An opponent's offensive number is one figure describing two completely different teams. The team that scores in the open floor and the team that has to score against a set defence are not the same side, do not have the same strengths, and do not lose to the same plan. Average them and you get a number that describes neither.
Split them and most scouting reports write themselves.
Why the split does more work than any other cut
Almost every other way of slicing an offence gives you a smaller version of the same information. Split by half and you learn about fatigue. Split by quarter and you learn about rotations. Split by half-court and transition and you learn which game they want to play, which is the only question that changes what you do at the defensive end.
The two are governed by different things. Transition offence is a function of how the possession before it ended, how many bodies they send, and whether you got back. Half-court offence is a function of spacing, personnel and execution against five set defenders. You defend them with different mechanisms, at different moments, using different players. A single blended rating hides which of the two is actually beating you.
The four shapes, and what each one asks of you
Good in transition, poor in the half court. The most common shape at our level and the easiest to plan for. Their offence is a consequence of your offence. Every long two you settle for and every unforced turnover is a possession you gave away twice. The plan is not a defensive plan at all: it is shot selection and taking care of the ball, plus a hard rule about who gets back. Wall the paint in the half court and live with it, because their half-court answer is a contested jumper.
Poor in transition, good in the half court. Rarer, and more dangerous over forty minutes because they do not need your mistakes. You can run at them. The game is decided by whether you can make their set offence uncomfortable, which usually means pressuring the entry rather than the finish.
Good at both. They are better than you and the report should say so. The plan becomes about volume rather than efficiency: shrink the game, take the extra pass out of it, and make the total number of possessions small.
Poor at both. Do not overplan. The most common error against a bad offence is inventing a scheme for a problem that does not exist and creating a new one.
What actually generates transition offence
It is worth saying plainly, because a lot of transition defence gets coached at the wrong end of the floor.
Live-ball turnovers and long rebounds are what produce running teams. Missed threes are longer rebounds than missed twos, and defensive-rebound leaks cost you twice. That means most of what you can do about their transition offence happens while you have the ball. If a team hurts you in the open floor, the intervention is your shot selection, your turnover profile, and your crash rule, and only then your matchups getting back.
Which is a slightly uncomfortable finding, because it means the report on their transition offence is partly a report on us.
What I put on the page
Two numbers, not one. Their efficiency in each state, and the share of their possessions that are in each state. Both matter and coaches routinely get handed only the first. A team that is devastating in transition on eight percent of possessions is a footnote. A team that is ordinary in transition on thirty percent of possessions is the game.
Stamp both with the sample. Splits eat sample size fast, and a transition number from six games is a rumour. If the split is thin, say so on the page rather than letting a coach build a plan on it.
Then, and only then, the verdict sentence: which of their two teams we are trying to make them be. That is the whole point of the split. Not to describe them more precisely, but to choose which version of them we would rather play.