How likely was that? A basketball replay that shows the odds behind each play

basketball.casa is a basketball league where every game is simulated. Nobody scripts the plays. Each one comes out of who the players are at that moment: how tall, fast and tired they are, what they can see, and what they decide. You can watch any game back exactly as it happened. This update is about seeing more of why a play turned out the way it did, and seeing it more clearly.

How likely was that?

Every time a shot goes up or a pass flies past a defender, the simulation works out a chance first and then lets the dice fall. A wide-open layup might go in most of the time; a heavily contested jumper far less often. Until now the replay showed you what happened, but never what the odds had been, so a lucky make looked the same as a sure one.

Now it does. When a shot goes in, the line at the top of the screen says how likely it was, as in "makes a 2 from 1 m (36% to go in)", and the shooter's card says it too, beside how close the nearest defender was. When a pass is stolen, the line shows two numbers: the real chance it would be cut off, and what the passer thought that chance was. Players in this league act on what they believe they see, which is not always what is there, and this is where you can catch them misjudging a pass. Strips, blocks and fumbles show their chance in the same way.

These are not numbers worked out afterwards for show. Each one is the exact chance the simulation drew against at that moment, read straight from the game's own record. Across a game, most made shots turn out to have been fair ones: in our measurements, only about one make in a hundred came at worse than a one-in-four chance. So when you do see a long shot drop, it really was one.

A camera that keeps the play in view

The replay follows the ball with a camera that moves on its own, the way a television director would. It used to have one blind spot: it was placed from where the play was, never from who was standing between it and the play. So now and then a player walking past filled half the screen.

The camera now checks the line to the ball. If someone is in the way, or close enough to fill the frame, it swings around the play by the smallest of a few turns that gives a clear view, looking a moment ahead so it is not caught by a player who is about to cross. When it does have to move away from someone, it moves a little faster; the rest of the time it keeps the steady pace that makes a replay easy to watch. In our test games the share of moments with a player blocking the view fell from about one in fourteen to about one in thirty-five.

Blocked shots had a framing problem of their own. The camera aims at a shot's path to the rim, and a blocked shot never gets there, so the shooter often ended up cut off at the edge of the screen just as the block happened. A blocked shot now keeps the camera on the place where the ball was stopped, so the shooter and the blocker are both in the picture: in our checks, at the moment of the block, in all ten blocks we looked at.

Teams that play at their own pace, within reason

In real basketball, a team has a shot clock but does not have to use all of it. A good team passes up an okay shot because it expects a better one if it waits. Until now, every team in this league judged "is this shot good enough?" against the same league-wide standard. Teams full of great shooters found that almost every look beat it, so they fired at the first chance and played at a pace no real team does.

Now each team waits for a shot about as good as the best one its own shooters usually get. A team of sharpshooters is patient, because it can afford to be; a team that struggles to score takes what it can get sooner. Nothing was tuned to make the pace come out right: it follows from who is on each team. In our test games, how much teams differed in their number of possessions (the spread, as a share of the average) fell from 18% to 8.5%, a little under half. Some difference between teams is real, since real teams differ in pace too.

Smaller things that make the court read true

• A blocked ball now flies where the blocker's hand sends it, instead of simply dropping.
• Two teammates moving to new spots no longer head for the same place, and a player never steps into a spot a teammate is already running to.

Open any game from the front page or the archive, pause on a shot, and look at the line at the top. Press O at a decision to see every option the player weighed. If you watch closely, you will start to see the difference between a good shot that missed and a bad one that went in.