Why Fouling Up 1 Point Actually Makes Sense

by Bobby Sylvester | @bobbyfantasypro | Featured Writer
Mar 17, 2017

Matthew Fisher-Davis did everything he could to help his team win

Last night, my wife and I were watching the Northwestern vs Vanderbilt game. Although the game was virtually meaningless in the grand scheme of my bracket, I had a rooting interest because my perfect bracket was still on the line. With 30 seconds remaining, my door bell rang. It was a solicitor. I hate solicitors. The game was too exciting so I just invited him in rather than hear his sales pitch or rudely tell him to get off my porch. Michael, the solicitor, disclosed that he had Vanderbilt in his bracket as well even though they already had 15 losses on the season. Then it happened: Vanderbilt took the lead and …intentionally fouled right away…!!!??? Michael was furious. Even my wife thought it was stupid and she isn’t much of a basketball fan. I, on the other hand, considered it a brilliant tactical move.

Poor Matthew Fisher-Davis is going to take a lot of heat for that intentional foul even though he was the primary reason Vanderbilt made the tournament and was in position to win in the first place. Sure, he apparently didn’t know the score, even for just a split second, but give the kid some credit. He attends Vanderbilt for Pete’s sake! To even be offered an athletic scholarship to a school like that, your IQ has to be at the very least a standard deviation and a half above the common human. Fisher-Davis is clearly an intelligent young man who happened to make a brief mental error as a 20-year-old. But remember, it wasn’t a mistake. The math was actually on his side.

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Without The Foul

Vanderbilt up 1 point with 15 seconds to go.
Northwestern gets the final shot.

You could look at their 48.6 Floor% and suggest Northwestern had a 48.6% chance to win since they will be guaranteed the final shot, but not all possessions are made equal. Northwestern shoots only 34.1% from beyond the arc and wouldn’t need that shot. We also have to discredit the possessions that end in free throw attempts since we know Vandy has a better chance to retake the lead with 15 seconds remaining rather than any time after that when a supposed foul took place.

That leaves us with two-point field goal attempts, turnovers and offensive rebounds. Take into account that turnovers are much more uncommon in a set offense with one final shot, but we will leave turnovers the same just to give naysayers the benefit of the doubt. Also, according to Seth Partnow’s Nylon Calculus, shots with the arc result in an offensive rebound for a standard team 33% of the time, while three-pointers are just 24% of the time.

  • Northwestern only turns the ball over on 15.5% of their possessions
  • Northwestern shot 619 for 1266 from inside the arc this season (48.9%)
  • They pulled in the offensive board in 366 of 1113 misses (32.9%)
  • Their odds of getting a second chance increase 14.3% with a shot inside the arc
  • A second chance would afford them another 48.9% chance to take the lead

Show your work: (1-0.155)*(0.489+((1-0.489)*(0.329*1.143)*0.489))

Northwestern had a 49.3% chance to win before the foul

With the Foul

86% free throw shooter goes to the line for 2 free throws down 1 point
Vanderbilt gets the ball for the final shot*

  • An 86% free throw shooter will make both shots 74% of the time
  • He will make 1 of 2 just 24% of the time and miss both 2% of the time

*There is a chance (2.5%) Northwestern could get the rebound on a missed second free throw (missed FT (0.14) * Off Reb on missed FTs (0.18)), but in close games with less than 20 seconds on the game clock, free throw shooting teams rarely go for an offensive board because they don’t want to foul.

If he makes both free throws (74% chance), Vanderbilt is in the same situation that I outlined Northwestern as having before the foul. The differences being that Vanderbilt turns the ball over more, shoots a lesser percentage from two-point range and gets less offensive rebounds. Of course, you have to factor in that Vanderbilt has the toughest schedule of strength in the country and that the two teams were virtually a pick ’em because, well, they have the same odds of scoring on any given possession. For this type of possession, we already established the odds (57.1%).

If he makes one and misses the other (24% chance), Vanderbilt has a 57.1% chance to score on the final shot and win or go to overtime, where they would be projected to win 50% of the remaining 42.9% of outcomes (21.45%).

If he misses both free throws (2% chance) there are any number of things that could happen. Most likely an immediate foul and Vanderbilt gets two free throws with 15 seconds left and up 1 point. You could write a novel about the odds of winning at that stage of the game so I’ll just cut to the chase. Vanderbilt would have a ~76% chance to win.

Show your work: (0.74*0.492)+(0.24*(0.571+0.2145))+(0.02*0.76)

Vanderbilt had a 56.8% chance to win after the foul

In case you didn’t know, 56.8% is greater than 50.7%. In fact, Fisher-Davis increased his team’s odds to win by 12% when he committed that foul (56.8/50.7 = 1.120, or a 12% increase)! I wrote Matthew Fisher-Davis to explain this math after this game and I hope he reads it because this game will be in his memory the rest of his life. I’d know; in the state baseball playoffs, I lost a ball in the sun and it dropped in front of me to score the tying run with Jake Odorizzi on the mound. Fisher-Davis’ game was on a much greater level, obviously, and it would be much easier for him if he realizes his “mistake” was actually a benefit to his teammates.

Thanks for reading and enjoy March Madness! If you are into fantasy baseball, please check out the podcast I host below:


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