Percentiles describe where observations fall within a defined population; they do not identify good or bad performance by themselves. Their meaning depends on metric direction, analytical unit, cohort, sample size, and weighting. Used with exposure and the underlying traces, they reveal both typical performance and repeatability.
Center and percentile rank answer different questions
The median is the middle sorted observation, also called P50. For connection times of 4.3, 4.5, 4.6, 4.7, 4.9, 5.0, 5.1, 5.3, and 11.8 minutes, the mean is 5.58 minutes and the median is 4.9 minutes. The median better represents a typical connection; the 11.8-minute event still matters as a slow-event opportunity. Retaining the distribution answers both questions.
Other percentiles describe different parts of the population. Using the conventional statistical definition:
- P10: 10% of observations are below this value.
- P25: 25% are below it.
- P50: 50% are below it.
- P75: 75% are below it.
- P90: 90% are below it.
For comparable rotary stands, a distribution might have:
- P10 = 145 ft/hr
- P25 = 175 ft/hr
- P50 = 205 ft/hr
- P75 = 230 ft/hr
- P90 = 255 ft/hr
Now we know considerably more than Average ROP = 207 ft/hr. We can see:
- the lower performance range,
- the typical center,
- the repeatably strong population,
- the high-performance tail.
P10 through P90 describe positions in the observed ROP distribution; engineering context determines whether those positions are desirable.
This terminology can create confusion in the energy industry. In ordinary sample statistics:
$$P90 > P10$$
for a metric such as ROP measured numerically from low to high. Engineers may also encounter exceedance-probability terminology in reserves and probabilistic forecasting, where a "P90 case" can represent a conservative outcome. Those conventions are not the same. Here P10 and P90 mean the 10th and 90th sample percentiles. No performance judgment is implied; whether high or low is desirable depends on the metric.
- ROP: Higher may generally be preferable, subject to drilling quality.
- Connection time: Lower is preferable.
- Tortuosity: Lower may generally represent smoother trajectory.
- Excess torque: Lower may be preferable.
A percentile describes the location of an observation in a distribution. It does not know what "good" means.
Spread measures repeatability
A useful measure of spread is:
$$IQR = P75-P25$$
Two rigs can both have a 5.0-minute median connection and very different repeatability:
| Rig | P25 | P75 | IQR |
|---|---|---|---|
| A | 4.8 min | 5.3 min | 0.5 min |
| B | 4.1 min | 6.6 min | 2.5 min |
The medians are identical, but Rig A is much more repeatable. That creates different improvement questions.
- Rig A: Can the entire stable process be made faster?
- Rig B: Why are we sometimes fast and sometimes slow?
Repeatability itself is therefore a drilling-performance metric.
Equal medians do not imply equal repeatability: the IQR reveals the difference in ordinary process variation.
Define the analytical population
Suppose we calculate a P90 ROP. P90 of what? Possible populations include:
- Raw 1-Hz samples: Every second is an observation.
- One-foot bins: Every foot drilled is an observation.
- Ten-foot intervals: Each interval has equal weight.
- Stands: Each stand is one observation.
- Entire wells: Each well contributes one section-level value.
Those distributions are not equivalent. This is particularly important because drilling data is normally sampled uniformly in time. As discussed in the time-versus-depth article, slow drilling generates more raw samples per foot than fast drilling. If P90 is calculated from raw 1-Hz observations, slow footage contributes more observations. If P90 is calculated from equal-footage bins, each foot or interval receives equal statistical representation. Neither method is universally correct. The analyst must define the population.
Separate typical, strong, and exceptional
Percentiles can be especially useful when historical data is being converted into an operating benchmark. Comparable rotary drilling might show:
| Parameter | P10 | P50 | P90 |
|---|---|---|---|
| WOB | 27 klbf | 34 klbf | 41 klbf |
| RPM | 105 | 125 | 145 |
These values should not automatically become: minimum / target / maximum because the WOB and RPM distributions are not independent. But they provide an immediate sense of the range historically used. Combined with:
- ROP,
- dysfunction,
- formation,
- BHA context,
the percentiles can help establish a historical operating envelope. This shows actual variation rather than reducing the history to Average WOB = 34 klbf.
The same principle applies to connection time. If P10 is 4.0 minutes, P25 is 4.4, P50 is 5.1, P75 is 5.9, and P90 is 7.2, the single fastest connection of 3.1 minutes should not automatically become the target. It may be a one-off event. P10 or P25 shows that relatively fast performance has been demonstrated repeatedly and may be a more defensible improvement benchmark. A useful framework is:
- Typical: P50.
- Repeatably strong: perhaps P25 for a lower-is-better metric.
- Exceptional: near the extreme tail.
The exact percentile selected should depend on the purpose rather than becoming a universal rule.
Percentile lines describe the observed process, while isolated slow connections identify events that merit trace-level review.
Extreme percentiles need evidence
Suppose only eight BHA runs are available. What does P90 really mean? There are not enough observations for a stable estimate of the upper tail. Likewise, calculating P99 from 20 events creates a number, but it conveys more numerical sophistication than the dataset supports. Extreme percentiles become more useful as sample size increases. With small datasets:
- median,
- quartiles,
- individual points
may be more transparent. This is important because drilling comparisons often involve small populations:
- three offset wells,
- six BHAs,
- two crews.
A P90 label does not magically make a six-well comparison statistically robust. SPE/IADC-194184 makes a related point in its performance analysis: the authors compared 25 wells across four rigs but explicitly warned that the dataset was still limited for drawing strong causal conclusions and that numerous operational factors affected performance.[1] The same caution applies to percentile interpretation.
Practical statistical workflow
A defensible drilling-performance workflow is:
| Stage | Requirement |
|---|---|
| Define the question | Specify whether the comparison concerns ROP, connection time, tortuosity, trip speed, or BHA performance. |
| Define the population | State the formation, section, rig state, BHA class, and operating context. |
| Define the analytical unit | Use the event, stand, footage interval, or well appropriate to the question. |
| Validate the data | Separate real operational extremes from sensor faults. |
| Describe center and spread | Report mean or median with suitable percentiles or IQR. |
| Inspect the shape | Check skew, multiple populations, long tails, and isolated extremes. |
| Return to the traces | Find the physical reason for the statistical difference. |
| Preserve provenance | Record population, weighting, percentile convention, and processing version. |
Related technical resources
- The Average Trap: Comparing Drilling Performance With Distributions
- When to Trust a Statistical Drilling Benchmark and When Not To
- Practical Considerations in Offset-Well Benchmarking
References
- Behounek, M., Millican, B., Nelson, B., Wicks, M., Rintala, E., White, M., Thetford, T., Ashok, P., and Ramos, D. Change Management Challenges Deploying a Rig-Based Drilling Advisory System. SPE/IADC-194184-MS, SPE/IADC International Drilling Conference and Exhibition, The Hague, 2019.