L.A. Math: Romance, Crime, and Mathematics in the City of Angels

by James D. Stein

  “Right again! In the long run, if you have two chances in three of winning $100,000 instead of one chance in three, it’s worth more than thirty-three thousand. Admittedly, there’s no long run here, but if I were in your shoes, I’d pay the $5,000 and switch in a flash. Especially since you’re playing with house money. Even if you switch and it’s wrong, you won’t have to pay our fee, and you’re $15,000 and an appearance on prime-time TV to the good.”

  Julie got out of her chair. “I’ve still got a few days until Tuesday. I’ll think about it.” She shook hands with both of us and departed.

  “Well, what do you think?” I asked Pete.

  “I think she understood what I was saying. She’s a very bright girl. If she’s rational, she’ll switch.” The enthusiasm of the moment was starting to fade from Pete’s voice. “Considering the luck I’ve been having recently, though, she’ll probably stick with her choice, figuring that she’ll save $5,000.”

  “Well, we’ll know Tuesday night. I’ll cross my fingers.”

  By now it should be evident that a lot of interesting things were about to go down Tuesday night. As far as I knew, Pete was still planning to attend the meeting of Gamblers Anonymous Tuesday evening.

  I got back to the house Tuesday evening at about 5:30. As I was taking off my jacket, the phone rang. I picked it up.

  “Freddy? It’s Pete. I want you to call my bookie and ask for the line on the UCLA–Washington basketball game. If UCLA is favored by four points or less, bet five hundred on the Bruins to win.”

  I was stunned. “I thought you were going to a meeting of Gamblers Anonymous, Pete.”

  “I am. But just in case it doesn’t take, I’ve had this flash of incredible insight into the game. Sorry, Freddy. I’ve got to go. I’ll be back in a couple of hours.” I replaced the phone.

  Mine not to reason why, etc. I made the phone call, found that I could get UCLA minus three and a half,1 and placed the bet.

  (See An Introduction to Sports Betting on pp. 231–33 and Notes to Chapter 10 on pp. 235–36.)

  Two hours later, Pete arrived back at the house. It didn’t look as if the meeting had “taken.” The tip-off was at eight o’clock, and Pete settled down to watch.

  At halftime the score was tied. Halftime was shortly before nine o’clock, and The Proud and the Passionate hit the airwaves at nine precisely. I reminded Pete of this fact.

  “Don’t worry, Freddy. I’ll just flip back and forth between the two stations with the channel changer. Besides, if you recall, Julie said they’d call her up at about 9:45. We’ve got plenty of time.”

  I know what you’re thinking. Why didn’t we just record either the game or the show as a backup? Well, we tried, except that Pete had backlogged the DVR with so much stuff that we were out of storage space. I know that seems difficult to accomplish, but it was an older-model DVR. And, as Pete said, we could always change channels.

  As you can well imagine, I was vastly more interested in the happenings on P&P than I was in a crummy basketball game. The next forty minutes or so passed incredibly slowly, at least for me. Pete, on the other hand, was glued intensely to the screen. Washington moved out by five early in the second half, but the Bruins put on a run and caught and passed them. With six seconds to go, UCLA was up by four, and Washington had the ball in their own backcourt.

  Pete’s teeth were clamped. “I’m doomed,” he said through gritted teeth. “They’ll just let them have an easy layup, and I’ll lose the bet. Why does this keep happening to me?”

  I thought of a thousand things to say and, in the interests of friendship and future business dealings, suppressed them. Washington brought the ball up court as time ticked off the clock. With two seconds to go, one of their players launched a rainbow jumper from beyond the three-point line. The buzzer sounded. The ball hit the backboard, rattled around the rim, and fell off. UCLA by four!

  “Chalk up a W!” Pete shouted, jumping off the sofa, in a frenzy of excitement. The channel changer fell off his lap, hit the coffee table, and bounced onto the floor.

  I looked at my watch. Quarter to ten. “It’s 9:45! Change the channel!” I yelled at Pete.

  He came back down to Earth. “Sure, Freddy.” He picked up the remote and poked the button. Nothing happened.

  On the screen, some commentator dressed in a sports jacket was interviewing a sweaty UCLA basketball player. I wanted to hear what Julie did and whom Debbie decided to marry.

  “Gimme the remote!” I screamed at Pete. He shoved it at me. I poked at the “last channel” button. Nothing happened. I punched in the three-digit combination for the channel for The Proud and the Passionate. No response.

  I’m no expert on electronics, but I pried off the back and looked at the batteries. They were leaking all over the place. “Have you got any AA batteries?” I yelled at Pete.

  He checked. “No. We’re all out.”

  I looked at my watch. 9:52. By now, everyone in the nation knew what Julie had decided to do. Everyone, that is, except us.

  “Well, who do you know who watches The Proud and the Passionate?” I asked Pete.

  He shook his head. “Just Julie. And I don’t think it’s advisable to call her up to get the dope. What about you, Freddy?”

  I gritted my teeth. “We should have watched the show. You can get the sports scores any hour of the day or night, from the radio, the TV, the Internet, or one of your degenerate sports-crazy friends.”

  Frantically, Pete and I thumbed through our respective phone books, looking for likely soap opera watchers. All of a sudden, inspiration struck me. It may have struck you even sooner reading this story, but you didn’t have five thousand bucks on the line.

  “Of course!” I burst out. “Angela! She’s Julie’s friend, so she’s certain to have watched the show.”

  Normally, I am somewhat reluctant to call people after ten p.m., but there are moments when exceptions have to be made. This was clearly one of those times. I placed the call.

  All’s well that ends well. Not only had Julie changed horses in midstream, but she had backed a winner. Debbie had decided to marry Ralph Lowell. Rumor had it that you could place bets in Vegas on how many episodes it would be before the marriage was in trouble.

  I relayed the good news to Pete. He nodded contentedly and then reached for the phone. “Bernie? What’s the line on the Knicks tomorrow night? Okay, gimme the Knicks for $200, and if it off2 on the Lakers if I can get them at minus six or better.” He replaced the receiver, contentment oozing from every pore.

  “I guess it didn’t take,” I muttered sarcastically.

  “What didn’t take?”

  “The Gamblers Anonymous meeting.”

  He sighed. “Well, Freddy, on the way back I got to thinking. It’s nice to show a profit on the baseball season, and nice to show a profit on the football season, but one should always remember that life is one long season.”

  I couldn’t argue with philosophy like that. Far-thinking businesses have the same view of their quarterly reports.

  The other day Pete and I spent a chunk of the $5,000 on some new equipment. We now have a brand new big-screen TV in the living room. With a fancy channel changer, and picture-in-picture so we can watch two shows simultaneously, in case something like this ever happens again.

  Oh, yes. We also got a smaller TV, ten bucks’ worth of AA batteries, and a stand-alone DVR in addition to the one supplied by the cable company. Speaking of the cable company, we rolled over our cable plan for two years, which entitled us to a DVR with massive storage.

  CHAPTER 11

  THE GREAT BASKETBALL FIX

  A little of Ollie Richardson, used car salesman, goes a long way. Unfortunately, at six feet four and closing in on the weight of an offensive lineman in the NFL, there is a lot of Ollie Richardson.

  Ollie is a regular at Pete’s Tuesday night poker game, held on Tuesday night in order not to interfere with Monday night football. In addition to being as obnoxious as used car salesm
en are generally reputed to be, Ollie is also a world-class gloater. This, of course, raises anyone’s obnoxiousness quotient. He does, however, have some saving virtues. When the recent budget cuts at L.A. Unified School District threatened to scrap girls’ basketball, Ollie stepped in and coached the girls’ team at MacMillan Junior High, where his daughter was a point guard. MacMillan was winning, and Ollie was gloating.

  You now have the same background that I did a month ago. It was then that Pete received a call from his Aunt Harriet, a soft-spoken lady with an unkempt halo of light gray hair, who was somewhat given to dithering. It seemed that Aunt Harriet’s daughter Irene attended Rutherford Junior High, which was in the same district as MacMillan, coached by the one and only Ollie, with whom you are already acquainted. The budget axe had wreaked havoc upon the extracurricular activities at Rutherford as well, and the girls’ basketball team was looking for someone to coach them. Would Pete be willing?

  Are you kidding? Within even the casual sports fan lurks the firm conviction that every manager or coach is a complete dunce, and that if the aforementioned fan were merely placed in charge of the team, he or she could lead the lowly out of the cellar, the mediocre to championship contention, and the good to a dynasty. And Pete was more than just a casual sports fan. Pete knew that it was unlikely that management would put him in charge of the Dodgers or the Lakers but, as he said to me, you have to start somewhere.

  It turned out that even though Pete had agreed to buy a pig in a poke, he had inherited a team that was closer to bacon than to hog jowls. The Rutherford Lady Basketeers had one major asset, a young lady by the name of Theresa Middlebury. At five feet seven, Theresa could be termed a giantess, at least for a thirteen-year-old. Even better, she could not only play good defense but also had a virtually unstoppable jumper, accurate from about twelve feet or closer. After the first practice session, Pete came back humming.

  “How’d it go, coach?” I asked him.

  Pete was clearly a happy camper. “They’re reasonably talented, and they work hard. That, plus my knowledge of basketball, should prove to be a virtually unbeatable combination.”

  I thought it was time to inject a note of reality into the proceedings. “Pete, you’ve never coached a day of basketball in your life.”

  “Remember what I told you about my father, Freddy? He was a player. Besides, I’ve watched thousands of basketball games.”

  “Maybe millions. But it’s easy to coach from the sidelines.”

  He digested this and nodded. “Nonetheless, coaching basketball is not rocket science.” How could I argue with that?

  I have to hand it to Pete. Either he was correct in his assessment of the talent and dedication of his young charges, or he really was a good basketball coach, or maybe a combination of both. It soon became evident that Rutherford and MacMillan were the class of the league and were on a collision course for the league championship. This rapidly became Topic A, or at least Topic B or C, at the Tuesday night poker game. The animosity that existed between Ollie and Pete (and between Ollie and everyone else, for that matter) induced spirited betting among the poker players. Both teams were undefeated, and since the game was to be held on Rutherford’s home court, they had been installed as a four-point favorite. It was felt that over–under betting1 would be out of place in a girls’ junior high basketball game.

  (See Notes to Chapter 11 on pp. 236–37.)

  As the day of the game approached, I could see the level of intensity pick up. Pete had invited me to practices, doubtless to have someone there as a towel boy, but even I was getting involved. It was clear that the girls were going to give it their all. Although MacMillan did not have a Theresa Middlebury in the low post, scouting reports (faithfully relayed to us by Irene, who was privy to all the inside dope) said that they had two five-feet-four forwards who could really crash the boards. This was bad news, as Theresa was also Rutherford’s best rebounder. On the other hand, MacMillan did not have a true point guard and was consequently a little weak on ball handling. Deciding that Irene’s information was the real McCoy, Pete decided to teach the girls an aggressive trapping defense in order to exert maximum pressure when MacMillan was trying to get out of its own backcourt.

  Pete had decided to use me as a sounding board because (a) I was developing a certain expertise and (b) I was usually within easy reach. After a recent practice session emphasizing Pete’s new defense, he downloaded some basketball theory to me as we drove back to the house.

  “You see, Freddy, in a game with only six-minute quarters, turnovers can be critical. I’m also planning on sending Theresa to the offensive basket whenever it seems that the trap is succeeding.”

  “Sounds good to me.” I paused for a moment, deciding how to phrase my next remark. “Pete, I’m very impressed with the job you are doing. Do you suppose you could find someone at the poker game willing to take a hundred-dollar bet on the game? On Rutherford, of course.”

  Pete chuckled. “Let me give you Arnie Schrafft’s number.” Arnie was one of the Tuesday night regulars. “He does a little book-making on the side. Confidentially, he told me he’s getting almost as much action on this game from the other Tuesday night poker players as he does on the USC–UCLA football game. Admittedly, USC has dominated in the past few years, which slows down the action.”

  I looked a little shocked. “Doesn’t Arnie work for the school district?”

  Pete nodded. “The budget cuts reduced his salary as well, so he’s making a few extra bucks.” He ruminated for a moment. “I think the line’s four at the moment, though it’s been jumping up and down a bit.” We stopped for a red light. “I must say, Freddy, I’m happy to see that you approve of my coaching strategy sufficiently to back it with hard cash.”

  “Of course.” I refrained from telling Pete that it wasn’t simply the soundness of his strategy that had made me interested in risking a hundred bucks. At the latest practice, I had seen Theresa stick eight straight jumpers from the twelve- to fifteen-foot range. Not to mention twenty-two consecutive free throws.

  By coincidence, I was asked to fill in at the next Tuesday night poker game. The atmosphere was certainly becoming charged. Pete had almost come to blows with Ollie, who had sneered at Pete’s coaching ability, pointedly mentioning that his own team had achieved its record without benefit of a beanpole like Theresa Middlebury. Now, there is no question that Theresa Middlebury was taller than the average thirteen-year-old girl, but she was a little sensitive about her appearance, as are most thirteen-year-olds. Pete told Ollie that if he said anything like that to Theresa during the game, he would be liable to end up with a black eye, or worse. Ollie may have outweighed Pete by nearly seventy pounds, but Pete was about six feet two with long arms and was considerably more mobile than Ollie.

  Practices were going extremely well, and it was beginning to look like the team was peaking at just the right moment. Then, three days before the game, disaster struck.

  I was blissfully unaware that disaster had struck, as it was about ten in the morning. I had just finished breakfast and had taken coffee and the morning paper into the living room of the guesthouse. Maybe I was getting a little greedy, but I had decided to put another hundred on the game. I looked up Arnie Schrafft’s number and gave him a call. He may not have been the only bookie in town, but even when Internet betting was legal, you couldn’t find any lines for girls’ junior high basketball games.

  Following Pete’s advice, I asked what the line was before I placed my bet. When I heard, the coffee I was sipping went down my windpipe the wrong way, and I nearly choked.

  Pete has made it abundantly clear that, when he is sleeping, he is to be awakened only if it is extremely urgent. It struck me that this probably qualified. I buzzed him in his bedroom. It took eight rings before he answered.

  “Yeah? What is it?” He knew it was me on the intercom, so he could afford to be rude.

  “Pete, something has happened. I don’t know what’s going on, but I just cal
led Arnie Schrafft to put another hundred on the game. He told me that the line was now MacMillan minus two. I thought I ought to tell you.”

  Pete whistled. “You’re kidding! I hope you didn’t fall into the trap of grabbing it. It’s probably a sucker bet, although I have no idea why the line would change like that.”

  “No, I was stunned. I just thanked him and got off the phone.”

  Pete was silent for a moment. Then he said, “The only thing I can think of that might cause that violent a swing would be an injury of some sort. Arnie works for LAUSD, so he’s privy to information we might not have. Well, we’ll find out at practice this afternoon.”

  When practice arrived, we were relieved to find that there were no injuries—at least, none that we could detect. However, it seemed that something had happened to Theresa. She was throwing up bricks, her defense was off, and her mind was definitely not on basketball. Pete told me to take her to the free throw line and have her shoot a hundred free throws and keep track of how many she made. I did so and reported back to Pete.

  “Sixty-six.”

  He consulted some numbers on a piece of paper and closed his eyes a moment. When he opened them, he said, “Freddy, you’re an investigator, and we’ve got a situation that needs investigation. Something’s happened to Theresa. Find out what’s going on.”

  I was a little surprised. “Sinking sixty-six free throws out of a hundred isn’t a crime.”

  “It is for Theresa. She’s an 80% foul shooter, and sinking only sixty-six out of a hundred is three and a half standard deviations below the mean. Maybe one chance in a thousand.”

  He lost me. “Say what, Pete?”

  “Freddy, if you were to keep track of how an 80% foul shooter does on a hundred free throws, it would form a bell-shaped curve. Theresa’s success probability for a single free throw is 0.8, and her failure probability is 0.2. You would expect Theresa to sink 80%, which is eighty out of one hundred. That’s the mean. To compute the standard deviation, you multiply 100 times 0.8 times 0.2, and take the square root of that number. So 100 is the number of free throws, 0.8 is the probability that Theresa will make a free throw, and the 0.2 is the probability that she’ll miss. Let’s see, 100 times 0.8 times 0.2 is 16, and the square root of 16 is 4.”