The three-dimensional offside graphic shown after a review is not evidence. It is a rendering produced from the system's numerical output for the benefit of viewers.
The system solves two problems
Offside requires knowing the moment the ball was played and the positions of the relevant players at that instant. Both were previously judged by eye at speed.
Automation addresses each separately. Sensors and tracking identify the moment of contact, and limb tracking establishes player positions at that timestamp.
The output is a set of coordinates and a time, which the system compares to determine whether a player was beyond the second-last defender.
Why the moment is the harder half
Player positions are tracked continuously and are relatively easy to interrogate at any instant. Identifying the exact frame of contact with the ball is less straightforward.
At normal frame rates, contact can fall between frames, and the difference of a single frame can change the outcome on a marginal call.
Ball sensors that detect the moment of a kick directly were introduced to address this, replacing a visual judgment with a measurement.
What the graphic actually shows
The rendered image places virtual lines through tracked limb positions at the determined timestamp. Every element is drawn from data rather than photographed.
This is why the graphic never disagrees with the decision. It is generated by the same system that made it, and it cannot show anything else.
Broadcasters present it as visual proof because it reads that way to an audience. It is closer to a diagram of a calculation.
Precision is not the same as certainty
Tracking systems have measurement tolerances, and a decision resting on a margin narrower than that tolerance is not really determined by the data.
Competitions have addressed this partly with tolerance rules and partly by not disclosing margins, since publishing a figure inside the error band invites argument.
The debate about whether offside should have a tolerance is therefore a debate about how to represent measurement uncertainty in a binary rule.
The speed gain is the actual change
The system's main effect is time. A decision that took a video official a minute to construct manually is produced in seconds.
Accuracy improved less than speed did, because the manual process was already accurate when given enough time. The bottleneck was the drawing of lines by hand.
What changed for the record is that offside determinations are now logged as data rather than as a human conclusion, which makes them reviewable in a way they were not.

