Sunday, March 4, 2007

The following article was written by Aaron Brown, the author of The Poker Face of Wall Street. I emailed Aaron about Rotohog, hoping that I could get him intrigued enough to write a few paragraphs of speculation on how Rotohog's open trading floor might impact trading in the game. What I got was a whole lot more...a long, detailed article that explained what should happen, and what strategies to use to take advantage. It confirmed some of what I've been thinking, but turned other ideas I had upside down. I definitely recommend you get ahold of Aaron's book if you haven't already read it, but first, enjoy his article about Rotohog...

If you are not a financial professional, you may have wondered why people get so excited about futures trading. You probably understand that you can make a lot of money if you bet correctly that pork bellies will increase in price or that frozen orange juice will fall. But that’s just gambling and the price patterns are random enough that it’s not much easier for an outsider to make money in the futures markets than in Las Vegas. So why do people care so much? Why does the opening of a trading market completely change the game and create entirely new economic opportunities? After all, people are just buying and selling pieces of paper representing stuff that people could buy and sell in real markets before the futures exchange opened.

If you know more about fantasy sports than economics, you can now see the reason demonstrated. Rotohog.com’s ingenious game completely changes the way you have to think about fantasy baseball, and sets an entirely different basis for player valuation. I’m going to begin the discussion ignoring the bid/ask spread rotohog.com is imposing on their trading floor. It’s easier to understand the impact of perfectly liquid trading before dealing with some of the complexities of transaction costs.

Let’s start with traditional fantasy valuation. You begin by projecting the stats of the available players. I just used their 2006 stats, so I’m valuing them for last year, under the assumption you knew exactly what each player would do. This produces unrealistic top valuations, because the best performers always do better than expected. That is, you might guess that the best fantasy hitter in the majors will have a season as good as Albert Pujols did in 2006, but at the beginning of 2006 you won’t know which hitter it’s going to be. You expect Pujols to have an excellent season, and he’s among a handful of hitters who might turn in the best overall season, but you have to price him before you know he’s going to be the best.

The top price I get for any player is $76.75 for Johan Santana, but at the beginning of 2006 he was probably worth more like $50 to $55; he might have gotten injured, he might have had a disappointing season, he might have just had a pretty good season. You wouldn’t be sure in advance that he’d lead the league in both innings pitched and ERA (and just about everything else). By the way, I use www.dougstats.com for data and my stats and positions sometimes differ slightly from the ones at rotohog.com.

Once you figure out how many points each player can be expected to generate, you take the top 12 players for each slot. The 13th best catcher in the majors in 2006 was Mike Piazza of the Padres, who produced 513 points. Since only 12 catchers will play in the fantasy league, Piazza is worthless. The top catcher, Joe Mauer, produced 921 points. But since you could get 513 for free, you’re paying for the extra 407 (numbers do not add due to rounding). This assumes there is no value to keeping players on the bench, you could add some small value to Piazza for that. Things are a little trickier to deal with utility players and optional pitching slots, but the basic idea is you rate each player based on the extra points they give you versus the 13th best player available for the slot. Sophisticated fantasy owners can refine these methods, but this is the basic idea.

If you add up all the extra points (that is, points above what the 13th best player will give you for free) from the 180 players who will fill all 12 fantasy rosters, you get 24,026 for hitters and 14,377 for pitchers. Add those numbers and divide by the $3,600 available to all 12 fantasy owners and you get $0.0937 per extra point. Mauer gave you 921 extra points, so he’s worth $38. If all the players are priced this way, and all owners spend their $300, there will be a 12-way tie for first. The top line-up given these assumptions is:

Player Team Pos Points Value
Garrett Atkins rock 3B 1,198 $45.43
Carlos Beltran mets OF 1,247 $50.00
Lance Berkman astr OF 1,216 $47.10
Chris Carpenter card P 1,142 $45.14
Ryan Howard phil U 1,321 $56.95
Joe Mauer twin C 921 $38.18
Joe Nathan twin RP 1,156 $46.47
Albert Pujols card 1B 1,418 $66.03
Jose Reyes mets SS 1,211 $51.94
Franc Rodriguez ange RP 1,168 $47.60
Johan Santana twin SP 1,479 $76.75
Alfonso Soriano nati OF 1,194 $45.07
Chase Utley phil 2B 1,139 $48.87
Brandon Webb diam SP 1,143 $45.26
Carlos Zambrano cubs P 1,105 $41.73

This line up would cost $752.52 and give you 18,057 points. Of course, you could never afford it in a traditional fantasy league. The key to this analysis is your constraint is slots, you can have only one player per slot. Now we’ll see how having a liquid trading market changes the constraint, and thereby the basis of valuation, and thereby completely changes the relative values of the players.

I looked at the schedules for the Anaheim Angels (picked because they were first on the list) and the New York Mets (picked because they’re on the other coast and in the other league). Over 2007, there are 28 days on which only one of the two teams is playing, 90 days when both are playing but the games (based on television slots) do not overlap and 58 days on which the two teams have games that overlap in time.

Carlos Beltram was the best fantasy outfielder on the Mets in 2006 and Vladmir Guerrero was the best on the Angels. Suppose that you could buy (and sell) each of them for $45 for the 2007 season. You draft Beltram for $45. After he plays in April 1, you sell him and buy Guerrero, who plays on April 2. You continue buying and selling, always holding the player who has a game. If the Mets and Angels have overlapping games, you pick one outfielder at random. By the end of the season, your $45 has bought you not 162 games, but 266 games.

Of course, you’re limited to 162 games per outfield slot. So budget another $45 to add Lance Berkman and Alfonso Soriano to your platoon. You can move the four dream-teamers around among the three outfield slots to be sure you have 162 games in each slot, a total of 486 outfield games. If one of the four falls off in production, or another player climbs up to their level, you can switch. You have the best outfielders in baseball playing every game, spending only $90 for to fill three slots.

The table below shows the results of this strategy for 2006. You always buy Beltram and Berkman if they have a game. If Soriano is playing, and one or both of Beltram and Berkman are not, you buy Soriano. You buy Guerrero for a few games when you don’t have two slots filled to get your total outfield games up to 486. This produces a total of 3,907 points. It uses a maximum of $97.10 at any one time, and often uses less. You never have more than two outfield slots filled at a time (the rules allow you to leave slots empty, but even if they didn’t, you could fill them with $0.25 scrubs who do not have games that day).

Player Team Pos Innings Points Value
Carlos Beltran mets OF 140 1,247 $50.00
Lance Berkman astr OF 152 1,216 $47.10
Alfonso Soriano nati OF 159 1,194 $45.07
Vladim Guerrero ange OF 35 249 $37.24

Suppose instead you elected to buy and hold Grady Sizemore, Bobby Abreu and Andruw Jones. This will cost you $101.76 all the time, instead of a maximum of $97.10 and often less. You will get 3,226 points, 680 less than the platoon strategy. Some of the difference comes from not using up all 486 games, but most of it comes from getting fewer points per game because the players you can afford to buy are not as productive as the players you can afford to rent when you need them.

Player Team Pos Innings Points Value
Grady Sizemore indi OF 162 1,104 $36.57
Bobby Abreu tota OF 156 1,064 $32.88
Andruw Jones brav OF 156 1,058 $32.30

Pitching offers even more opportunities to platoon. Starting pitching is worthless, because there is a limit of 1,300 innings for all pitching slots combined, and closers are put up about three times the points per inning as starters. Suppose in 2006 you had bought the four best closers playing at any given time, until you got up to 1,300 innings. You would have the following contributions:

Player Team Pos Innings Points Value
Chad Cordero nati RP 73.3 857 $18.48
Francis Cordero brew RP 26.7 429 $0.00
Brian Fuentes rock RP 65.3 766 $9.93
Mike Gonzalez pira RP 54.0 662 $0.18
Tom Gordon phil RP 59.3 787 $11.93
Trevor Hoffman padr RP 63.0 986 $30.60
Jason Isringhausen card RP 58.3 715 $5.12
Bobby Jenks whit RP 69.7 884 $21.00
Joe Nathan twin RP 68.3 1,156 $46.47
Akinori Otsuka rang RP 59.7 767 $10.05
Jon Papelbon rsox RP 68.3 1,060 $37.47
J.J. Putz mari RP 78.3 1,075 $38.89
Chris Ray orio RP 66.0 839 $16.74
Mariano Rivera yank RP 75.0 950 $27.23
Franc Rodriguez ange RP 73.0 1,168 $47.60
B.J. Ryan blue RP 72.3 1,073 $38.75
Takashi Saito dodg RP 78.3 962 $28.34
Huston Street as RP 70.7 893 $21.88
Billy Wagner mets RP 72.3 1,044 $35.95
Bob Wickman tota RP 54.0 682 $2.07

The total is an astounding 17,756 points. This is only slightly less than the 18,057 a buy-and-hold owner could earn with an unlimited budget and perfect foresight. And you get it all from relief pitching. One of your contributors, Francis Cordero, would not even be playing in a traditional league, and another, Mike Gonzalez, would be worth only $0.18. When the top closers are all playing, you have to devote $171.71 of your budget to owning Rodriguez, Nathan, Putz and Ryan. But most of the time you have less than $100 allocated to relievers, with the rest available to rent hitters.

The infield positions use the same idea as outfielders and pitchers, except you have to pay attention to make sure you’re getting enough games at each position individually. So instead of getting the best hitters playing at any given time, you have to spread games around among the best catcher, the best shortstop and so forth. You need 162 more games to fill the utility slot, but you can use any batter for those, so it makes sense to fill them only after a defensive position has its full quota of 162. Generally, you’ll fill it with games from outfielders, first basemen and designated hitters.

So far, I’ve assumed everyone else sticks with traditional fantasy valuation. In reality, a lot of people will start platooning. That will drive up the values of the best players, especially relief pitchers, at the expense of the others. Also, a player’s value will be highest right before his team has a game (or right before he has a start for a starting pitcher) and drop afterwards.

This last point is crucial, and changes the valuation equation again. If you follow the obvious platooning strategy above, you will lose money on each buy and sell. You might buy Carlos Beltram for $45 just before he plays on April 1, and find he’s only worth $44 after the game. No one wants to buy him until just before his next game on April 3. You can’t wait for that, because you want to sell him and use the money to buy Vladmir Guerrero for his April 2 game. These game-by-game losses will erode your initial $300. If you don’t do anything about them, you’ll be forced to choose between settling for less than the best players, or not filling all your innings and games. You won’t be able to keep enough stars in play to add up to 162 games per batting slot and 1,300 pitching innings.

One way around this would be to use your traditional fantasy skills. You could buy relatively cheap players who deliver good stats, and hold them for price appreciation. You could watch for games in parks or against pitchers where certain batters can be expected to do much better than their average; or closers in situations likely to offer a save opportunity.

You may have noticed that my entire discussion has ignored these factors, in fact anything to do with baseball or talent evaluation. Professional traders in the financial markets have to know little or nothing about the underlying economics of what they trade. You may now see why that’s true. My strategies demand only basic projections of value that any casual fan would have, or can be easily found on the internet. I’m going to concentrate on analysis that assumes you do not have superior knowledge of baseball. If you do have that knowledge, you can use it to refine the strategies. But trading skills are far more important than baseball skills at rotohog.com.

The trader’s way to recoup the money lost from buying players just before games and selling them right afterwards is to lend out spare cash. Suppose, for example, that at one point you are playing only four players for some reason, with $150 total salary. You have $150 idle. You can use this to buy players who have just finished games, with the idea of selling them just before their next games. You should earn a reliable profit doing that, replacing losses from other transactions. In the financial market, this is known as a “reverse repo” transaction (for “repurchase agreement,” the person on the other side, who is effectively borrowing your $150, is doing a repo). You are doing a mental reverse repo, that is you have made up your mind to resell the player and are buying him only to earn interest on spare cash; in a real reverse repo you sign a contract to resell him. The repo market is one of the most common ways a trading organization earns interest on its spare cash, or borrows extra money to fund short-term trading positions.

One danger in all this is holding a player at the time he gets injured. You might buy him for $40, planning to sell him for $38 after the game. In your mind, you’re renting him for one game for $2. But if he gets a season-ending injury, you lose the entire $40. And injuries are just an extreme case of value volatility. A player’s value may fluctuate depending on his performance or other factors. If he has a bad game, you may end up paying $4 as his price drops to $36 instead of $38. If he has a good game, you might get him free, or even earn a profit from having him.

That’s why the real world developed futures markets. If rotohog.com added those, you could buy him for $40, agree in advance to sell him for $38 after the game (healthy or dead, great game or terrible, it doesn’t matter). That way you get the game for $2 as you wanted. Someone else takes the risk of value volatility.

Player health and performance are not the only risks. You never know if a closer will pitch. A rain-out can wipe out the game for all players. In these cases, you don’t lose principal, but you don’t earn the expected return. An east-coast game may go into extra innings, frustrating your plans to sell one of the players in it to buy a player for a west-coast game the same day. You don’t lose money on your long position (owning the player), but the funding costs were higher than expected (you pay “interest” over two game windows instead of one), which has the same effect.

The next evolution in the real world is specialized institutions to help with these activities by trading in the markets, just like other participants. One institution might take spare cash from owners and pay a fixed rate of interest, then use the money to hold players in between games. It is effectively providing banking and insurance services to other owners. Another institution might sell derivatives, such as the stats to the next game a pitcher pitches, regardless of the day it happens, or the stats to his next nine full innings, or the best stats posted by any shortstop on a given day. This allows owners to pursue more flexible strategies, while financial engineers can create the derivative payoffs by buying and selling in the underlying player market. These institutions cannot evolve at rotohog.com, because you can’t transfer money among players, and the institutions would build up a lot of fantasy cash in profit, but that would be worthless without stats.

Another difference between rotohog.com and real markets is that you cannot short players. In a fully-efficient market, you can sell players you don’t own (called “shorting”). Their stats would be subtracted from your totals, but you could use the money from selling them to buy other players who would (hopefully) more than make up for that. You would also hope the players you shorted went down in value, so you could buy them back for less than the original sales price; thereby making a profit. You could short players between games, effectively borrowing money to field a more expensive team than your bankroll supports. Your stats wouldn’t suffer, because the player wouldn’t play. But since player value tends to rise in between games, you pay an expected cost for this borrowing. Another strategy would be to leverage your slots by buying games from all-stars, then shorting scrubs to reduce your games-played total without much decrease to your point total. This could dramatically increase the gain when you’re doing well, but increase the losses by the same ratio when you’re doing badly. One effect of shorting is that true scrubs would acquire negative values, you would be paid to own them, and would have to pay to remove them from your roster.

A key economic statistic in the rotohog.com world is the interest rate versus the cost-per-game of owning a player. If the effective interest rate is relatively high, team owners can pursue the platooning strategy without much constraint. All the value will be concentrated in the top players. But if the interest rate is relatively low, team owners will have to allocate more cash to holding players between games to earn interest. This will distribute value more evenly among players.

The interest rate and the cost of ownership are clearly related. If players drop a lot in value immediately after games (high cost of ownership), they can be expected to rise a lot before the next game (high interest rate). But the two amounts will not be equal, because the season has a finite length. The initial endowments ($300) set the initial prices. Rational owners who plan perfectly want to be broke by the end of the season (there’s no reward for having spare cash left in your account, or players on your roster at season end). We therefore expect inflation as the season continues. Stats have constant value, but money heads to zero value. So we expect the loss from owning a player for a game to exceed, on average, the profit earned from holding the same player between games. The average difference should be about 1/162 of the initial player value ($0.25 for a $40 player), but it could vary considerably during the season, and even become negative in some circumstances.

But not everyone has to go broke at the same rate. One owner might choose to spend recklessly at the beginning of the season, when cost of ownership is lowest, hoping to fill up his 162 games and 1,300 innings by June with an insurmountable lead (and no money or players left). Another might choose to compile no stats early in the season, holding players only when they have no games, hoping to build up a large enough bankroll to buy victory in August through September. Most owners will pursue alternating strategies, piling up stats and spending money when they judge the price of talent is relatively low, and ignoring stats to pile up money when they judge the price of talent is relatively high. And the game might not be the same for all positions. There may be times when outfielders are cheap and pitchers dear, or vice versa.

Things are complex because two prices matter. Absolute price limits the number of players you can play at one time. The price drop from before to after a game is what you have to pay for one game’s stats. Traditional fantasy owners are looking only at absolute price, and are holding full rosters all the time. Trader owners concentrate mostly on rental cost per game. They might have only 8 of their 15 roster spots filled on average, buying and selling intraday to get 15 roster spots of production without ever owning 15 players at once.

In the real world, we have the Federal Reserve (and other countries have their central banks) to worry about the relation between return on real assets (cost of owning a player during a game) and interest rates (profit from owning a player between games). The Fed can change the rules, and buy and sell securities, to keep the supply of money in line with the demand for assets. In the real world, the season doesn’t end, and the Fed doesn’t want people playing as if it does (that results in first inflation, then a crash, just like the season end in fantasy baseball). In the game, the people running rotohog.com have the ability to adjust several parameters. My guess is they’ll use them to keep the amount of trading high enough to distinguish rotohog.com from traditional fantasy leagues, but low enough that baseball acumen matters more than trading skills. I’d say that means top owners having turnover ratios of about 100% per month (the average player stays on the roster for a month); most owners will trade much less, and not be in contention as a result; owners who try to trade more will find it suboptimal. Of course, I have no connection to the site, so I could be wildly off in my guesses.

That brings up the bid/ask spread, rotohog.com’s primarily “lever” for regulating the marketplace. The real-world Fed regulates interest rates (it sets the Discount Rate and influences the Fed Funds rate strongly), rotohog.com has instead chosen to regulate via real asset returns. The example in the rotohog.com rules is $0.50 on a $30 athlete. It’s not a true bid/ask spread, it is a transaction cost imposed by the market regulator.

If all owners played perfectly, the bid/ask spread should eat up endowments over the course of the season so everyone ends up broke. At $0.50 per trade, that’s 600 trades. If the entire $300 were eaten up by bid/ask spread, there would be nothing left for a spread between interest rates and the cost of owning a player. Player values would stay constant, on average, throughout the season. The natural inflation of the rotohog.com economy from the season winding down would be kept in check by removing money from the system via transaction fees.

It doesn’t take a prophet to know owners will be far from perfect. Many will sign up and never look at the site again. Others will fall behind in their leagues, and be far out of the running for the overall cash prizes, and give up. Many who do play actively will fail to grasp the difference between rotohog.com and traditional fantasy leagues, and will buy and hold good players, hoping for good stats and price appreciation.

Since lots of owners will not be thinking in terms of spending their money and ending up broke, not all the initial endowments will be eaten up by transaction costs. Active owners will spend some of their $300 on net losses from owning players during games versus earning income by holding players between games. This extra money will go to the smarter traditional owners, who will use it to improve gradually the quality of their teams through long-term acquisitions. Some of them will end the season with an all-star roster valued at $600 or more, but without filling their quotas of 162 games per spot or 1,300 innings, and without getting major-league best stats from the games they do have. We’d expect Warren Buffet to play this way if he enters. They’ll win their local leagues with huge leads over owners who didn’t trade much, or who relied upon baseball acumen rather than economics, but they won’t be in contention for the overall money spots. The $100,000 will go to a hedge fund guy with great trading skills and the luck not to blow up.

Because there is a net cost of ownership (you lose more money owning a player for a game than you gain holding him between games), the entire $300 initial endowment is not available to pay bid/ask spreads, so owners should trade fewer than 600 times per year. The average price of players has to fall, because money is leaving the system but players aren’t. Top player values should increase. This will be more than offset by decline in the values of lesser players. The decline will start from the bottom, the players with lowest initial values will fall to zero, as owners fill up position slots with 162 games. If you want to win your league without much effort, draft only closers, stars and scrubs, then swap them for all starting pitchers and second-tier players as the season progresses.

If you want to win the $100,000, my advice is to draft the seven best relief pitchers you can get, then trade up for better ones as soon as the market opens. Use your additional money, if any, to buy only stars and scrubs. Focus entirely on closers, activating your four best ones for every game opportunity and swapping in the trading market to pick up extra innings (that is, if you don’t have four closers playing at any given time, sell one to buy a closer who is playing). Your goal is to accumulate closer innings as quickly as possible.

Never play a starting pitcher, this uses up precious pitching innings. Don’t worry about your batting slots. Use your extra money, when available, to purchase stars; but never miss a closer opportunity to get a superstar hitter. You’ll make up your hitting games later in the season.

As people catch on to the game, the value of closers and star hitters will soar. Since you’ll have lots of closer innings already, you will be able to take profits to buy more star hitters. With luck, you’ll be able to fill up 162 games at each hitting slot, using only stars. As the season progresses, you may find that even with your profits from owning relief pitchers and stars early, the price of top hitters has increased so you can’t play enough of them at a time to get your full quota of games. If that happens, you’ll have to drop down in hitter quality. Remember, even a player with zero value in a buy-and-hold league produces valuable stats. The 13th best player at a position typically gives you about 2/3 of the points of the best player. You don’t want to waste games early on average major leaguers, because you might be able to fill them later with stars. But if it becomes clear you cannot fill your games with stars, don’t miss the opportunity to fill them period.

So focus on closers, then on batting stars, platoon early, chart interest rates and player-ownership costs, seize the best available opportunities whether for stats or cash and figure you can even things out later; and be sure to invite me for the party celebrating your $100,000 payout.

1 comment:

David said...

wow, this is really great stuff!