Law of Averages

A sales guru gave an inspirational presentation in which he argued that each no brings you closer to a yes because 1 out of every 100 phone calls results in a sale. You just have to get through those 99 nos to get to a yes. What do you say?

Answer this Ask Marilyn letter: "During the last year, I've gone on a lot of job interviews, but I haven't been able to get a decent job.... Doesn't the law of averages work here?"

Waldemar Kaempffert, science editor of The New York Times for nearly 30 years, dismissed the argument that ESP experiments were mostly lucky and unlucky guesses: "The run-of-luck theory has also been invoked with some disregard of the obvious fact that runs of bad luck will cause runs of good luck in the course of 100,000 trials."

Explaining why he was driving to a judicial conference in South Dakota, the Chief Justice of the West Virginia State Supreme Court said that, "I've flown a lot in my life. I've used my statistical miles. I don't fly except when there is no viable alternative." What do you suppose the phrase "used my statistical miles" means? Explain why you either agree or disagree with the judge's reasoning.

After Republicans lost control of the US Senate in the 2020 election, Senator Roy Blunt (R-Mo.) said that, "The optimist in me would say the odds of us getting a break in the future are greater because we've had such a run of bad luck." As a statistician, what do you say?

After a year of underperformance that was a "complete disappointment," the CEO of an AI-powered fund was optimistic:

The Horizons Active A.I. Global Equity ETF (MIND), which uses a proprietary AI-directed selection process to invest in major global equity indexes through a basket of ETFs, has trailed the market over the past year, down 1.04 on a return basis, versus a positive total return, in Canadian dollar terms, of 5.76 for the MSCI World Index.... > "To the extent that they may have underperformed today, there is a strong possibility that they can outperform in the future," Mr. Hawkins [CEO] said.

Explain Hawkins' reasoning and why you either agree or disagree with it.

Answer this question to columnist Marilyn vos Savant:

At a lecture on fire safety that I attended, the speaker said: "One in 10 Americans will experience a destructive fire this year. Now, I know that some of you can say you have lived in your homes for 25 years and never had any type of fire. To that I would respond that you have been lucky. But it only means that you are moving not farther away from a fire, but closer to one." Is this last statement correct? Why?

At the midpoint of the 1991 Cape Cod League baseball season, Chatham was in first with 18 wins, 10 losses, and 1 tie. (Games are sometimes stopped due to darkness or fog.) The Brewster coach, whose team had 14 wins and 14 losses, said his team was in a better position than Chatham to win the championship: "If you're winning right now, you should be worried. Every team goes through slumps and streaks. It's good that we're getting [our slump] out of the way." Do you either agree or disagree with his reasoning?

Answer this letter to advice columnist Dear Abby:

My husband and I just had our eighth child. Another girl, and I am really one disappointed women. I suppose I should thank God she was healthy, but, Abby, this one was supposed to have been a boy. Even the doctor told me that the law of averages was in our favor 100 to 1.

As a statistician, how would you answer this March 20, 2024, Yahoo Sports question? > [Shohei] Ohtani went 2-for-5 with an RBI and a walk but he also committed his first [mistake] with the Dodgers, failing to tag second base before heading back to first in the eighth inning. At least he got [his mistake] out of the way early, right?

The father of a Little League baseball player told his son to lend his baseball bat to a poor hitter "to use up the bat's outs." Explain why you agree or disagree.

While a baseball pitcher was making warmup throws before a game, his coach said, "Stop throwing good pitches; you need to get your bad pitches out of the way." What do you think?

After having lost election contests for Governor of the State of Washington in 2004 and 2008, Dino Rossi ran for the US Senate in 2010. A Washington Post columnist wrote, "Is the argument for Dino Rossi basically that, by the law of averages, he has to win something eventually?" As a statistician, how would you respond?

Casey reasons that if you haven't had a driving accident, your insurance company should raise your rates-not lower them-because you are due for an accident. When he had an accident, he wrote to his insurance company, arguing that everyone has accidents and they should lower his rates now that he has gotten an accident out of the way. Explain why you either agree or disagree with his reasoning.

Explain why you either agree or disagree with the following:

The golden theorem proven by the Swiss mathematician Jacob Bernoulli states that a variable will revert to a mean in the long run. For example, a small number of flips of one coin might be mostly heads while a small number of flips of another coin might be mostly tails, but, inevitably, a large number of flips will be 50-50 for both coins. In the same way, earnings might be high for one company and low for another, but, inevitably, will be the same for both.

The law of large number implies that as the number of coin flips increases, it is increasingly likely that the fraction of flips that are heads will be close to $50 \%$. The writer Arthur Koestler once argued that the law of large numbers is wrong because it requires coin flips to be related-a preponderance of heads must be balanced by a preponderance of tails at some point in order for the law of large numbers to be true-yet coin flips are independent, which makes the law of large numbers false. Explain why you either agree or disagree with Koestler's argument.

Explain why you either agree or disagree with this argument in Leo Gould's book, You Bet Your Life:

There are many systems of all kinds but in talking to gamblers you will find the one they believe in most (and it can be used for most gambling games) is the "watch" or "patience" system. It's simple. If you are playing dice and certain bets pay even money, before you put your first [bet] on any of the numbers, watch until one shows up at least three of four consecutive times and then put your first [bet] on the opposite chance.

A 2013 Bloomberg Businessweek article noted that Warren Buffett's Berkshire Hathaway had underperformed the SP500 for four months in a row, June, July, August, and September, and concluded that "Berkshire stock is due for a comeback vs. the SP." Do you agree?

Explain and evaluate this Los Angeles Times writer's appeal to the law of averages:

Thursday night's game was another chapter in the Raiders' stunning success in prime time. Put the Raiders on Monday night, Thursday night, Sunday night football and the only thing in the opponent's favor is the law of averages. Thursday night's win gave the Raiders a 22-2-1 record in prime time.

Jimmy the Greek, a celebrity gambler, said that,

The professional gambler, when heads comes up four times in a row, will bet that it comes up again....The amateur will figure that heads can't come up again, that tails is "due."

Do you agree with the professional or the amateur? Why?

Orel Hershiser, before pitching a baseball game for the Los Angels Dodgers, who had not scored a run for 24 consecutive innings, said, "I prefer pitching on the day after we've been shut out because I figure we're going to score. I guess the odds are really in my favor now." Do you agree?

After the New England Patriots beat the Miami Dolphins in the 1986 National Football League playoffs, a Los Angeles Times sportswriter offered this analysis:

In the Orange Bowl, though, the Dolphins were basically losing to the law of averages. They had won 18 straight from New England in that stadium. Explain and evaluate this use of the law of averages.

Explain the error in this reasoning: "My next marriage is sure to work; the odds against five divorces are astronomical."

In his final newspaper column, Melvin Durslag reminisced about what he had learned in his 51 years as a sports columnist, including this advice from a famous gambler:

Nick the Greek tipped his secret. He trained himself so that he could stand at the table eight hours at a time without going to the washroom. It was Nick's theory that one in action shouldn't lose the continuity of the dice. Explain why you agree or disagree with Nick's secret.

The "Texas Lotto Guide" gave this advice: "The 'law of probability' essentially means that over a given period of time a number that has not hit [been selected] for a long period of time is due to come in." Do you agree?