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

by James D. Stein

  Pete perked up, as anyone would when a $5,000 fee that one thought had flown out the window might be coming back home to roost. “Let’s hear it.”

  “Ask Packard to give us copies of any material relating to the election, such as the club constitution and the actual ballots for starters. Maybe there’s something somewhere that will invalidate the election.”

  Pete looked at me. “You may have something there. I wonder why I didn’t think of that.”

  Praise from Caesar is praise indeed. “I think you probably got hung up by the thought that if a Nobel Prize winner couldn’t solve it, how could you? Anyway, let’s get Packard on the phone and see what happens.”

  A lawyer once told me that there was no such thing as an unbreakable contract, and I had spent a lot of time while I was working in New York poring over contracts. This one turned out to be a cinch. The ballots had been printed with no mention as to when the votes must be cast, which was specifically mandated by the club constitution. We called Packard, told him the good news, and recommended that he reissue the ballots in accordance with the club’s prior practices.

  A few days later, we received a very cheerful call from our erstwhile client. “Sorry this has to be such a short call,” he bubbled, “but I’m in the middle of packing. I’m heading for Pebble Beach in another hour or so. But my invitation to the Williams’s party stands. By the way, Freddy, you were right. It seems that Celia Morris broke up with her CPA, and I’ve got a dinner date!”

  We were delighted to hear it. He was evidently so pleased with the outcome that he was going to send us another three thousand bucks. We were certainly not going to be so unmannerly as to refuse to accept it.

  “You know, Pete,” I reflected later, “I wonder what would have happened if we hadn’t been able to find a loophole through which to wiggle.”

  “I can tell you that. We would have returned his retainer.”

  Returning retainers goes against everything I believe in. “Why would we have done that?”

  “Freddy, when a mathematical theorem says that something’s impossible, it is flat-out impossible. It’s not impossible as in “the difficult we do today, the impossible takes a little longer.” We would have been unable to solve his problem, at least from a mathematical standpoint. It’s a good thing you figured out how to get around the impossible.”

  “Well, Pete, I’ll tell you what. Maybe we can work out a new division of labor. You take care of the possible cases, and when an impossible one comes along, just let me know.” I don’t mind telling you, I was feeling more than a little smug.

  Packard’s check arrived a day later. Pete contemplated it with satisfaction.

  “That’s eight thousand added to the account, Freddy.”

  “Minus fifty for insurance,” I said.

  Pete looked blank. “Insurance?”

  “Yeah, I thought a little insurance might be necessary. I didn’t tell you the full story of the party where I met Celia Morris. She wasn’t spending all her time at the party with that Farnsworth character. Maybe she really did have tax problems. At any rate, Farnsworth clearly seemed more interested in her than vice versa. Also, while I was getting my car, she got into a black Lexus and drove off alone. You don’t have to be a detective to work out that she’s almost certainly a free agent.”

  “She’s listed in the phone directory,” I continued, “so I took the liberty of sending her a dozen roses in Packard’s name. In case you’re unfamiliar with market conditions, that’s fifty bucks’ worth of roses.”

  CHAPTER 14

  THE QUARTERBACK CONTROVERSY

  ’Twas the night before Christmas, but that didn’t prevent creatures from stirring all through the house. Every other year, Pete gives a Christmas party, but this was the year to receive rather than to give, and we had received invitations to six different parties, scattered throughout the length and breadth of the entire L.A. area.

  The bank balance was in good shape, and Pete had settled down to prepare for the forthcoming NFL playoffs and bowl games. So that he could concentrate on the pigskin finales, I had agreed to plan our party-going travels. I didn’t give it a whole lot of thought because I thought traffic would be light on Christmas, so if I took us a little out of our way it wouldn’t be a tragedy. It was late, and I was a little sleepy, but I made out a schedule and took it in to Pete for him to look at. He looked at it and didn’t like what he saw.

  “I think you could do better, Freddy.”

  As I said, I was sleepy. “It can’t be so bad. I started with Harvey Davenport’s party in Malibu and simply went to the nearest party after that. I just continued going to the nearest party until we were out of invitations.”

  He shook his head. “A lot of people will be on the road.” I guess Pete and I had different views of Christmas traffic; but I had to admit he had more experience with what it might be like in L.A.

  “I’d like to spend as little time as possible being stuck in traffic jams,” he continued. “The ‘nearest neighbor’ algorithm can be very inefficient in dealing with traveling salesman problems.”

  I was still sleepy. “Say what?”

  Pete put aside his football paperwork and took out a pen and a piece of paper. He then spent a moment writing down a table, which I have reproduced here:

  “Here’s the idea. This table represents the distances between the four different locales. Anyway, suppose that we start from A. The nearest city to A is D, so we would travel 20 miles. From D, the nearest city not yet visited is B, which would be 35 miles. We would then be forced to go to C, a distance of 60 miles. That would be a total of 20 + 35 + 60 = 115 miles.”

  Now, nothing makes me sleepier than a deluge of numbers. However, I was pretty sleepy to begin with, so I thought if I paid attention, I’d get to go to sleep faster.

  “I’m with you so far, Pete. And I think I see the trouble. We would like to avoid the 60 mile segment, wouldn’t we? That’s what creates the problems.”

  “That’s it. It would be better to go from A to B, then from B to D, and finally from D to C. That would be 25 + 35 + 40 = 100 miles. In the absence of any other information, this would be a clearly superior route to take.”

  I yawned. “Well, I suppose you know a shortcut for figuring out the best route.”

  “Nope.”

  “What?” Hearing Pete confess that he didn’t know how to solve a problem would have been almost as surprising as hearing him admit that he couldn’t decide whom he liked in the upcoming football games.

  “I don’t know a shortcut. But no one does, not even the best mathematicians in the world. Other than simply listing all possible routes and calculating the total distance for each one, there is no known shortcut for selecting the optimal route. This is known as the Traveling Salesman Problem.” He spoke the words as if they were in capital letters.

  (Traveling Salesman Problem continued on p. 227)

  “I’m shocked. But I’m also sleepy. If you don’t like my planned itinerary, you might start by making up one of your own.” I yawned again and turned to go. “Me, I’m going to hang my stocking by the chimney with care. Good night.”

  After opening our presents the next morning and having a late brunch, we embarked upon our all-day partython. As we prepared to depart, Pete handed me a computer printout.

  “What’s this?” I asked. “Another Christmas present?”

  “I took your advice last night and wrote a computer program to list all possible routes and compute the mileage. This is the shortest route.”

  Since I had been elected to drive, I took a look. The game plan was to start at the bottom in Orange County, go north to Long Beach, go to a couple of parties in Beverly Hills, and close the day’s festivities at Harvey Davenport’s Malibu estate. Harvey was majority owner of the Raiders, who had recently moved—again—from Oakland to Los Angeles, where they were playing—again—at the Coliseum and where they still had—again—a devoted Los Angeles segment of Raider Nation. Since we had helped u
ntangle a small personnel problem in one of his companies, we were on the guest list.

  I was surprised that Davenport even remembered who we were. When we got there, it was a little surprising that Davenport even remembered who anybody was, since it was clear that no one had been monitoring his eggnog intake. He welcomed us enthusiastically. “If it isn’t the sleuths! Merry Christmas!”

  We wished him a Merry Christmas right back. At first I thought it was our greeting that triggered his reaction of peace on Earth, good will to detectives, but later events made it clear that more weight could be attached to the Raiders cap that Pete had the foresight to wear. He put an arm around Pete’s shoulder and said, “What are you doing on Saturday, buddy?”

  It didn’t seem like a trick question, so Pete gave him a straightforward answer. “I’m going to camp in front of the tube and watch the wildcard games.”

  This remark did nothing to decrease Davenport’s desire to spread peace on Earth and promote good will toward detectives. “Then this may be your lucky day, buddy.” Davenport was probably one of those guys who call everybody “buddy” whose name they can’t remember. “Phil Donaldson and his wife have to go to Hawaii on Saturday. So how would you and your buddy like to sit in my Sky Box at the Coliseum and watch the game?”

  “We’d love to!” Pete was obviously elated.

  “Terrific!” Davenport was delighted to see his largesse so warmly received. “Go to the will-call counter at noon, and tell them that Mr. Davenport has left tickets for you. Then say ‘gingerbread.’” There were other guests at the party, and Davenport headed off to jaw with them. We put in another couple of hours at the party and returned home. Needless to say, Davenport’s unexpected bonus had made a big hit with Pete, so much so that the next day he boosted his action to three hundred on the Raiders minus four.

  Saturday morning dawned clear and bright, and we headed over to the Coliseum in plenty of time to get there for a noon will-call, to say nothing of a one p.m. kickoff. The burning question of the day was whether Bobby Joe Whitney, the Raiders’ aging star quarterback, his backup Dan Driscoll, or the rookie flash Mike Stankowitz would start at quarterback.

  The Raiders had stumbled at the start of the season. The word was that Bobby Joe was injured but wouldn’t admit it, and Driscoll didn’t seem to fit into the Raiders scheme. Midway through the season, the silver-and-black had posted a lackluster four and four record, and the betting was that they’d be out of the playoffs for the first time in five years. With the L.A. media on his back, the coach had made a brave decision: He decided to start Stankowitz for the ninth game of the season, a home game against a perennial doormat. Stankowitz had been signed out of Washington State for a multimillion-dollar contract. Along with Stankowitz had come Hugh Dryden, Stankowitz’s former high school coach, who early in Stankowitz’s career had sensed that the big guy was a potential meal ticket. Stankowitz had turned down offers from numerous football powerhouses because Washington State had allowed Dryden to join the staff as an assistant coach, and Stankowitz had made the same deal for Dryden with the Raiders.

  The Raiders had never looked back. In his first game, Stankowitz had thrown for three hundred fifty yards, four touchdowns, and no interceptions. The Raiders had gone six and two in the last half of the season to finish with a record good enough to host the playoff game between two wildcard teams: the Raiders and the Pittsburgh Steelers.

  The magic word “gingerbread” got us to Davenport’s Sky Box, where our host greeted us with his traditional, “Hi ya, buddy!” He led us to a couple of extremely comfortable chairs and handed each of us a pair of binoculars (the field is some distance away from the Sky Boxes, as you can well imagine).

  Evidently, Davenport favored the hands-on style of management, for the Sky Box next door housed a PC and several seats by the big plate glass window for the coaching section that constituted the Eye in the Sky. It was currently inhabited by Tom Woodhouse, special teams coach, and the aforementioned Hugh Dryden. The two of them reminded me of Mission Control at NASA, as they were equipped with headsets, playbooks, and an armful of multicolored charts. It was clear from the hustle and bustle that the two coaches were in “do not disturb” mode.

  Pete watched the pregame preparations through his binoculars. Before I knew it, it was 12:45, fifteen minutes to kickoff. The Raiders trotted back on the field. Pete was still glued to the binoculars. Then I noticed that there was a general air of unease circulating through the Sky Box.

  “That’s funny,” Davenport remarked. “Where’s Stankowitz?”

  The other members of the residential portion of the Sky Box took up their binoculars. Nobody seemed to know. Woodhouse and Dryden were certainly able to overhear Davenport’s remark, but evidently they were preoccupied with planning strategy, for they seemed to take no notice of the proceedings.

  “Tom!” Davenport snapped at Woodhouse. Woodhouse came to attention, as no doubt would I when addressed in an imperious fashion by the source of my daily bread.

  “Yes, Mr. Davenport?”

  “Call the coach and ask him where Stankowitz is!”

  Woodhouse complied. A short discussion followed. “Nobody seems to have seen him since the team left the locker room.”

  “Well, tell somebody to get back to the locker room and find him real quick. And if he isn’t found and we win the coin toss, elect to kick off.”

  “Right away, Mr. Davenport.”

  By now the crowd was abuzz. The big clock by the peristyle end of the Coliseum showed a couple of minutes before one. The cocaptains walked out to the center of the field to enact the coin-toss ritual.

  A cry came from Woodhouse. “They’ve found him. He’s in the locker room, lying on the floor, passed out. Unconscious or something. There’s half a banana lying by his side.”

  Pete had put down his binoculars and was paying close attention. Since I was clearly at sea, he said, “Stankowitz always eats three bananas before the start of a game. Bananas are a great source of potassium and carbohydrates.”

  Well, at least Pete was on the case, even though at that time I don’t think either of us knew it was a case. The Steelers punted after going three and out in their first series of downs. The Raiders had the ball at their own thirty-five, and Bobby Joe Whitney walked onto the field to direct the Raiders’ efforts.

  “Wonderful!” Pete muttered disgustedly.

  “What’s the problem?” I asked.

  “Whitney’s not in shape. He hasn’t played for almost two months, except in garbage time, and he’s got bruised ribs. I don’t like my chances.”

  By now, I had hung around Pete and other bettors long enough to learn that betting on a team entitled the bettor to temporary possession of that team, even if that possession existed only in the mind of the bettor. The Raiders, who were four-point favorites, played a gallant first half and left the field tied at ten apiece. By now, reports were being relayed almost continuously on Stankowitz’s condition.

  Those reports were extremely disquieting. The banana had been sent out to a lab for analysis and was shown to have been drugged. Since there was evidently a lot of fruit in the locker room for players to eat, I wondered how the individual who drugged the bananas could have been sure that Stankowitz, and not a third-string offensive tackle, would have eaten them. That was cleared up by a statement from the trainer, who said that Stankowitz favored bananas that were only partially ripe. He usually came in early and chose three, which were then set aside. So anyone could have drugged them.

  Even though Stankowitz couldn’t come back to lead the team, it was a tremendously exciting game. The two teams were never more than a touchdown apart. The Raiders, trailing by a point with a minute and a half to play, took over at their own eight-yard line and mounted a last-ditch desperation drive. Whitney fought the clock, the Steelers’ defense, and his own injuries to a standstill, showing flashes of the brilliance that had made him the Raiders’ number one for the better part of a decade. Finally, with three secon
ds to go, the ball was positioned for a forty-five yard field goal try. With the season hanging in the balance, the ball hit the crossbar and bounced through. Raiders 19, Steelers 17.

  Needless to say, there was jubilation in the Sky Box. After all the tumult and the shouting had died down, I saw Pete pull Davenport aside and whisper a few words in his ear. At first, Davenport looked perplexed, but then he appeared to understand.

  We retrieved our car and headed home. Pete was not a happy camper. I tried to cheer him up.

  “Come on, Pete, you’ve lost bets before. Three hundred bucks isn’t the end of the world.”

  “Five fifty,” he muttered through clenched teeth.

  “Huh?”

  “Three hundred on the Raiders. Two hundred on over thirty-seven and a half. And fifty vig. Not only that, I analyzed it right. I know Stankowitz would have made the difference. Bobby Joe was so banged up, he could only throw short passes.”

  (See An Introduction to Sports Betting for an explanation of vig on p. 233.)

  As we got back to the house, a thought occurred to me. “By the way, Pete, I saw you pull Davenport aside at the end of the game for a little chit-chat. What were you talking about?”

  “I just had an idea. Maybe it wasn’t very important.” Pete seemed strangely disinclined to discuss it, so I switched to another topic of conversation.

  I had some time to myself the next day, so I engaged in a little game of “Who Doped the Banana?” which had already risen to the top of the charts as L.A.’s favorite quiz show. The leading candidate, according to the papers, was the trainer, who was obviously in closest touch with the eating habits of the players. Bobby Joe Whitney also fell under suspicion, as he was playing out his option year, and his value would decrease substantially in next year’s market unless he could show that he still had the right stuff. There was a tie for third among everyone else but Stankowitz, as astronomical sums of money could be made betting on a game in which the star quarterback would be unable to play. Pete still wouldn’t discuss it.