Apr 24, 2014; Oakland, CA, USA; Los Angeles Clippers forward Blake Griffin (32) misses both his free throws after a technical by the Golden State Warriors during the third quarter of game three of the first round of the 2014 NBA Playoffs at Oracle Arena. The Los Angeles Clippers defeated the Golden State Warriors 98-96. Mandatory Credit: Kelley L Cox-USA TODAY Sports
Yesterday, ESPN writer Kevin Arnovitz wrote that league officials have been considering adjusting how foul shots are approached to try and reduce the amount of boring stoppage time that occurs while shooting free throws. Apparently, the league has been seriously mulling solutions since the All-Star break last season, and some members of league offices think they’ve found a decent solution.
Instead of shooting two free throws every time the player is sent to the free throw line, where each foul shot is one point, the game could be adjusted so that when a player is fouled, they only shoot one free throw attempt, that is instead worth two points. The removal of one extra free throw from all standard trips to the free throw line could cut out as much as five minutes of stoppage time from the game, per Arnovitz.
This is a seriously interesting proposal that Arnovitz is revealing, here, for a number of reasons: it wouldn’t meaningfully affect how long the games are on (and the league has been adamant on shortening of the time it takes to finish a game) so this seems like an odd measure, in the sense that five minutes doesn’t make a big difference one way or another, where a reduction in game length or in amount of commercials could be a pretty obvious way to more significantly reduce game time.
What’s a bit more important, though, is that cutting down five minutes of free throw shooting just makes basketball more fun to watch. Everyone implicitly accepts that watching free throws is the most boring part of the game. Cutting them down makes it easier to watch.
Still, what impact does fewer free throws have on how teams approach an offense?
Conceptually, by removing a second free throw, you’re removing a team’s chance to get 1 point from a play where the team might otherwise get nothing. So, this should ultimately hurt teams, right?
That’s actually not the case. See, teams realized that three-pointers, shots at the rim, and free throws were more valuable than other shots on the court because their expected value (or, how many points you can “expect” when you shoot) was so much higher than the other shots on the court.
Free throws have been the most efficient shot in the game for the entirety of the modern basketball era, even more so than corner three’s, by the measure of expected value. You can expect more points than on any other play, on average, when you can draw more free throws (though this obviously isn’t true of, say, Dwight Howard).
This won’t change with a shift to shooting only one free throw worth 2 points. You can find expected value by multiplying the odds of any one occurrence by the value you get when that thing happens. In the case of free throws right now, that formula looks like:
2*(FT%*(1-FT%))*(1) + (FT%*FT%)(2)
Or, the odds that you make one free throw and miss another, times one — because making one free throw is worth one point — times two, because there are two ways you can make only one free throw. You then add that to the odds of making two free throws in a row, times the two points you get.
This can be transformed by some algebra, to equal:
2*(FT%),
which is the same as the expected value of shooting a single free throw that’s worth two points. Meaning, you can expect the same exact value, long term, from shooting only once at the free throw line as shooting twice.
But, there has to be an impact of changing free throws to only shooting once, right? That lack of the chance to get only two point has to make a difference, right?
Well, yeah, it does change things a little bit. Without doing the math, because I’m sure you’re not particularly interested, the variance on how much value a free throw will return goes up noticeably if you’re only shooting one free throw instead of two. So, even though in the long run the two things will net the same value, in the short run, free throws could net much higher or much lower values from shot-to-shot than they do right now. Which makes sense: the gap in possible point values would be much larger.
Does that change how a team would approach free throws regarding team building, though? Would that change a team’s offensive strategy?
On the face of it, it wouldn’t be a good idea for a team to do so. Free throws still have the same value, and that value is still really high. Here’s the thing though: a higher variance could mean that the range of points from free throws that a team actually is likely to get from game to game becomes larger. That could mean two more or less points for a team from game to game.
Those two more or less points could ultimately account for one or two extra wins or losses across the span of an entire season. A team would be remiss to not take this into account, to an extent.
Variance can be minimized with a greater sample size: so teams that draw more free throws would be more likely to get a more predictable number of points from free throws from game-to-game than a team that draws less.
The ultimate implication, here, is that teams who draw more foul shots would be a bit more consistent and a bit more predictable than the teams who draw fewer. In the end, a team who loses a game because of poorer foul shooting than they might have had otherwise will also probably win a game because of better shooting. The big implication isn’t a change to wins or losses so much as it is a change to the predictability of teams.
All of this is a very long way of saying: changing the league rules so that a foul results in a single foul shot that’s worth two points, rather than two shots worth one, would have very little impact on the league at large, and to how teams approach their team-building or their offense.
It might, in the end, impact our experience of the games, both because time spent on free throws would be (thankfully) reduced, and because game results would be a smidgeon more variable, and, probably, just a smidgeon more fun.