## Posts tagged ‘spreadsheet’

### Hiring, Firing, and Flipping Coins

Tomorrow, I become the Director of Mathematics at Discovery Education, and I am slated to spend five hours with the Human Resources department, filling out paperwork and such. By the end of it, I suspect I’ll feel like Arlo Guthrie in *Alice’s Restaurant*:

…the sergeant came over, had some paper in his hand, held it up and said, “Kids, this piece of paper’s got 47 words, 37 sentences, 58 words, we wanna know [blah, blah, blah, blah],” and he talked for 45 minutes and nobody understood a word that he said, but we had fun filling out the forms and playing with the pencils…

I do not mean to disparage Discovery’s HR department, but my new boss has described this orientation as “a test of attrition.”

The following two days will be less bureaucratic but similarly intense. As I am the first employee hired for “the math team,” it will be my job to hire others, so my second and third days at Discovery will consist of six interviews with potential math specialists. Six! Hopefully it won’t go like this:

Three candidates are being considered for a job. The first candidate, a pure mathematician, steps into the interview room. The interviewer asks just one question, “What is 1/3 + 2/3?”

Without hesitation, the pure mathematician answers, “1.”

An applied mathematician enters next and is asked the same question. He takes out his calculator, punches some buttons, and announces, “0.99999999.”

Finally, a statistician enters the room and is asked the same question. “What is 1/3 + 2/3?” the interviewer asks.

The statistician responds, “That depends. What would you like it to be?”

My worry with so many back-to-back interviews is falling into the Gambler’s Fallacy. Just as a gambler incorrectly assumes that a string of successive heads must eventually be broken by tails, interviewers often believe that a string of successive weak candidates must eventually be broken by a strong candidate. In a recent interview with Steve Inskeep on NPR (*Deciphering Hidden Biases During Interviews*), Shankar Vedantam said…

…interviewers add the equivalent of two years of job experience to the last candidate in a row, who is weak, in order to break the streak.

Vedantam went on to say that Uri Simonsohn from the Wharton School of Business thinks interviewers should…

…have a spreadsheet where they can see all the candidates they’ve interviewed, not just on that one day, but over several days. And when you step back and actually say, “Yeah, there are an equal number of strong and weak candidates,” even though you may have the streaks of four or five really strong or really weak candidates in a row.

And who am I to argue with advice like that?

For you, I offer the **Clusters spreadsheet**, which can be used to simulate 100 coin tosses. Press F9 to generate a new set of tosses. The spreadsheet will then calculate the number of heads, the number of tails, and the longest run of either type. It shows that unexpected strings of consecutive heads and tails occur, but over the long run, the number of heads and tails are roughly equal, just as the number of strong and weak candidates who are being interviewed.

Just between you and me, though, I’m hoping for a slight imbalance toward the strong end.

### Kicking Off Could Become Flipping Off in NFL

One of the most exciting plays in the history of professional (American) football was the opening play of the second half of Super Bowl XLIV, when the New Orleans Saints recovered an onside kick. They then scored to take a 13–10 lead, and eventually won the game 31–17.

But onside kicks could be a thing of the past. Yesterday, New York Giants’ co-owner John Mara suggested that kickoffs might someday be eliminated from the NFL. This caused a lot of sports pundits to react, saying that it would inherently change the game. On the *Mike and Mike Show*, analyst Mark Schlereth responded with these rhetorical questions:

What’re you gonna do, flip a coin three times in a row? You gotta get heads three times in a row to get an onside kick?

Once again, probability was placed front-and-center in recent football discussions. While I like Schlereth’s new, less violent, and more mathematical approach to onside kicks, I just wish he had gotten the math right.

If you flip three coins, the probability of getting three heads is 12.5%. That’s not enough. Data shows that onside kicks in the NFL are successful 26% of the time. So the following would be a reasonable modification to Schlereth’s proposal:

Flip two coins. Two heads results in a successful onside kick.

Then the probability would be 25%, closer to the current reality.

Unfortunately, that’s not exactly right, either — it’s based on a misleading statistic. The success rate of onside kicks is highly dependent on whether the team receiving the kickoff is expecting it or not. When teams are expecting it, the success rate hovers around 20%; when teams aren’t expecting it, however, the success rate jumps to 60%. Considering that data, the process might be modified as follows:

- Kicking team indicates to referee that they will try an onside kick.
- Of course, this must be done secretly, so as not to arouse the suspision of the receiving team. I propose that one referee be assigned to each team; the team would encode the message using RSA encryption, and the assigned referee would be given the corresponding RSA numbers. A message can then be passed without fear of interception by the receiving team. To ensure that this procedure does not signficantly delay the game, messages stating “we WILL try an onside kick” and “we WILL NOT try an onside kick” could be prepared in advance, and unemployed math PhD’s could be hired as NFL referees to decode the messages.

- The receiving team must similarly indicate whether or not they suspect an onside kick.
- Again, use RSA encryption.

- If the kicking team chooses an onside kick, and the receiving team suspects an onside kick, then:
- Flip 9 coins. If 9, 8, 3, or 1 of them land heads, the onside kick is successful.
- P(9, 8, 3, or 1 head with 9 coins) = 20.1%

- If the kicking team chooses an onside kick, but the receiving team does not suspect it, then:
- Flip 9 coins. If 9, 8, 5, 4, or 2 of them land heads, the onside kick is successful.
- P(9, 8, 5, 4, or 2 heads with 9 coins) = 60.0%

- If the kicking team does not choose an onside kick, then:
- Flip 9 coins, just so the receiving team is unaware of what the kicking team decided to do, which will allow for the element of surprise with future kicks.

If the NFL decides to accept Mark Schlereth’s suggestion for using coins to determine onside kicks, I am hopeful that they will give my proposal serious consideration. If necessary, I have an Excel spreadsheet that I would be willing to share with them.