# William M. Briggs

### Statistician to the Stars!

#### Page 151 of 573

Cardinal Duc de Richelieu

From France in the Age of Louis XIII and Richelieu by Victor-L. Tapié translated by D. McN. Lockie, Praeger Publishers, New York, 1975, p. 172:

He regarded a multiplication in the number of colleges or the uncontrolled proliferation of all sorts of ideas as a source of spiritual danger: ‘If learning were profaned by being made available to all and sundry, it would be found that there were more people capable of creating doubts than of resolving them, and many would shows themselves more apt in opposing truth than in depending it,’ he observed in 1625.

And in a footnote to the same, “In 1611 Bacon wrote to James I as follows:”

Concerning the advancement of learning, I do not subscribe to the opinion…that, for grammar schools, there are already too many…The great number of schools which are in your Highness’s realm doth cause a want, and likewise an overthrow—both of them inconvenient and one of them dangerous; for by means thereof they find want in the country and towns, both of servants for husbandry and of apprentices for trade; and on the other side there being more Scholars bred than the State can prefer and employ…it must needs fall out the many persons will be bred unfit for other vocations and unprofitable for that in which they were bred up, which fill the realm full of indignant, idle and wanton people… [p 478; ellipses original]

In re education today: plus ça change, plus c’est la même chose?

Richelieu’s observation came from his Maximes D’Etat, Or Testament Politique, p. 169 at that link.

Source: Replays are for wimps.

There is a lawyer in each of us struggling to claw its way out and sue. Yet most of us—because we learnt to heed our mothers and are kind to animals and children, and because we imbibe freely the consolations of philosophy and lead a balanced, moral life—restrain these dark impulses.

Others—giving themselves over to the demons of Anger, Envy, and Greed, and who hold the detestable belief that perfection can be had in this Earthly life—fail. It is these intemperate fellows responsible for besieging mankind with awful Utopian schemes, like car alarms, back-up warning beepers, NPR, and “instant” replay in sports.

Instant my foot. Why, it’s very name is a lie. As is the belief that by instituting this vile scheme finally—finally!—the sport will have reached its ideal.

What is the biggest complaint you hear about baseball? Boring? Slow? Too long? The Powers That Be have discovered a way to boost these lamentations and drive away even more potential viewers. In other sports it takes minutes for each scan of the video, minutes which grow longer and more frequent every year. Why should baseball be different?

The kicker is that the most ardent admirers of Technology as Salvation forget about false complaints. How often does a peeved coach petition the referees for a review only to discover his petition is groundless and that the referees were right after all? Often. And how often is the reply ambiguous? Often. Are we now to be treated to the absurd spectacle of Billy-Martin-type managers kicking dirt onto the screens of “instant” replay machines?

The example on everybody’s mind is Detroit Tigers’ pitcher Armando Galarraga, who had been throwing a perfect game—a true rarity in the game—until, in the ninth inning in nearly the last play of the game, umpire Jim Joyce blew a call at first and called a man safe who was so obviously out that even my Grandmother could see it, and she has been gone these ten years.

Outrageous! Calumny! Pandemonium! Tears of rage! Tears of remorse! Tears galore! Sickening. Ty Cobb would have charged the field with a bat and beat, not the umpire, but the whiners on the diamond and in the stadium. (Incidentally, unlike fans and sports writers, Galarraga took it like a man and laughed it off on the mound.)

Maybe you’re still concerned about Galarraga, but that means you don’t see it. That you can’t guess from the clues. We are still talking about it! If Joyce hadn’t been concentrating on trying to clear the baseline with a stream of spittle and had made the right call, then what? Well, Galarraga, who is already on his way out (Rockies’ AAA affiliate the Sky Sox), would soon be sitting on a barstool in some back-alley bar in Caracas trying to tell the poor sot next to him how he had once thrown a perfect game. Yawn.

But now he has a story worth retelling. “I had a perfect game,” he probably starts. “But for an inept umpire.” His listeners move closer. “It was the top of the ninth…”

And we each of us have the same story! Tell me, average baseball fan, the names and teams of all the other pitchers who have had perfect games. A few stats geeks have this ferreted away in their little grey cells, but most don’t. But everybody knows the story of Galarraga the Unlucky, Galarraga the Betrayed. Galarraga the man who has at least this one great thing he can carry with him for the rest of his life.

Right now the scheme is to allow reviews for everything but balls and strikes. That’s right now. But the impatience of Utopians is legendary and it won’t be long before there are ear-splitting calls for devices to replace umpires. Think not? Then read this:

Washington Nationals Manager Davey Johnson said the expanded replay might not go far enough. Johnson told reporters in Washington that the league ought to consider an “electronic strike zone” to monitor calls of balls and strikes.

Yes, change the game irrevocably. Make comparisons between now and the past impossible. Forget that the game is a human event and imperfect and it is the imperfections that make it vivid and worth following. But why stop at replacing umpires with machines? Replace the players, too! Heck, simulate the whole thing on a computer and run the “season” flawlessly in a snap and report the results to whatever fans are left.

Sigh. All we have left to us is soccer, the only sport which still (mostly) holds out.

Henk Tijms

Henk Tijms, emeritus professor at the Vrije University in Amsterdam, is author of Understanding Probability (excerpt; Amazon at this writing has it for only \$31.29, a steal for textbooks).

Football (“soccer”) is the most popular sport in the world, particularly in Europe, South-America, Africa and Asia. The most watched tournament is the UEFA Champions League, UEFA being the Union of European Football Associations. The UEFA Champions League is also the most-revenue generating tournament in football. Professional football has been troubled by multiple scandals in the past few years, including accusations of corruption and match-fixing.

Recently, the UEFA fell again under a cloud of suspicion. The 2013 Champions League draw ceremony for the quarter-finals resulted in the following four matches:

• Málaga—Borussia Dortmund
• Paris Saint Germain—Barcelona
• Bayern München—Juventus

The outcome of the quarter-finals draw led to heated discussions in European sports programs on television and radio. Several sport journalists accused the UEFA of manipulation in order to make possible the commercially most interesting semi-finals and final. The most explicit accusations came from a former international soccer referee (details here).

It is quite remarkable that the Big Four of the eight teams avoided each other in the quarter finals. The Big Four are the two Spanish teams Barcelona and Real Madrid and the two German teams Bayern München and Borussia Dortmund. Moreover, it is remarkable that none of the Spanish teams was paired with the third Spanish team Málaga, an unattractive opponent for both Barcelona and Real Madrid. The quarter-finals draw kept open the possibility of a dream final between Barcelona and Real Madrid. What are the chances that this particular quarter-finals draw is rigged?

To answer this question, let us first calculate the probability that the Big Four avoid each other and neither Barcelona nor Real Madrid plays against Málaga when it is assumed that the eight teams are paired randomly. Under random pairing the Big Four avoid each other with probability

$\frac{4}{7}\times \frac{3}{5}\times \frac{2}{3}=\frac{8}{35}.$

Since the draw ceremony involves eight teams, Málaga must be paired with one of the teams from the Big Four if the Big Four avoid each other. Hence, under the assumption of random pairing of the teams, the probability that the Big Four avoid each other and neither Barcelona nor Real Madrid is paired with Málaga is given by $\frac{8}{35} \times \frac{1}{2}=\frac{4}{35}$. This probability is small but not exceptionally small and therefore frequentists may argue that the result of the quarter-finals draw is no surprise when taking into account that there are many soccer tournament draw ceremonies over the years.

However, this is bad reasoning. The discussion is not about many tournament draw ceremonies, but about a particular soccer tournament ceremony for which there is reasonable ground to believe beforehand that the draw ceremony could be manipulated. In this situation it is appropriate to use the Bayesian approach. Bayesian analysis requires that before the draw ceremony takes place you quantify your personal belief that the draw ceremony will be manipulated.

Suppose you believe that the prior probability of a manipulated draw ceremony is at least 20%. Many soccer fans will consider a prior probability of 20% for a manipulated draw as a conservative estimate. By the formula of Bayes, your personal belief of a manipulated draw after hearing the result of the draw is given by a posterior probability of at least 68.6% if your prior probability is at least 20%. The easiest way to calculate the posterior probability is to use Bayes formula in odds form:

$\frac{P(H\mid E)}{P(\overline{H}\mid E)}=\frac{P(H)}{P(\overline{H})}\times \frac{P(E\mid H)}{P(E\mid \overline{H})}.$

In our example the hypothesis H is the event that the draw ceremony is manipulated so that the Big Four avoid each other and neither Barcelona nor Real Madrid is paired with Málaga, $\overline{H}$ is the complement event that the teams are paired at random, and the evidence E is the event that the Big Four avoid each other and neither Barcelona nor Real Madrid is paired with Málaga. If your prior probability that the draw ceremony will be manipulated is r%, then the prior odds $\frac{P(H)}{P(\overline{H})}$ is $\frac{r/100}{1-r/100}$ and the likelihood ratio $\frac{P(E\mid H)}{P(E\mid \overline{H})}$ is $\frac{1}{4/35}$. This gives the posterior odds

$\frac{P(H\mid E)}{P(\overline{H}\mid E)}=\frac{r}{100-r}\times \frac{35}{4}.$

Since $P(\overline{H}\mid E)=1-P(H\mid E)$, it follows that your posterior probability of a manipulated draw ceremony is given by

$P(H\mid E)=\frac{35r/4}{100-r+35r/4}.$

This posterior probability is equal to 0.6863 if your prior probability is represented by r=20%. The Bayesian analysis show that the suspicion voiced in the sports programs after the announcement of the result of the Champions League quarter-finals draw is certainly not unwarranted. Incidentally, in the end the final was not played between the two Spanish teams Barcelona and Real Madrid but between the two German teams Bayern München and Borussia Dortmund with Bayern München as winner.

This post emphasizes once again the importance of Bayesian thinking which is an indispensable part of statistical reasoning. Bayesian thinking is advocated in my book Understanding Probability (Cambridge University Press, third edition, 2012). This feature distinguishes my book from other introductory probability books and was praised in this book review.

I dare to say that the leading textbooks for introductory probability courses badly fail in the attention paid to the Bayesian approach. Students should be better trained to think in the Bayesian way. Every modern course on introductory probability should give greater recognition to the probabilistic ideas of Bayesian thinking and show that Bayes’ rule is the rational basis for answering probabilistic questions from real life.

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Here is a performance, atypical, marred by paying insufficient attention to the iron (linen wrinkles easily) and from meeting my pals Willie Soon and Juan Ramirez (who picked up the check) in the lobby bar the night before.

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1Forgive me the garish titles.