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Why isn’t baseball’s free agent market clearing? February 21, 2019

Posted by tomflesher in Baseball, Economics.
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There’s been some discussion of the free agent market in baseball and its alleged inefficiency – that players like Manny Machado don’t sign until February and Bryce Harper is still unsigned, for example. Adam Wainwright, for example, has threatened a strike over free agency.

Certainly, there are many factors in play. However, the fact that there are stars who aren’t being picked up doesn’t mean that there’s anything nefarious afoot. Brad Brach, who signed with the Cubs on February 11, has complained about the teams’ use of algorithms to value players:


Let’s take that at face value and build a model of algorithms and noise. (It seems that Brach is implying collusion by teams, but in a future post I’ll discuss why I don’t think that’s likely.)

First, the simplifying assumptions:

  1. Players have an accurate valuation of their own talent levels (This is difficult to justify because players have an incentive to overvalue themselves, but the conclusions would not change qualitatively by relaxing this assumption)
  2. Teams have a noisy valuation of players based on the players’ talent levels (This is essentially the face value Brach’s claim: that teams use ‘algorithms’ based on player talent.)
  3. There are two teams with similar noise levels. (Modeling different forms of bias, or different preferences by teams, would probably not change the outcome very much, but would affect the distribution of players. Meanwhile, the market for some players is fairly large, but for many it’s very small, especially as prices rise.)
  4. All contracts are for one year. (This avoids the trouble of modeling players’ intertemporal rates of substitution, but a future version of this model may include preferences about both pay and number of years.)
  5. If a player is offered a contract that he thinks accurately reflects or overpays him, he signs with the team that offers him the bigger contract.

Poorly-constructed R code for a simulated free agent season:

for (i in c(1:1000)){data[i,1] <- runif(1)
data[i,2] <- data[i,1]+rnorm(1,mean=0,sd=.05)
data[i,3] <- data[i,1]+rnorm(1,mean=0,sd=.1)
data[i,4] <- max(data[i,2],data[i,3])
data[i,5] <- if(data[i,4]>=data[i,1]) data[i,5]=1 else data[i,5]=0}

Basically, generate a vector of random player talent levels; team 1 accurately values players with a standard deviation of .05, while team 2 accurately values them with a standard deviation of .1. 1000 players go on the market. Outcome:

V1 V2 V3 V4 V5
Min.     :0.0008885 Min.   : -0.1324 Min.   : -0.2024 Min.   : -0.1324 Min.   :0.000
1st Qu.:0.2613380 1st Qu.: 0.2621 1st Qu.: 0.2608 1st Qu.: 0.3012 1st Qu.:1.000
Median :0.4984726 Median : 0.4968 Median : 0.5133 Median : 0.5511 Median :1.000
Mean     :0.4997539 Mean   : 0.4987 Mean   : 0.5087 Mean   : 0.548 Mean   :0.754
3rd Qu.:0.7425434 3rd Qu.: 0.743 3rd Qu.: 0.7566 3rd Qu.: 0.7912 3rd Qu.:1.000
Max.     :0.9995596 Max.   : 1.1115 Max.   : 1.2508 Max.   : 1.2508 Max.   :1.000

That’s right – only 754 of the 1000 players signed. (In multiple simulations, the signing rate hovers around 75%. This makes sense theoretically, since valuations are independent: half the players will be undervalued by each team so 1/4 will be undervalued by both teams.)

Interestingly, player 973 is unsigned:

[973,] 0.9683805341  0.9472948838  0.874961530  0.9472948838    0

He evaluated himself at below the 97th percentile, but got unlucky in that both teams evaluated him below that: team 1 would offer him a 95th percentile contract and team 2 would rank him even further down.

Meanwhile, player 25 gets lucky:

[25,] 0.0109281745  0.0236191242  0.089982324  0.0899823237    1

Despite being in the 1st percentile, both teams accidentally overvalue him, and his contract ends up being suited to a player with nearly 9 times his value. (For the phenomenon where competition leads reliably to overpayment, see “winner’s curse.”)

We’re going to see both of these types of errors in any market where there’s a subjective evaluation of players. Particularly if the teams are using algorithmic valuations, much of the information they’re based on is going to be publicly available; even if teams weight it differently, efficient algorithms are likely to produce similar results.


E-Reader Price Wars June 21, 2010

Posted by tomflesher in Economics.
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Holy cow… two non-baseball updates in a row! I’ll have to fix that later on.

The news all over is that Amazon has cut the price of the Kindle from $259 to $189. By all accounts, this was prompted by the $60 price cut that Barnes & Noble gave the Nook ($259 to $199), which in turn was prompted by the low price of the Borders brand Kobo ($149). The availability of the iPad, an augmented substitute good for e-readers, will also potentially cause trouble, but the mere existence of the iPad doesn’t necessarily create downward price pressure in and of itself.

The Nook, Kindle, and Kobo are all extremely similar goods. I’d go so far as to say they’re perfect substitutes, if we consider this Kobo advertising table. Taking the American market, the price differential will disappear when the new price cuts take effect. The weight and thickness differences are negligible. The memory is similar. The only major difference is that the Kobo can use Bluetooth, while the Nook uses Wi-Fi and 3G, and the Kindle uses 3G. This difference is probably not going to result in significant market segmentation and no one will be likely to buy a Nook and a Kindle to take advantage of the Nook’s Wi-Fi capabilities, so it’s fair to consider these substitute goods with negative cross-elasticities of demand.

When prices for substitute goods with different producers move together, there are three options, two of which are sensible in a rational market:

  1. The firms could be colluding.
  2. The firms could be in a price war.
  3. The price change could be coincidental.

Coincidence isn’t very likely or very interesting, so we’ll only consider options 1 and 2. Collusion is fun to consider, but probably not relevant here. For one, when prices move due to collusion, they generally move up because firms are no longer attempting to price each other out of the market. Tacit collusion might be the reason that about $200 is the floor for 3G devices, but it’s unlikely to be the reason both firms cut prices.

The price war would explain the fact that the changes in price are negative and that they’re meeting at a similar level. Price war means increased competition. Assuming demand doesn’t change (it will), the firm with the lower price will sell its product. Assuming demand increases as price decreases (it will), each lowering of price should bring additional marginal consumers to the pool of people willing to buy these devices, so while prices fall, profits may or may not increase. If profits increase, however, it will likely be profitable to cut the price even further, because additional consumers can still be reached, and there will be downward pressure from other firms trying to keep up. As a result, price will approach the cost of production. Price won’t reach the marginal cost of production, however, since there are barriers to entry into the e-reader market (including specialized equipment, R&D for a new device since the current devices are protected by patents and trade secrets, and acquisition of rights to books).

A quick rule of thumb to see if we’re dealing with price war or collusion is to check the stock prices of the producer companies. All things being equal, if a price move increases stock price, then the move is the result of anti-competitive measures like collusion, because there will be higher profits. If a price move decreases stock price, then the move is likely to increase competition and lower profits will result. Here, to quote KTTC:

Barnes&Noble shares fell 55 cents, or 3.2 percent, to finish trading at $16.52. Amazon shares declined $3.28, or 2.6 percent, to $122.55.

(Apple’s stock, for the record, ticked down today without much else to explain the drop.) This is probably a pro-competition move. The likely winners fall into two groups:

  1. E-reader consumers, who will benefit from lower prices and more competition for amenities. The producers will likely be fighting for contracts with publishing houses, and a larger selection of books may be forthcoming.
  2. iPad users. E-readers are an imperfect substitute for the iPad, so in order for the iPad to remain a rational choice after the price cuts, it will have to become a better product to avoid losing out to people who will get a better value by buying a cheaper product. This should mean more of a focus on the differential aspects of the iPad like the App Store, iTunes, and (yes) iBooks.

This should be fun to watch.

Arbitration in MLB – "File and Go" and Market Inefficiency January 27, 2009

Posted by tomflesher in Baseball.
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Ed Edmonds at the Sports Law Blog wrote up a piece on Tampa Bay’s “File-and-Go” strategy for arbitration. The blog references an MLB.com article; more information is available at USA Today, but I’ve preserved the text of the article here. Some thoughts on arbitration as market inefficiency, plus a haiku, behind the cut.


Afterthought: "Undue inducement" January 25, 2009

Posted by tomflesher in Uncategorized.
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In the previous post, I mentioned the Singapore government’s fear that too high a level of compensation for kidneys would provide an “undue inducement” for a citizen to sell a kidney. I assume this means that the government doesn’t want to set a price so high that it will cause an unethically high influence on a person’s decision to donate an organ.

In microeconomics as we know it, however, the market-clearing price of a widget is the point at which its supply curve intersects its demand curve – that is, the price where suppliers want to sell exactly as many widgets as customers want to buy. Price theory doesn’t take ethics into account. From the academic standpoint, it’s impossible for a price to be an undue inducement because price is based on the indifference point of the supplier.

Can a price be an unethical inducement to action? How can that be determined? Is it right, ethically, to set price controls under certain circumstances?

The Market for Kidneys in Singapore January 25, 2009

Posted by tomflesher in Uncategorized.
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Singapore is lifting its ban on compensating kidney donors. Behind the cut, I’ll analyze some of the effects, examine the welfare generated by such a policy, and include a summary in the form of an economics haiku.


A 500-level interlude September 17, 2008

Posted by tomflesher in Academia.
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Today’s post doesn’t deal with baseball or the Canadian federal election. I’m working on an article and question cluster for my Financial Economics course (discussion is tomorrow!) and in order to get my thoughts organized I’ll be working on them behind the cut.

If you need a Canadian Politics fix, check out The Globe and Mail’s Opinion section. If you’re after an analysis of baseball until the numbers cry, try Recondite Baseball. For pure money talk, check out TwentiesMoneyMag. If you want a brief discussion of Radford, The Economic Organization of a P.O.W. Camp, 12 Economica (New) 189 (1945), you’ve come to the right place.