard deviation of 37.5.
If one team wins 4 dollars from every other owner, making it 296 versus 256, that is a 30% chance.
I think there are flaws with the way Rep is doing this. There is no accounting for correlation between categories, and the simulator does not keep the pool fixed at 2600, but rather it allows each team value to flutuate in isolation.
However, I think that it is still somewhat useful for showing the relationship luck plays in winning.