Chapter 38: Probability
Connie had claimed the far end of the couch at some point during the third quarter and had not moved since.
Her Lone Star sat untouched on the side table beside her, which was how Mike knew she was genuinely invested in the outcome. Connie didn't forget her beer for anything less than real stakes.
"Come on," she said, to the television, with the focused intensity of someone having a private conversation with it. "Come on, come on, come on—"
The Longhorns punted.
"No!" She sat back with the specific despair of someone who had been hoping against evidence and had run out of evidence to hope against.
Mary, in the armchair beside her with a half-finished scarf in her lap, looked at her mother over her knitting needles. "Connie."
"I'm just watching the game," Connie said.
"You've been talking to the television for forty minutes."
"I'm an engaged viewer."
"Do you have money on this game?"
Connie picked up her Lone Star. "That's a very personal question, Mary."
Mary's expression had the specific quality it got when she already knew the answer and was giving someone the opportunity to arrive at honesty voluntarily.
Connie drank her beer.
The thing was — and Connie would not have explained this to Mary — the Longhorns had appealed to her on name alone. There was something about the word Longhorns that had felt like a winner when she'd called her guy on Friday, and she had placed a modest amount of money on that feeling, and the feeling was currently proving itself incorrect.
She was not, she would readily admit, a statistics-based gambler. She was an instinct-based gambler. Her instincts had been running about fifty-fifty lately, which was exactly average, which was not what instincts were supposed to be.
From the other end of the couch, a voice said: "Statistically speaking, punting on fourth down from inside your own ten is actually the suboptimal choice."
Everyone looked.
Sheldon had migrated to the couch at some point during the second half — drawn, apparently, by the social gravity of a room full of people paying attention to something, even if the something was a sport he found athletically uninteresting. He had his physics textbook open on his lap, which suggested he'd been planning to read and had gotten pulled in despite himself.
He looked up from the page with the mild expression of someone offering a useful correction.
George Sr. turned around from his spot near the TV. "What did you just say?"
"I said the punt was the suboptimal decision," Sheldon said. "Statistically."
"You've never played a down of football in your life."
"Correct. I've also never performed cardiac surgery, but I could describe the procedure accurately." Sheldon turned a page. "The two things aren't related."
George Sr. opened his mouth.
Sheldon continued, with the patient tone of someone who had already done the math: "When an offense is pinned inside their own ten-yard line and turns the ball over on downs, the opposing team scores approximately 92% of the time. When that same offense punts from inside their ten, the opposing team still scores approximately 77% of the time." He looked up. "The differential is 15 percentage points. However — if the offense attempts the conversion and draws a penalty, they get a fresh set of downs, which resets the field position entirely. The expected value calculation doesn't favor the punt."
The room was quiet.
Georgie was staring at Sheldon with the expression of someone who had lived with this person for nine years and still occasionally got surprised.
Mike was watching the exchange with the quiet attention he gave things that were about to become interesting.
George Sr. looked at his youngest son. Looked at the television. Looked back at Sheldon.
Connie leaned toward Mary and lowered her voice to what she believed was a whisper. "Mary. Honestly. Where did he come from?"
"Mother," Mary said.
"I'm asking from a purely genetic standpoint—"
"Mother."
Connie straightened up and folded her hands with great dignity.
George Sr. had regrouped. "Sheldon. I have been coaching football for fifteen years. I have been watching football for thirty. Experience tells me the punt was the right call."
Sheldon considered this the way he considered all empirically unsupported positions — with genuine patience and complete immovability. "Experience introduces confirmation bias," he said. "The data disagrees with your experience. I'd suggest the data is more reliable." He paused. "No offense."
"Some offense taken," George Sr. said.
On the television, the Cardinals returned the Longhorns' punt to the forty-two yard line. Two plays later they were in the end zone.
The room absorbed this.
Connie looked at the ceiling.
"Sheldon," she said, with sudden brightness, "come sit next to me."
George Sr. had gone quiet in the specific way he went quiet when he was thinking rather than processing — the working-it-through silence, not the giving-up-on-it silence.
Mike recognized the difference.
He also recognized that Sheldon's analysis, while correct as far as it went, had a gap in it.
He waited until the commercial break.
"Sheldon's numbers are right," Mike said, to the room generally and to George specifically. "But the calculation assumed the teams were evenly matched. They're not."
George looked at him.
"The Longhorns have been getting pushed around since the first quarter," Mike said. "Their offensive line isn't winning the physical matchup. If they'd gone for it on fourth down, they'd have been converting against a defense that's been beating them all afternoon." He looked at the screen. "The probability of making that conversion — given how this specific game had been going — was lower than the general statistical average. Which shifts the expected value calculation."
He looked at Sheldon.
Sheldon had his head tilted at the angle he used when he was genuinely processing something rather than waiting for his turn to talk.
"You're accounting for performance variance within a specific game context," Sheldon said.
"Right."
"That would require adjusting the base rates for situational factors." Sheldon was quiet for a moment. "I didn't do that."
"The base rates were still useful," Mike said. "They told you the general shape of the decision. The game context tells you which version of that decision you're actually in."
Sheldon looked at his textbook. Then at the television. Then at Mike.
"I'll incorporate situational weighting in future analyses," he said, with the specific tone of someone updating a model rather than conceding a point. He stood up, collected his textbook, and tucked it under his arm with the crisp efficiency of someone who had gotten what they came for. "Thank you for the addition."
He headed down the hall toward his room.
Connie watched him go, felt the betting slip in her jacket pocket, and got up to follow him.
George waited until Sheldon's door closed.
Then he said, to Mike: "I want you to know that I think he's wrong about the punt."
"I know," Mike said.
"The math doesn't account for what you can't measure. Heart. Effort. A team that decides to fight." He looked at the screen, where the Cardinals were now running out the clock. "That's the whole point of sports. The numbers say 99% and the other team still shows up and plays the one percent."
"I agree," Mike said. "That's why I left point one percent."
George looked at him.
"When I said the Longhorns had a 99.9% chance of losing," Mike said. "I left the point one."
George held his gaze for a moment. Then he sat back with the expression of a man who had been given something he wanted and wasn't going to over-explain his appreciation for it.
"Sam's coming back next week," he said.
The subject change was abrupt enough that it was clearly something he'd been working up to.
Mike nodded. He'd been expecting this conversation.
"He's served the suspension. He's a senior. He's been on the starting roster for two years." George said it plainly, without the apologetic framing he could have used. That was something Mike respected about him — he delivered difficult things straight. "I can't pull him from the starting lineup without a performance reason. Not before a game. It wouldn't be fair to him and it wouldn't be fair to the team."
"I understand," Mike said.
"That means you're coming in as second back." George looked at him. "For the first game, probably. After that—" He spread his hands slightly. "After that, it's what you show me on the field."
"That's fair," Mike said.
George studied him. "You're not going to argue it."
"No."
"Most kids would argue it."
"Most kids haven't been here three weeks," Mike said. "I'll earn it."
George was quiet for a moment.
Outside, through the living room window, the Texas evening was settling in — the particular deep blue of a summer sky at eight o'clock, the neighborhood going quiet in the way it did on Sunday nights.
"Medford's been first-round exit for three years running," George said, mostly to himself. "This year I want to change that." He looked at Mike. "You're part of how."
"I know," Mike said.
"Good." George reached for the remote. "Game's over. You want to watch the highlights or head home?"
"Highlights," Mike said.
George turned up the volume.
From down the hall, muffled by the closed door, came the sound of Sheldon's voice — apparently explaining something to Connie, who appeared to have followed him for football-related statistical consultation, which was its own development entirely.
Georgie looked at the hallway. Looked at Mike. Shook his head slowly.
"Every Sunday," he said.
"Every Sunday," Mike agreed.
(End of Chapter 38)
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