Theoretical best, optimal lap, and time available

Three numbers, one idea

After a session you have one number you would quote: your best lap. It is a fact, but it hides most of what happened. On almost every evening, some of your slower laps were quicker than your best lap somewhere — one sector, one corner, one exit — and the best lap itself left time in places another lap did not.

The theoretical best and the optimal lap collect those pieces. Here are all three for the eight-lap example session this guide works through:

The example is a synthetic session built from StintLab's demo laps of a circuit the length of Monza, and every figure on this page was computed by StintLab's own report code — the numbers are real outputs of the method, not a driver's record.

The theoretical best, worked through

Here is the session as StintLab lists it, every lap in the order it was driven. A ◆ marks the session's best of each sector, and the best lap:

The arithmetic:

Two details are worth noticing. None of the three laps that set a sector best is the best lap: the quickest overall lap was simply the one with no bad sector. And lap 4, the quickest lap of the evening at 1:20.623, contributes nothing — it was invalidated, and a lap binned for track limits sets no sector best however quick it was.

StintLab's debrief says it in one sentence:

Your best sectors add up to 1:20.667 — 0.283 under your best lap. You have already driven every part of that lap; you have not yet driven them in the same one.

StintLab session report · debrief

The optimal lap: the same idea, every 100 metres

The theoretical best is honest and useful, and it is also coarse. Three sectors over nearly six kilometres tell you which third of the lap to work on — which you probably knew. The traces can say much more, because they record every few metres of every lap.

So StintLab cuts the lap into 100 m pieces — about a corner's entry or its exit — and for each piece takes the quickest time any counted lap of the session took through it. Add those up and you have the optimal lap: still nothing invented, still every piece of it driven, but now the answer to “where?” is a hundred metres wide.

The same pieces show where your best lap gave time away. StintLab lists the stretches where the best lap was 50 ms or more slower than the quickest anyone drove that stretch, worst first — up to five. In the example, two stretches clear that bar:

That table is a to-do list with evidence attached. The 600–700 m stretch — the slowest part of the first corner — was driven 0.092 s quicker on lap 5 than on the best lap. You do not need a coach's lap to learn that corner: tick laps 8 and 5, compare them, and look at what lap 5 did through those hundred metres.

Time available — and why there are two

“Time available” is your best lap minus the lap you have already driven in pieces. There are two versions because there are two ways of cutting the lap:

• Against the theoretical best: 1:20.950 − 1:20.667 = 0.283 s. This is the figure in the debrief sentence above.
• Against the optimal lap: 1:20.950 − 1:20.637 = 0.313 s. When an optimal lap exists, this is the one the session view's “Time available” tile shows, with the table of where.

The finer cut usually finds a little more, because a lap can have a good sector with one bad corner inside it: three sectors average the corner away, 100 m pieces do not. Part of the difference can also be the few metres at the start and finish of a lap that no sample covers: the optimal lap is added up over the traced distance, while your best lap is the game's full lap time. Neither figure is a promise — both are measurements of time that has already happened.

What these numbers are not

The optimal lap is not a lap anyone can drive end to end. You cannot take one corner's entry from a lap that was seconds off and keep the next corner's exit from the lap that was on it — the pieces came from different laps with different speeds going in, different fuel and different tyres. What the number is is a floor you have evidence for: every piece of it happened, in this car, on this track, today.

It is also not a comparison with anyone else. For that you need a faster lap to chase — your best from another session, or a friend's — and the practice plan. The theoretical best is you against you.

The rules that keep them honest

Any tool can print a flattering number. StintLab prints a dash when the number is not real, and these are the rules that decide:

• Only counted laps. Valid, timed, driven from the line and not through the pits. An out-lap starts at the pit exit and covers less ground; an invalid lap sets nothing; a pit lap never sets the pace.
• Sectors must add up. The theoretical best is shown only when the sectors of every counted lap that has them add up to its lap time within 100 ms. Otherwise sectors that do not cover the lap would produce a “theoretical best” two thirds of a lap long — a number that looks like a lap record.
• No holes. If any 100 m of the circuit was never covered by a usable trace, there is no optimal lap, because a total with a gap in it is short by however much is missing.
• Nothing from nothing. A session with one counted lap has a best lap and no spread; the report says so rather than printing a zero.

The same sum you see on the broadcast

If you watch F1 you have seen this idea on screen: a driver's best sectors added up into a theoretical or “ideal” lap, usually in qualifying, usually to show that someone had pole in them and did not string it together. It is the same arithmetic — best of each sector, summed — and it makes the same point: the lap was there, in pieces.

The colours that go with it — purple for the best sector of the session, green for a personal best — are explained in F1 sector times explained.

Questions