Bastiat’s Bastions

I watched the Yanks beat up on the Tigers last night. I’m floored by how much love is been giving to Derek Jeter (aka Mr. October, Captain Clutch) by the Fox crew. And again on ESPN.

Suppose we wanted to take a scientific approach in determining who is a “clutch” player. Obviously we’ll have to figure out what a “clutch” situation is, and then look at players’ performance in those situations.

A very important consideration though, and one that will be pointed out strongly and often when you take your QBA classes, is that sample size is extremely important in making statistical inferences.

I am pretty sure when you flip a coin that it comes up heads with probability very near 0.50. But if you flip a coin 4 times and if it comes up heads three times (75% of the time), is that strong evidence that the coin is loaded (that in fact heads come up more than 50% of the time)? The answer is no. A certain amount of random variation is to be expected.

In fact, in this situation, even with a coin that we were certain would come up heads with probability 50% of the time, we’d expect to see 3 or more heads 31.25% of the time if we flipped the coin 4 times. Now if we flipped a coin 400 times and sow more than 300 heads, that would be strong evidence that our coin is not “fair”.

Likewise, if you only saw last night’s game, Derek Jeter is the greatest baseball player in history. Of course, drawing inferences based on only 5 plate appearances is clearly dangerous if not entirely ridiculous. (Anyone remember Tuffy Rhodes?) Yet, if you listened to the broadcast, everyone knows Derek Jeter is “Captain Clutch”. How?

We could all disagree about exactly what is meant by “clutch”. Perhaps late in close games? Bottom of the ninth? Or simply in the playoffs? But even if we settle this disagreement, it is still very difficult to tell who is a clutch player, because by the nature of these situations, there are very few “clutch” situations during a season (or even a career).

Can we make inferences from these small sample sizes? Perhaps not with much confidence we are right. Just as flipping 4 coins will occasionally result in 3 or even 4 heads (is that “clutch” coin flipping or random variation), some players will may appear to be clutch players when in fact it is just random variation.

Is the case for Jeter? I don’t know. But neither do the announcers on Fox.

But for your amusement, I have taken Jeter’s stats and the much maligned Alex Rodriguez’s stats in all the playoff games they have played and listed them below. Because they have played different numbers of playoff games, I have adjusted their statistics – the numbers you see will are for each 100 playoff at bats they have. (Jeter’s sample size is much larger than A Rod’s). You can make your own conclusion. Could you do something fancier? Absolutely. You’ll see I purposely left off the names of the players.

Dr. Jahn Hakes and Dr. Skip Sauer (both economists at Clemson while I was in graduate school) have done some work on identifying clutch hitting in major league baseball. For an example of their work, click here. What do they find? They cannot find statistical evidence of persistently clutch hitters.

Why is that a couple of sports nuts economists, armed with PhDs from top schools, years of play by play data, and tons of computing power can’t find evidence of consistent clutch hitting, but the talking heads on Fox know it? Hmmmn.

If you like this type of analysis, then read a book called Moneyball by Michael Lewis. It’s about how the GM of the Oakland A’s (Billy Beane) listened to scouts (announcers?) less and started doing more statistical analysis in drafting baseball players. The A’s have been quite successful despite their relatively low payroll. It’s an awesome book for someone interested in baseball, statistics, economics, or even business in general.

–CT

I’ll post a comment later with the identities of the players. And for those of you looking for extra credit, bashing Jeter or A-Rod won’t do.

Credit where it's due – I snagged the article from thesportseconomist.

The topic is whether or not college athletes should be paid. The article, written by John Wilner at the Mercury News, reports a reasonable estimate of the amount of revenue that is "generated" by Cal's running back Marshawn Lynch.

Lynch is no average player – he is on a lot of pundits' short lists for the Heisman Trophy, an award given to the best college football player each year. The article points out that the scholarship Lynch receives as compensation for his services is worth in the neighborhood of $20,000, while Lynch brings in roughly $800,000 of revenue to the University. By the metric, Lynch is vastly underpaid.

Of course the source of this underpayment is the fact that the NCAA prohitibits colleges to pay college athletes – effectively capping their compensation at the value of the scholarship they receive. If Lynch were able to sell his services in a unrestricted market, there is no doubt he would earn much more money.

Do you expect athletes to be "paid" anytime soon? Three things to consider first.

1. The rhetoric on idealism, traditionalism, and amateurism. Is this just rhetoric? Or do people really like amateurism. Is college football even "amateur"?

2. Universities compete to field winning football programs. Univerities can improve their chances of winning by recruiting more talented players, more talented coaches, and by enhancing facilities, just to name a few. Since direct monetary compensation for athletes is prohibited, this will increase the intensity of competition on other margins. Fortunately for the folks who are coaches and athletic diretors, there is no cap on the compensation of coaches and athletic directors. In a world with pay for athletes, might coaches and administrators get a smaller fraction of the pie? Would these folks be in favor of paying players if it reduces their compensation? Who is on the front line of making the decisions about pay for athletes?

3. At big-time Division I programs, the football program turns a surplus (profit). Some of this surplus (which of course is larger because they do not have to pay players) is spread around to other athletic programs within the university that do not generate a surplus. For instance, women's soccer or men's golf – these programs are subsidized by the football program. If football players were paid, would this limit the funds available for these so called "non-revenue sports" (title IX considerations aside)? Will the women's soccer coach be in favor of paying footall players if it ultimately cuts in to the soccer budget?

–CT

Read this article on an instant replay system in tennis. It sounds eerily similar to the NFL system. Computers, two challenges per set, etc. Interestingly, there will be no videotape and interpretation – it will be wholely a machine that makes the call as I understand it. This begs the questions of why not on all calls? Why limit it to only a few calls a match?

I for one am not sure fans would like this. We’ll see. I personally enjoyed John McEnroe berating officials.

Are bad calls part of the game? It’s an old tired story. Who can forget JM yelling “You can’t be serious?”

One more reason for posting; I think this article contains the understatment of the year. When asked his opinion, John McEnroe himself, suggested:

“If anyone’s been listening to my commentary the past year then they know I’m in favor of using replay…”

Is John McEnroe serious? I bet he is.

–CT

In light of the recent threat made by the owner of the Seattle Supersonics to move to another city, James Thayer writes an article in the Weekly Standard concerning the impact that stadiums (and profesional sports teams) have on the local economy. The Supersonics are threatening to leave unless a stadium upgrade is paid for the by the taxpayers of Seattle.

To justify spending public tax dollars on a stadium, the claim would have to be that stadiums “pay for themselves” through enhanced economic devlopment, more jobs, and all the income generated in and around the stadium. An excerpt, edited every so slightly so as not to give away the answer:

…team owners promise urban renewal and a stronger local economy…Regarding the Sonics proposed stadium refurbishment, Washington State Senator Margarita Prentice gushed, “The ripple effect defies our imagination.”

So the question is – are the politicians right? What happens when you do the math.

Thayer tells you what happens when the leading economists studying the problem add it up. You might be surprised. Read the article!

Once you read the article, can you blame the Seattle Supersonics owner?

–CT

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