Hold Your Bets
Michael Sokolove writes an interesting article in the New York Times Magazine titled “From Pastime to Nap Time” on the effect that drug testing will have on Major League Baseball. This is not your tired article on steroids that points out that Mark McGwire is four dress sizes smaller since he left baseball. This article addresses how testing for amphetamines will change the game.
The claim is that the practice of taking amphetamines (“greenies”) to deal with the rigors of the daily grind of a 162 game schedule was widespread. MLB’s new improved drug testing policy includes testing for amphetamines. Therefore, testing will reduce the use of greenies and change the way the game is played. Let us make some assumptions…
(1) Players are able to play a higher level of play when taking amphetamines.
(2) Some players are taking amphetamines.
(3) Day games following night games are particularly difficult, and therefore the time where amphetamine use is expected to be highest.
(4) The testing process causes (some players) to stop taking amphetamines
A result of effective testing would be to reduce amphetamine use. Thus, we would expect…
(1) A fall off in the level of play to occur as the overall level of concentration or energy would be lower.
(2) The fall off in level of play will be largest for day games following night games.
Interesting in its own right, but there is more economics tucked away later in the article. Sokolove includes a quote from Billy Sample, a former player, who gives us some gambling advice. Hold your horses before calling your bookie (or go to the track instead). Here is an excerpt from the article that quotes Sample…
Billy Sample, who played nine seasons in the big leagues before retiring in 1986, believes the most difficult challenge in the post-greenies universe will be those pesky day games after night games. He says, “People who bet on the over-under line” — a wager on how many total runs will be scored — “they should probably take the under on those games.”
An over/under bet is fairly simple. Bookmakers determine a number of runs, called the “over/under line”, that they think will be the number of runs scored in a game by both teams combined. If the line is 7, and you bet the “under,” you are betting that fewer than 7 total runs will be scored. If you bet the “over,” you are betting that more than 7 runs will be scored. Bookmakers try to get the line “right” – so that half of betters wish to bet the over, and half wish to bet the under. Without getting into the details, the bookie takes a cut of winning bets, and as a result can earn money even with equal numbers of people betting the over and under. In fact by doing so, he earns money without taking any risk.
Sample’s argument is that everyone will be too tired to swing a bat during those pesky day games, fewer runs will be scored in these games, thus making the under bet more desirable. Sample may be right about the runs scored. (He is assuming that greenies affect hitting more than pitching and defense.) However, even if there are fewer runs scored in these games, you still should not run out and bet the under and expect to win more than half the time. Why?
Begin for a second by making the dubious assumption that bookmakers do not realize the effect of the amphetamines ban. They set the over/under at 7, thinking this is the correct line. However, suppose some “informed” bettors realize the “true” line should be less than 7. They would see a profit opportunity, as betting the under would win more than half of the time, perhaps often enough to pay the bookie’s commission and still come out ahead. The large bets being placed by informed betters on the under will result in more money being bet on the under than the over. Bookies are sure to notice this imbalance and try to induce more betting on the over. How? By lowering the over/ under line. How far will the line have to adjust before the betters are evenly distributed? Until the line is set at the “correct” level. The point is, eventually, the market settles on the correct line.
If this sounds like the story you heard in your microeconomics class about “excess quantity demanded” and how prices adjust to equilibrium, it should. You can think of the betting lines as prices.
As economists, we believe gambling markets (and financial markets in general) are wonderful aggregators of information. Related is the idea we call “market efficiency.” A person that has superior information will indeed find profit opportunities. These profit opportunities provide incentives for many people to seek out superior information. People finding this information and acting on this information (a bunch of people betting on the under in our case) causes the information to be transmitted to markets. As economists, we say that all publically available information is quickly “priced into the market.”
While profit opportunities may occur for short periods, they disappear quickly. You cannot consistently “beat” the gambling market (or the stock market), unless you have truly “insider information” (information not publically available), and lots of it.
Do not think that bookies are slouches. They are in the information business, and it pays for bookies to adjust the lines quickly. Those who do not quickly adjust soon find they are paying off a lot of bets and may end up selling furniture before too long.
While Billy’s story might be right, this information is publically available and is already priced into the market. If Billy was the only one who knew this, he should not have had this information printed by the New York Times! Rest assured, if you bet the under every time a day games follows a night game this season, you will win about 50% of the time.
Epilogue:
An enterprising student could collect the lines and the time of days of games to see if lines for day games following night games were, on average, lower than other day games for past seasons. In fact, if amphetamines were important, and testing is effective, we should see this gap increase for this coming season.
Also, I once went to a Cubs game with my sister. She told me during the game that she was rooting, not for the Cubs, nor the hated Cardinals, but instead for the pitchers! I thought she was a moron. Now I wonder if she had money on the under!
A hat tip to the folks over at The Sports Economist for pointing out the article.
–CT
February 15th, 2006 at 9:53 pm
I definitely agree with a couple of points. One is yes, there is no way to beat the system. A bet is a bet. Its a gamble people take and while information such as the new testing policy for amphetamines may give those who know a upperhand, there is no sure shot of being 100% sure. I also agree with the idea on price equalibrium. Once any information is leaked into the genral public, bookies will quickly react to the information. In the business, I believe its a battle of the brains. Those with the knowledge will always have the upperhand, thus Billy should have kept this information and became a better himself. HOwever, like I said in the beginning, a bet is a bet. If you look at the economics behind it, like everything, is two handed. There’s no way of beating the system. While Billy’s statement may have been news to some, may have seemed common since to others. Of course a day game after a rough night may not be as eventful. Now if the information about the new testing policies were kept only to a few insiders, I believe that holds reason for them having a “better” chance because its whose in the “know”. But once again, a bet is a bet.
February 22nd, 2006 at 9:33 am
I agree with the more testing for steriods. The drug (amphetamines) is really good for the athlete taking it but also very bad at the same time. It kills the user and close relative or friend. It should be an illegal substance. The takers of this drug has a greater advantage in succeeding than the non-takers of the drug. Random drug testing is a requirement but our world is so caught in cheating and not doing the right thing, some teams will know their is use and would not say anything to stop just to win a game. Is that a shame or what?
February 25th, 2006 at 1:10 am
Jelly – you are right on. Let me make one point on probability. Even if you could win the over-under bet of 56% of the time, you are right, “a bet is a bet”, you would lose 44% of the time.
However, if you could make a large number of bets with a 56% chance of winning, the probability that you would come out ahead gets quite large.
50 bets – 67%
100 bets – 69%
200 bets – 82%
500 bets – 93%
If your information is even better (so you win 58% of the time), the chance you come out ahead with 500 bets is now 99.2% – hardly a coin flip!
Sterling – I am not sure what you mean when you write “It kills the user and close relative or friend.” While I don’t want to take a stand that amphetamines should be legal, there have been relatively few deaths attributed to amphetamines in sports. In fact, I know of two in cycling in the 1960s or 1970s, but I have not heard of any in baseball. If you know of some that I don’t know of, let me know.
Sokolove suggests in his article that fans may not enjoy baseball without players taking amphetamines, perhaps because people won’t enjoy watching “sluggish” players. Â Perhaps the benefits of amphetamine use are not enjoyed just by the player and their team. We’ll see this year.
–CT