Every number below is real: the official transponder timing from the 9/19 night race at Buttonwillow (warm-up, qualifying, pre-main, main), plus the 9/19 session entry in the kart's ledger. Nothing on this page is modeled. Two cleaning rules, applied everywhere: lap 1 of each session is dropped (it is the out lap or the start, not a flying lap), and any lap over 70 s is dropped as traffic or an incident. Both rules are stated so you can disagree with them.
The one idea
One lap is one sample. A best lap tells you what the kart CAN do; the average and the spread tell you what it DOES. A setup change that moves the average by less than the spread is invisible from one session, no matter how convinced anyone is. Before you believe a difference, ask two questions: how big is the spread, and how many laps went into each side. The whole lesson is those two questions with numbers on them.
Three facts worth knowing
- Spread is a measurement of the driver, not the kart. In the main, the three leaders' laps from lap 4 on had a standard deviation (the typical distance of a lap from the average; "SD" below) of 0.16 s over 32 laps. Yours from laps 4-9 was 0.13 s. On pace, you were as consistent as they were. The 0.30 s gap was pace, not scatter. Those are different problems with different fixes.
- The average of n laps is more trustworthy than one lap by a factor of the square root of n. Five laps with a spread of 0.13 s pin the average to about 0.06 s. That "standard error" rule assumes the laps are independent draws from the same conditions: no traffic, no tires going off, no driver fading. When one of those is happening, the rule breaks - and the way it breaks is the lesson.
- Pole was not faster than you. Pole ran 58.38 in a 3-lap session. Your 7-lap warm-up best was 58.33. The 3-lap format rewards whoever gets heat in the tires first; your qualifying laps went 59.56, 59.10, 58.79 and the flag came out. Small n favors the fast starter, and the statistic that decides the grid is "best of 3," which is nearly a coin flip between karts 0.4 s apart.
Worksheet
Units on every line. "Spread" below means standard deviation (SD): the typical distance of a lap from the average. Range is max minus min.
1. Best vs mean. Your warm-up laps after the out lap: 58.74, 58.33, 58.66, 58.70, 59.56, 59.16. Compute the best, the mean, and the range. Which number would you tell someone who asked "how fast is the kart"? Which would you use to predict your next lap?
2. Standard deviation by hand. Same six laps. Subtract the mean from each lap, square each difference, add them, divide by (n - 1), take the square root. That is the SD. Then drop the last two laps (59.56, 59.16
- the session entry flags them as traffic or tires) and redo it. How much does the SD change? Which SD describes the kart?
3. Standard error. SD / sqrt(n) is how well the mean is pinned down. Using your warm-up SD from Q2 (all six laps), how tight is the mean? Using the four clean laps? Now: two setups whose true laps differ by 0.2 s, with n laps on each. Roughly, you can tell them apart when the difference is at least twice the standard error of the difference between the two means, which is SD x sqrt(2 / n) (typical rule). With the clean-lap SD, how many laps per setup do you need?
4. Hand timing. Bakersfield (8/15) was hand-timed, which the ledger rates at +/- 0.3 s per lap. Treat that as an SD of 0.3 s added to every lap. Using the same rule as Q3, how many laps per setup does it take to tell a 0.2 s change apart? A 0.5 s change? What does that say about using a hand stopwatch to judge a pressure change?
5. The gauge, generalized. The JOES gauge is rated 2.5% of full scale on 0-30 psi, which is 0.75 psi (lesson 1 Q7). Its repeatability (same tire, same person, chuck on/off) is unmeasured - say 0.4 psi (typical). The qualifying change was 0.5 psi on the right rear, read once. Using the Q3 rule with 0.4 psi as the SD, how many readings per pressure would you need to know the 0.5 psi was even set? Redo it for a repeatability of 0.2 psi, and for 0.75 psi. Which number should we go measure first?
6. Qualifying is a coin flip. Pole 58.38, you 58.79 (P4), P2 58.67, P3 58.75. Everyone's laps got faster each lap and the session ended at lap 3. The three karts P2-P4 are covered by 0.12 s - less than one SD of a typical session (Q2). What is the honest description of the grid: "you were fourth fastest," or something else? What would make qualifying a better measurement (two answers: one about n, one about the tires)?
7. Pace, not scatter. Main event, laps 4-9. The top three finishers (pooled): mean 58.41, SD 0.15, 17 laps. You: 58.69, 58.66, 58.58, 58.91, 58.75 (lap 7 is missing from the timing feed) - compute your mean and SD. Is the gap between the means bigger than the spread? Is your SD bigger than theirs? Write one sentence on what that says about where the 0.3 s comes from.
8. The fade is not noise. Your laps 10-14: 59.06, 59.41, 59.78, 60.40, 62.86. Take your laps 4-9 mean and SD from Q7. For each late lap, how many SDs above your own mean is it? (A lap 2 SDs out happens about one time in 20 by chance; 3 SDs, about one in 400.) At what lap would a careful engineer have called it "something is wrong" from the timing screen alone, before the driver said "scraping"?
9. The leaders' spread as a benchmark. All three leaders, laps 4-14 pooled: 32 laps, mean 58.42, SD 0.16, range 0.63. Your pre-main after the start lap: 59.32, 58.79, 58.58, 59.19, 58.97, 58.75, 58.86, 58.62, 58.42. Compute mean and SD. Compare both to the leaders. Then compare your pre-main to your main laps 4-9 (Q7). What changed between the two races, pace or consistency?
10. Decide the sprocket test. Next practice day, you want to know whether the 70 is faster than the 72. Lesson 2 said the model puts them within 0.15 s. Using Q3's rule and a clean-lap SD of 0.15 s: how many laps on each sprocket? What else has to be equal for the comparison to mean anything (list three things)? What is the cheapest way to make the two runs comparable in time?
Done? Q5 is the measurement: ten readings on one tire, same person, chuck on and off each time, and write down the spread. That number decides whether half-psi experiments are readable with this gauge, and it takes ten minutes in the garage.