A charge-off rate looks like a measurement, and on a large book of loans it behaves like one. On a few dozen loans it behaves more like a coin tossed thirty times: the share of heads is a true record of those tosses and a poor guide to the coin. For that reason the Loan Analytics loan dataset declines to print a cancellation or charge-off rate when its denominator holds fewer than 30 loans, and the data page carries a label in place of a number. This article sets out the arithmetic behind that rule, the public statistical standards it borrows from, how it differs from the separate count gate that decides whether a data page exists at all, and what a feasibility study should do when the local cell it wants is too thin to carry a rate.

A rate on a small cell moves in whole loans

Every rate in the dataset is a plain fraction. For a charge-off rate, the numerator counts loans in an approval cohort that have been charged off so far, and the denominator counts the loans in that cohort that were disbursed. Both are whole numbers, and that ordinary fact is where small cells start to go wrong. On a denominator of 30, each loan that changes status shifts the printed rate by 3.33 points (Table 2). On 100 loans the step is 1.00 point, and on 1,000 loans it shrinks to 0.10 point. A thin cell cannot report anything between those steps, so its rate is always some whole number of single loans, each carrying several points of weight.

The car wash cells in the dataset show the effect on real figures (Table 5). In Washington, the state by asset car wash cell holds 30 disbursed loans in its charge-off cohort and none has been charged off, so the page prints 0.00 percent [1]. Had a single borrower failed, the same page would read 3.33 percent. In Pennsylvania, 2 of 33 disbursed car wash loans have been charged off, a rate of 6.06 percent [2], and a third failure would lift it to 9.09 percent. Nationally, car washes financed under 7(a) carry a charge-off rate of 2.47 percent [3] across 1,337 disbursed loans, and one more failure there would move the figure only to 2.54 percent.

The program totals sit at the far end of the same scale. For the FY2017 to FY2021 approval cohort, the 7(a) charge-off rate to date across all industries stands at 6.33 percent [4]; read it as a lower bound, like every rate measured to date. The 504 rate for the same cohort is 0.35 percent [5], also a floor, and its denominator alone still holds 22,353 [6] open loans. With denominators of that size a single loan barely registers. The statistical agencies put the principle in one line: the National Center for Health Statistics calls the sample size, meaning the denominator, an important indicator of an estimate's precision [7], and the Census Bureau notes that the larger the sample, the smaller the standard error of what is estimated from it [8].

None of this is a criticism of small markets. A state with a few dozen car wash loans may be a perfectly good place to build a car wash. The point is narrower. When a figure can jump by three points because one borrower in one town had a bad year, the figure is describing that borrower as much as it is describing the market, and a lender who reads it as a market statistic is reading noise. Quarterly releases make the point sharper still, because SBA updates the 7(a) and 504 files every quarter [9], and a thin cell can change its printed rate from one release to the next on the status of one loan.

The loan file is complete, so where does sampling come in?

A fair objection is that the SBA files are not a sample. They list every 7(a) and 504 approval, the dataset ties them to the agency's own year-end totals for every year since FY2010, and nothing in a cell has been drawn at random from a larger set. As a record of what has happened so far to the 33 Pennsylvania car wash loans, the fraction is exact. There is no error in it to estimate.

The objection is right about the record and wrong about the question. Nobody underwriting a new car wash asks what happened to those particular 33 loans. The question is what is likely to happen to the next loan of that kind, and for that question the 33 historical loans are one realisation of a process: borrowers of a certain type, in certain markets, through a certain stretch of the economy, each with some chance of failing. A different set of 33 car wash loans made under the same conditions could easily show a different count. That is the same idea the Census Bureau uses when it describes sampling error as including the gap between an estimate and the values that would have been obtained had a different set of units been selected [10]. The units here are loans rather than households, but the logic carries over intact.

Treating each loan as an independent trial with the same underlying chance of default gives the binomial model, the simplest honest description of how much a count can wander. It is a generous model, not a harsh one. Real loans are not independent: a regional downturn, a new competitor or a change in a lender's servicing practice can push several loans in one state into trouble at once. Correlation of that kind widens the true uncertainty beyond anything a binomial interval shows. If the binomial view says a small cell is too noisy to read, the real world says so more loudly.

The binomial view also leaves out a second problem, which has nothing to do with sample size. A charge-off rate to date is a floor, because loans still open can still fail and the file withholds the status of open loans. How that floor arises, and how far below the eventual figure it can sit, is the subject of a separate piece on loss floors; the point here is only to keep the two issues apart. A small cell's rate is both noisy and incomplete, and the 30-loan rule addresses only the first.

The binomial view at 30, 100, 300 and 1,000 loans

The cleanest way to see how much a small cohort can mislead is to fix a true rate and ask what cohorts of different sizes would report. The three tables below do that with labelled assumptions. The cohort sizes and the two assumed rates are illustrations, not forecasts for any project, and the critical value and confidence level follow the published conventions cited in the inputs.

Table 1. Inputs and assumptions
InputValueBasis
Illustrative cohort A (loans)30Assumption; the smallest cohort the dataset prints a rate on
Illustrative cohort B (loans)100Assumption
Illustrative cohort C (loans)300Assumption
Illustrative cohort D (loans)1,000Assumption
Assumed true charge-off rate, higher case6.0%Assumption; for illustration only, not a forecast for any project
Assumed true charge-off rate, lower case2.0%Assumption; for illustration only, not a forecast for any project
Normal critical value for a two-sided 95 percent interval1.96Sourced [11]
Two-sided confidence level95%Sourced [12]
Pennsylvania car wash: charge-offs to date2Loan data [2], key SA-PA-C02:metrics.charge_off_rate.numerator
Pennsylvania car wash: disbursed loans in the cohort33Loan data [2], key SA-PA-C02:metrics.charge_off_rate.denominator
Washington car wash: charge-offs to date0Loan data [1], key SA-WA-C02:metrics.charge_off_rate.numerator
Washington car wash: disbursed loans in the cohort30Loan data [1], key SA-WA-C02:metrics.charge_off_rate.denominator
Car wash, 7(a), national: charge-offs to date33Loan data [3], key PA-C02-7A:metrics.charge_off_rate.numerator
Car wash, 7(a), national: disbursed loans in the cohort1,337Loan data [3], key PA-C02-7A:metrics.charge_off_rate.denominator

Rounded as shown; lines may not foot by one unit in the last place.

Table 2. Illustrative cohorts at an assumed 6.0 percent charge-off rate
Measure30 loans100 loans300 loans1,000 loans
Loans in the cohort301003001,000
Expected charge-offs at the assumed rate1.86.018.060.0
Step in the printed rate from one loan (points)3.33%1.00%0.33%0.10%
Wilson 95 percent interval, lower bound1.56%2.78%3.83%4.69%
Wilson 95 percent interval, upper bound20.43%12.48%9.28%7.65%
Interval width (points)18.86%9.70%5.46%2.96%
Relative interval width (width over the rate)314%162%91%49%
Chance the cohort shows no charge-off at all15.63%0.21%0.00%0.00%
Table 3. Illustrative cohorts at an assumed 2.0 percent charge-off rate
Measure30 loans100 loans300 loans1,000 loans
Loans in the cohort301003001,000
Expected charge-offs at the assumed rate0.62.06.020.0
Step in the printed rate from one loan (points)3.33%1.00%0.33%0.10%
Wilson 95 percent interval, lower bound0.24%0.55%0.92%1.30%
Wilson 95 percent interval, upper bound14.66%7.00%4.29%3.07%
Interval width (points)14.41%6.45%3.37%1.77%
Relative interval width (width over the rate)721%323%169%89%
Chance the cohort shows no charge-off at all54.55%13.26%0.23%0.00%
Highest true rate consistent with zero charge-offs (exact two-sided bound)11.57%3.62%1.22%0.37%

Take the higher case first. If the true charge-off rate for some class of loans were 6.0 percent, a cohort of 30 loans would expect 1.8 charge-offs (Table 2). It cannot show 1.8. It shows 0, 1, 2, 3 or more, which print as multiples of 3.33 points, and the Wilson interval around a 6.0 percent reading on 30 loans runs from 1.56 percent to 20.43 percent. That band is 18.86 points wide, more than three times the rate it surrounds. At 1,000 loans the same true rate produces an interval from 4.69 percent to 7.65 percent, a width of 2.96 points. The tenfold step from 30 to 300 loans narrows the band to 5.46 points, roughly a third of its width at 30, which is the square root law at work: precision grows with the square root of the loan count, so each further gain costs more loans than the last.

The lower case is more instructive, because many of the asset classes a feasibility study meets show charge-off floors in the low single digits, and the 504 classes sit lower still. At an assumed 2.0 percent, a cohort of 30 loans expects 0.6 charge-offs (Table 3), and the chance that it shows none at all is 54.55 percent. More often than not, a thin cell drawn from a low-loss class will print a rate of zero. That zero is real as a count and nearly worthless as evidence: the highest true rate consistent with zero charge-offs on 30 loans, on the exact two-sided bound, is 11.57 percent. Only at 1,000 loans does a zero become informative, because the exact bound falls to 0.37 percent.

Why the Wilson formula rather than the textbook one? The usual normal-approximation interval, the rate plus or minus 1.96 standard errors, is the familiar one, and the National Center for Health Statistics says plainly that this Wald interval performs poorly for proportions [13]. It can return a negative lower bound for a small proportion, and its coverage falls short of what it claims [14]. On a cell with no charge-offs it fails completely: the standard error of a zero rate is zero, so the Wald interval collapses to a single point and reports a 0.00 percent rate as if it were certain. The Wilson score interval does not have that defect. Its lower bound never falls below zero and its upper bound stays well above zero when no event has been seen, which is the behaviour a careful reader needs.

NCHS itself uses a third method. Its standard calls for a two-sided 95 percent Clopper-Pearson interval once the sample size test is met [12], and it describes that interval's coverage as generally conservative [15]. The tables here use Wilson because it comes from a closed formula that anyone can recompute from the inputs table. For the small counts that matter in this article, a Clopper-Pearson band would generally be wider still. The exact zero-event bound in the last row of Table 3 is that conservative calculation for the one case where it reduces to a simple expression, and on 30 loans it sits at 11.57 percent against a Wilson upper bound of 11.35 percent for the Washington cell (Table 5).

Where public statistical agencies draw the line

The 30-loan rule was not invented for loan data. It is the same denominator that the National Center for Health Statistics sets for every proportion it publishes. Under the NCHS Data Presentation Standards for Proportions, estimates with a denominator sample size, or an effective sample size where that applies, "less than 30 should be suppressed" [16]. The agency explains why fixed rules matter most in the kind of publication the dataset's pages resemble: large reports in which estimates cannot be evaluated one at a time and measures of precision cannot be printed beside each figure [17].

What NCHS does next is the part worth studying. Passing the denominator test does not clear a proportion for publication. The agency then computes the interval and judges the estimate by its width. A proportion whose interval is 0.30 or more wide should be suppressed outright [18]. A proportion whose interval is between 0.05 and 0.30 wide should be suppressed when its relative width, the interval width divided by the proportion, is more than 130 percent [19]. An estimate based on zero events that meets every other criterion is not published automatically either: it should be flagged for statistical review by a clearance official [20]. And in every publication, an estimate judged unreliable should be footnoted whether it is shown or withheld [21].

Run the illustrative cohorts through those tests and the 30-loan rule looks modest. At an assumed 6.0 percent rate, the Wilson band is 18.86 points wide at 30 loans and 9.70 points at 100 (Table 2); in the proportion terms NCHS uses, both widths lie between 0.05 and 0.30, where the relative test applies, and their relative widths of 314 and 162 percent are over the NCHS limit of 130 percent [19]. At 300 loans the band is 5.46 points wide, still inside that range, but its relative width falls to 91 percent, so the proportion would pass. At an assumed 2.0 percent rate the 30 and 100 loan cohorts fail by a wider margin, with relative widths of 721 and 323 percent on bands 14.41 and 6.45 points wide (Table 3). At 300 loans the outcome changes for a different reason: the band narrows to 3.37 points, under the 0.05 absolute width at which the relative test starts, and NCHS lets a proportion that narrow be presented if it rests on more than zero events and meets the degrees of freedom criterion [22], a criterion that applies to complex surveys [23]. The same absolute test clears the 1,000 loan cohorts at both rates, whose bands are 2.96 and 1.77 points wide. These widths come from Wilson intervals, and the agency's own conservative method would generally give somewhat wider bands. The lesson is that 30 loans is the first gate in a serious reliability standard, not the whole of one. A rate that clears it has earned the right to be printed, not the right to be believed.

Two further details of the NCHS standard bear directly on loan rates. The proportions standard sets a minimum denominator but no minimum number of events in the numerator [24], so a proportion with one or even zero events can pass the first test. For rates drawn from vital statistics, by contrast, the agency keeps a separate rule of 20 or more events before a rate is reported [25]. That is a numerator rule. Applied to charge-offs it would withhold nearly every state cell in a low-loss class, since even the national 7(a) car wash cell has only 33 charge-offs, and it would blank the charge-off rate of every national 504 class in the dataset. The dataset follows the proportions standard, which counts loans at risk, because a loan rate is a proportion of loans and not a rate per head of population.

The Census Bureau takes a looser line. Its handbook for the American Community Survey says there are "no hard-and-fast rules for determining an acceptable range of error" and leaves users to judge the precision each application needs [26]. It does give a measure for the judgement: when the standard error comes close to the estimate itself, the coefficient of variation is large and the estimate is not very reliable [27]. And it builds the answer to small samples into what it publishes, releasing estimates for less populous areas only from multiple years of data [28]. Even the confidence level is a convention rather than a law of nature: ACS margins of error are published at 90 percent [29], while NCHS works at 95 percent, the level used in the tables above.

The rule the dataset applies, and what a page shows in its place

The dataset applies one denominator test to every rate it computes. A rate is printed only when 30 or more loans stand in its denominator. The test covers the cancellation rate and its ceiling, which are measured on the FY2017 to FY2024 approval cohort, and the charge-off rate to date, the charge-off dollar rate and the rate within five years of approval, which are measured on loans disbursed from the FY2017 to FY2021 cohort. Below the line the cell keeps its counts, sets the rate to empty and carries the label too few loans. It never stores the withheld rate as zero, because a zero on a page reads as a clean record, and a cell below the line has no record clean enough to read either way.

The rule is enforced in code at more than one point, so it does not depend on a writer's care. The dataset's own cell audit plants a rate on a 29-loan denominator as a control and confirms that the check catches it, and the build that assembles these articles refuses any rate marker whose denominator is under 30 or that a cell marks as suppressed. A withheld rate therefore cannot reach a page by being typed, rounded, described as approximate or recomputed from the counts.

The Arizona car wash cell shows the rule at work. Over FY2017 to FY2026 it holds 91 [30] approvals across both programs, comfortably above the count needed for a state by asset page. Its cancellation rate is shown, 12.99 percent [30] on 77 [30] approvals in the cancellation cohort, and like every cancellation rate it is a floor. Its charge-off cohort holds 29 [30] disbursed loans, one short of the line, so the charge-off rate is withheld. The page exists, the count stands, the cancellation rate stands, and the charge-off rate is replaced by the label. That is the intended outcome, not a gap in the data.

It would be easy to argue that one loan should not matter, and that a rate resting on one loan fewer is barely worse than a rate that clears the line. That is true, and it is the nature of any line. The interval at 29 loans is a little wider than the interval at 30, and the interval at 30 is already wider than most readers expect. A rule that moved to suit each borderline cell would stop being a rule. NCHS does allow an analyst writing a report in which each estimate is evaluated on its own to show a proportion that fails the standard, labelled as unreliable, when context makes it interpretable [31]. The dataset's pages are not that kind of document. They are produced for thousands of cells at once, so the line is held fixed, and the judgement that NCHS leaves to an analyst is left to the study that uses the page.

Why 30 and not 100? A higher line would print fewer rates and each printed rate would be steadier, and the illustrative tables show how much steadier: the band at an assumed 6.0 percent falls from 18.86 points on 30 loans to 9.70 points on 100 (Table 2). But a higher line would also blank the rate on a large share of the state pages that exist, including many in exactly the thin markets where a study most needs some benchmark, and it would push readers toward the national figures anyway. Thirty matches the minimum the National Center for Health Statistics applies to every proportion it publishes [16], so the dataset adopts a line with a public precedent instead of tuning its own. The cost of that choice is that a printed rate near the line is still wide, and the sections that follow show what a reader should do with one.

Loan Data Behind This Article

Every figure in this table comes from the Loan Analytics loan dataset, analytics-loan-data freeze-3 (commit 360c856), and carries its key. SBA rates are approval-cohort floors and are withheld when fewer than 30 loans stand behind them.

Table 4. Loan figures this article uses
FigureValueBasisKey
7(a) charge-off rate to date, all industries, FY2017 to FY2021 approval cohort (a floor)6.33 percentFIGURES SBA.7A.COHORT_FY2017_2021.CHGOFF_RATE [4]
504 charge-off rate to date, all industries, same cohort (a floor)0.35 percentFIGURES SBA.504.COHORT_FY2017_2021.CHGOFF_RATE [5]
Car wash, 7(a), national: charge-off rate to date (a floor)2.47 percent33 of 1,337 loanscell PA-C02-7A (metrics.charge_off_rate.rate) [3]
Arizona car wash: approvals FY2017 to FY2026, both programs91cell SA-AZ-C02 (metrics.approval_count.value) [30]
Arizona car wash: cancellation rate, FY2017 to FY2024 cohort (a floor)12.99 percent10 of 77 loanscell SA-AZ-C02 (metrics.cancellation_rate.rate) [30]
Arizona car wash: disbursed loans in the charge-off cohort29charge-off rate withheld: fewer than 30 loanscell SA-AZ-C02 (provenance.counts.charge_off_denominator) [30]
Pennsylvania car wash: charge-off rate to date (a floor)6.06 percent2 of 33 loanscell SA-PA-C02 (metrics.charge_off_rate.rate) [2]
Washington car wash: charge-off rate to date (a floor)0.00 percent0 of 30 loanscell SA-WA-C02 (metrics.charge_off_rate.rate) [1]

A count gate and a rate rule answer different questions

Separate from the 30-loan rule, the dataset applies a page gate that decides whether a data page exists. It counts gross approvals over the ten fiscal years FY2017 to FY2026: a state by asset page needs at least 25 approved loans, a national program by asset page also needs at least 25, and a state by asset by program page needs at least 50. The gate counts approvals and nothing else. It does not ask whether any rate on the page can be shown.

The two tests disagree often, by design. The dataset's threshold table at freeze 3 shows that 900 [32] state by asset cells pass the page gate, yet a cancellation rate can be shown in only 743 [32] of them and a charge-off rate in only 533 [32]. At the state by asset by program gate, 693 [32] cells qualify and every one shows a cancellation rate, but only 538 [32] show a charge-off rate. Even among the 418 [32] state by asset cells with at least a hundred approved loans, 415 [32] show a charge-off rate and three do not. A page that passes its gate and still prints too few loans for a rate is the normal case for a thin market, not a fault.

The reasons are structural. The page gate counts all approvals across ten years; the charge-off rate counts only loans disbursed from the five oldest of those years, because younger loans have had too little time to fail; and the cancellation rate counts the eight oldest years of approvals. A cell built mostly from recent lending can pass the gate on its approvals and still have a small charge-off cohort. The Arizona car wash cell is exactly that case, and its 7(a) side shows it again: the state by asset by program cell holds 65 [33] 7(a) approvals, enough for a page of its own, while its charge-off cohort holds 26 [33] disbursed loans, so that rate is withheld as well. The 504 side, with 26 [30] approvals, falls below the program page gate and has no page.

The deeper reason is that a count and a rate are different kinds of evidence. A count of approvals is a fact about lending activity: lenders approved that many loans for that kind of business in that state. It needs no interval, because it does not claim to predict anything. A study can use it to show that the asset class is financed locally, that lenders know it and that loan sizes cluster in a given range. A rate claims more. It is offered, explicitly or not, as a guide to the chance that the next loan fails or never closes, and a guide to a chance needs enough trials behind it. NCHS draws a similar distinction between rules about reliability and rules about disclosure: some estimates need a minimum number of events to reduce disclosure risk, judged on different criteria such as confidentiality [34]. The dataset's page gate is not a confidentiality rule, since the SBA files are public, but it shares that feature: it answers whether there is enough to show, not whether a figure is precise.

What a study does when the local rate is withheld

When a cell's rate is withheld, a feasibility study does what the statistical agencies do with small areas and small groups: it climbs to a larger, coarser figure and states plainly that it has climbed. NCHS notes that collapsing subgroups and aggregating years gives estimates with less uncertainty, and that this can be the better choice even when the minimum presentation guidelines are met [35]. The Census Bureau recommends the same move for small geographies, aggregating areas to get larger samples and more reliable estimates [36]. In the dataset the ladder has three rungs: the state by asset cell or its program variant, then the national program by asset cell for the same class, then the national program figure across all industries.

For an Arizona car wash, the study would stand on the second rung. A car wash financed through 7(a) is compared with the national 7(a) car wash rate of 2.47 percent [3], a floor that rests on 1,337 disbursed loans. A car wash financed through 504 is compared with the national 504 car wash rate of 1.00 percent [37], which is also a floor. The third rung, the all-industry floor of 6.33 percent [4] for 7(a) or 0.35 percent [5] for 504, is useful only as context, since it mixes every kind of business the programs finance. The program matters more than the state's lending mix. The Arizona cell blends 65 [30] 7(a) approvals with its 504 approvals, but the project in front of the lender is one or the other, and its benchmark should match.

Three habits keep the step honest. First, the study names the figure it used and why: a national class rate is not a local rate, and the text should never let a reader take it for one. Second, the study does not rebuild a local figure by other means. Pooling a thin state with its neighbours, recombining published counts to recover a withheld rate, or calling a near-miss approximate all defeat the purpose of the rule and quietly present a number the dataset declined to stand behind. If a regional figure would genuinely help, it belongs in a separate analysis with its own denominator and its own interval, stated as such. Third, the study keeps what the local cell can still say. The Arizona page still shows the approval count, the loan sizes, the lenders, the program mix and a cancellation rate that clears the line. Those are facts about the local market and remain useful even when the charge-off rate is withheld.

It also helps to remember what any loss rate is for in a study. Under SBA's lending criteria the test falls on the applicant, not on its industry: it must be creditworthy, and the loan must be sound enough to reasonably assure repayment [38]. In weighing that, lenders may consider, among other criteria, the applicant's earnings or cash flow and, where applicable, its equity or collateral [39]. The regulations let SBA attach conditions to a loan, a feasibility study among them [40], and the question such a study has to settle is whether this project's market and cash flow can carry this debt. A class rate cannot answer that. At best it tells the lender how often loans of this kind have failed so far, which frames the questions a study must answer about demand, competition and operating margins. A study uses a class rate as context and as a lower bound for the class, never as the probability that one project will fail.

A rate above the line can still be too wide to lean on

Clearing 30 loans earns a rate its place on the page. It does not make the rate precise, and the cells just above the line show how far apart a printed figure and a reliable one can be (Table 5). The Pennsylvania car wash cell prints 6.06 percent [2] on 33 disbursed loans, more than twice the national 7(a) car wash figure. A reader who stopped there would conclude that Pennsylvania car washes are a markedly riskier credit. The Wilson interval says otherwise. It runs from 1.68 percent to 19.61 percent, a band nearly three times as wide as the rate itself, and the national car wash interval of 1.76 percent to 3.45 percent sits inside it. On the evidence of 33 loans, Pennsylvania car washes could be safer than the national class, much riskier, or about the same.

Table 5. Three car wash charge-off rates and their Wilson 95 percent intervals
MeasurePennsylvania, state by assetWashington, state by assetNational, 7(a)
Disbursed loans in the charge-off cohort33301,337
Charge-offs to date2033
Charge-off rate to date (a floor)6.06%0.00%2.47%
Wilson 95 percent interval, lower bound1.68%0.00%1.76%
Wilson 95 percent interval, upper bound19.61%11.35%3.45%
Interval width (points)17.93%11.35%1.68%
Rate if one more loan had charged off9.09%3.33%2.54%

The dataset's own distinctness test agrees. A cell is marked distinct only when a headline figure differs from both parents by at least a fifth and the difference also survives a two-sided 95 percent test against the parent rate, with a floor of half a percentage point. The Pennsylvania cell is marked distinct, but on its cancellation figure, not on its charge-off rate: the charge-off gap, large as it looks, does not pass the noise test. That is the right way to compare a small cell with a large one. The Census Bureau warns that overlapping confidence intervals are not a reliable test of significance [41], and eyeballing two intervals can mislead in either direction. A formal test, of the kind the dataset runs, is what decides whether a difference is worth emphasising. Cancellation is a different outcome with its own meaning, which the series treats on its own.

The Washington cell is the mirror image. It prints 0.00 percent [1] on exactly 30 loans, the smallest denominator the rule allows. A zero invites the reading that Washington car wash loans do not fail. The interval says only that the true rate is probably below 11.35 percent on the Wilson calculation, or 11.57 percent on the exact bound, which is no reassurance at all for an asset class whose national figure is a fraction of that. NCHS treats exactly this kind of estimate with caution: even when it meets the other criteria, an estimate based on zero events should be flagged for statistical review rather than go straight into print [20]. A study that cites a zero from a thin cell should say how many loans stand behind it and what upper bound those loans allow.

Small cells also make the dollar view unstable. The Pennsylvania cell's charge-off dollar rate is 0.06 percent [2], against a count rate of 6.06 percent, because the dollars charged off on those two loans were small beside the cell's total lending. On a large cohort the gap between count and dollar rates says something about which loans fail. On 33 loans it mostly says which two borrowers happened to fail. Which loans default is itself a matter of chance when only a handful do.

What a lender or borrower should check

A short set of checks covers most of what can go wrong with a rate drawn from a small cell. None needs special software, only the counts that a dataset page already prints beside every rate.

  • The denominator and the cohort. Every rate should come with the number of loans behind it and the cohort it measures. A cancellation rate counts approvals in one window and a charge-off rate counts disbursed loans in an older one, so the same page can carry rates on very different bases. A rate printed without its denominator cannot be weighed at all.
  • The label. Too few loans means the rate was withheld, not that it was zero. NCHS asks that an unreliable estimate be footnoted whether it is shown or not [21], and the label does the same job. A study or a memo that turns a withheld rate into a zero, or into a figure described as approximate, has changed the evidence.
  • The zero. A zero on a few dozen loans is consistent with a true rate near one in nine. Ask for the upper bound the loans allow before treating a zero as good news, especially for an asset class that loses loans at low single-digit rates nationally.
  • The width. A rate on a few dozen loans carries an interval many points wide. The tables in this article give the scale: at an assumed 6.0 percent, the band is 18.86 points wide on 30 loans and 9.70 points on 100. If the decision would change anywhere within that band, the local rate cannot carry the decision.
  • The step up. Where a study uses a national class figure in place of a withheld local one, it should say so in the sentence that uses it, name the program and the class, and match the program to the project's own financing.
  • The floor. Every charge-off rate to date is a floor, because open loans can still fail. A small cell's rate is a noisy floor, which is two reasons for caution, not one.
  • The release. SBA refreshes the 7(a) and 504 files quarterly [9]. A rate near the line can appear or disappear between releases, so a figure should be quoted with the date of the data it comes from.
  • The arithmetic. Cancellation and charge-off rates measure different outcomes on different denominators and should never be added into a single failure rate.

These checks cut both ways. A lender should not decline a project because a thin cell prints a high rate, and a borrower should not cite a thin cell's zero as proof of safety. Both readings take a handful of loans as a verdict on a market. Reading a whole data page, block by block, is the subject of a companion article listed among the related pages below, and the archived Loan Analytics post on charge-off rates by industry, listed there too, ranks industries only at far higher loan counts for the same underlying reason.

Why the rule serves the reader

A withheld rate is sometimes taken as missing information, as if the dataset were hiding a number that a determined reader could still use. The opposite is closer to the truth. The number exists in the loan file, and it is correct as a count of what happened. What is withheld is the suggestion that the number means something about the next loan. On fewer than 30 loans it usually does not, and the public statistical agencies that publish figures for a living reached the same conclusion: the NCHS standards say a proportion on a denominator under 30 should be suppressed [16], and the Census Bureau publishes ACS estimates for its less populous areas only from pooled years [28].

For a feasibility study the rule is a discipline rather than an obstacle. It forces the study to say where its benchmark comes from, to choose the broadest figure that fits the project rather than the narrowest one that flatters or alarms, and to rest its conclusions on the project's own market and cash flow. The loss record of an asset class is context for those questions. It is never the answer to them, and on a few dozen loans it is barely context at all.

Related Pages on Loan Analytics

Commission a Feasibility Study

Loan Analytics prepares lender-grade feasibility studies for SBA 7(a), SBA 504, USDA Business and Industry, conventional and EB-5 financing, built on the methods this series sets out. A study is not an appraisal: it tests whether a project's market, costs and cash flow can carry the debt a lender is asked to approve. To discuss a study for your project, contact Loan Analytics.

Daniel Smith, MAI, Loan Analytics

Sources

  1. Loan Analytics loan dataset, analytics-loan-data freeze-3 (commit 360c856), cell SA-WA-C02 (WA, Car wash, 7(a) and 504, approvals FY2017 to FY2026). Source: U.S. Small Business Administration, 7(a) and 504 FOIA loan files as of 2026-09-30 (data.sba.gov), as compiled by Loan Analytics. Data as of 2026-09-30; cell computed 2026-11-11.
  2. Loan Analytics loan dataset, analytics-loan-data freeze-3 (commit 360c856), cell SA-PA-C02 (PA, Car wash, 7(a) and 504, approvals FY2017 to FY2026). Source: U.S. Small Business Administration, 7(a) and 504 FOIA loan files as of 2026-09-30 (data.sba.gov), as compiled by Loan Analytics. Data as of 2026-09-30; cell computed 2026-11-11.
  3. Loan Analytics loan dataset, analytics-loan-data freeze-3 (commit 360c856), cell PA-C02-7A (all states, Car wash, 7(a), approvals FY2017 to FY2026). Source: U.S. Small Business Administration, 7(a) and 504 FOIA loan files as of 2026-09-30 (data.sba.gov), as compiled by Loan Analytics. Data as of 2026-09-30; cell computed 2026-11-11.
  4. Loan Analytics loan dataset, analytics-loan-data freeze-3 (commit 360c856), FIGURES id SBA.7A.COHORT_FY2017_2021.CHGOFF_RATE: Charge-offs to date / disbursed loans, 7A approval cohort FY2017-FY2021, seasoning 5.0 to 10.0 years at 2026-09-30; a floor: open loans are exempt from status disclosure (count: .CHGOFF_OPEN_IN_DEN) and the cohort is still accruing charge-offs. Source: U.S. Small Business Administration, 7(a) and 504 FOIA loan files as of 2026-09-30 (data.sba.gov), as compiled by Loan Analytics. Data as of 2026-09-30; FIGURES compiled 2026-11-11.
  5. Loan Analytics loan dataset, analytics-loan-data freeze-3 (commit 360c856), FIGURES id SBA.504.COHORT_FY2017_2021.CHGOFF_RATE: Charge-offs to date / disbursed loans, 504 approval cohort FY2017-FY2021, seasoning 5.0 to 10.0 years at 2026-09-30; a floor: open loans are exempt from status disclosure (count: .CHGOFF_OPEN_IN_DEN) and the cohort is still accruing charge-offs. Source: U.S. Small Business Administration, 7(a) and 504 FOIA loan files as of 2026-09-30 (data.sba.gov), as compiled by Loan Analytics. Data as of 2026-09-30; FIGURES compiled 2026-11-11.
  6. Loan Analytics loan dataset, analytics-loan-data freeze-3 (commit 360c856), FIGURES id SBA.504.COHORT_FY2017_2021.CHGOFF_OPEN_IN_DEN: Open (status withheld) loans in the charge-off denominator, 504 cohort FY2017-FY2021, at 2026-09-30. Source: U.S. Small Business Administration, 7(a) and 504 FOIA loan files as of 2026-09-30 (data.sba.gov), as compiled by Loan Analytics. Data as of 2026-09-30; FIGURES compiled 2026-11-11.
  7. National Center for Health Statistics, Centers for Disease Control and Prevention. National Center for Health Statistics Data Presentation Standards for Proportions, Vital and Health Statistics Series 2, Number 175. Data period August 2017. https://www.cdc.gov/nchs/data/series/sr_02/sr02_175.pdf (retrieved 2026-11-11).
  8. U.S. Census Bureau. Understanding and Using American Community Survey Data: What All Data Users Need to Know, Chapter 7, Understanding Error and Determining Statistical Significance. Data period 2020. https://www.census.gov/content/dam/Census/library/publications/2020/acs/acs_general_handbook_2020_ch07.pdf (retrieved 2026-11-11).
  9. U.S. Small Business Administration, data.sba.gov. 7(a) and 504 FOIA dataset page. Data period files as of September 30, 2026. https://data.sba.gov/dataset/7a-504-foia (retrieved 2026-11-11).
  10. U.S. Census Bureau. Understanding and Using American Community Survey Data: What All Data Users Need to Know, Chapter 7, Understanding Error and Determining Statistical Significance. Data period 2020. https://www.census.gov/content/dam/Census/library/publications/2020/acs/acs_general_handbook_2020_ch07.pdf (retrieved 2026-11-11).
  11. U.S. Census Bureau. Understanding and Using American Community Survey Data: What All Data Users Need to Know, Chapter 7, Understanding Error and Determining Statistical Significance. Data period 2020. https://www.census.gov/content/dam/Census/library/publications/2020/acs/acs_general_handbook_2020_ch07.pdf (retrieved 2026-11-11).
  12. National Center for Health Statistics, Centers for Disease Control and Prevention. National Center for Health Statistics Data Presentation Standards for Proportions, Vital and Health Statistics Series 2, Number 175. Data period August 2017. https://www.cdc.gov/nchs/data/series/sr_02/sr02_175.pdf (retrieved 2026-11-11).
  13. National Center for Health Statistics, Centers for Disease Control and Prevention. National Center for Health Statistics Data Presentation Standards for Proportions, Vital and Health Statistics Series 2, Number 175. Data period August 2017. https://www.cdc.gov/nchs/data/series/sr_02/sr02_175.pdf (retrieved 2026-11-11).
  14. National Center for Health Statistics, Centers for Disease Control and Prevention. National Center for Health Statistics Data Presentation Standards for Proportions, Vital and Health Statistics Series 2, Number 175. Data period August 2017. https://www.cdc.gov/nchs/data/series/sr_02/sr02_175.pdf (retrieved 2026-11-11).
  15. National Center for Health Statistics, Centers for Disease Control and Prevention. National Center for Health Statistics Data Presentation Standards for Proportions, Vital and Health Statistics Series 2, Number 175. Data period August 2017. https://www.cdc.gov/nchs/data/series/sr_02/sr02_175.pdf (retrieved 2026-11-11).
  16. National Center for Health Statistics, Centers for Disease Control and Prevention. National Center for Health Statistics Data Presentation Standards for Proportions, Vital and Health Statistics Series 2, Number 175. Data period August 2017. https://www.cdc.gov/nchs/data/series/sr_02/sr02_175.pdf (retrieved 2026-11-11).
  17. National Center for Health Statistics, Centers for Disease Control and Prevention. National Center for Health Statistics Data Presentation Standards for Proportions, Vital and Health Statistics Series 2, Number 175. Data period August 2017. https://www.cdc.gov/nchs/data/series/sr_02/sr02_175.pdf (retrieved 2026-11-11).
  18. National Center for Health Statistics, Centers for Disease Control and Prevention. National Center for Health Statistics Data Presentation Standards for Proportions, Vital and Health Statistics Series 2, Number 175. Data period August 2017. https://www.cdc.gov/nchs/data/series/sr_02/sr02_175.pdf (retrieved 2026-11-11).
  19. National Center for Health Statistics, Centers for Disease Control and Prevention. National Center for Health Statistics Data Presentation Standards for Proportions, Vital and Health Statistics Series 2, Number 175. Data period August 2017. https://www.cdc.gov/nchs/data/series/sr_02/sr02_175.pdf (retrieved 2026-11-11).
  20. National Center for Health Statistics, Centers for Disease Control and Prevention. National Center for Health Statistics Data Presentation Standards for Proportions, Vital and Health Statistics Series 2, Number 175. Data period August 2017. https://www.cdc.gov/nchs/data/series/sr_02/sr02_175.pdf (retrieved 2026-11-11).
  21. National Center for Health Statistics, Centers for Disease Control and Prevention. National Center for Health Statistics Data Presentation Standards for Proportions, Vital and Health Statistics Series 2, Number 175. Data period August 2017. https://www.cdc.gov/nchs/data/series/sr_02/sr02_175.pdf (retrieved 2026-11-11).
  22. National Center for Health Statistics, Centers for Disease Control and Prevention. National Center for Health Statistics Data Presentation Standards for Proportions, Vital and Health Statistics Series 2, Number 175. Data period August 2017. https://www.cdc.gov/nchs/data/series/sr_02/sr02_175.pdf (retrieved 2026-11-11).
  23. National Center for Health Statistics, Centers for Disease Control and Prevention. National Center for Health Statistics Data Presentation Standards for Proportions, Vital and Health Statistics Series 2, Number 175. Data period August 2017. https://www.cdc.gov/nchs/data/series/sr_02/sr02_175.pdf (retrieved 2026-11-11).
  24. National Center for Health Statistics, Centers for Disease Control and Prevention. National Center for Health Statistics Data Presentation Standards for Proportions, Vital and Health Statistics Series 2, Number 175. Data period August 2017. https://www.cdc.gov/nchs/data/series/sr_02/sr02_175.pdf (retrieved 2026-11-11).
  25. National Center for Health Statistics, Centers for Disease Control and Prevention. National Center for Health Statistics Data Presentation Standards for Proportions, Vital and Health Statistics Series 2, Number 175. Data period August 2017. https://www.cdc.gov/nchs/data/series/sr_02/sr02_175.pdf (retrieved 2026-11-11).
  26. U.S. Census Bureau. Understanding and Using American Community Survey Data: What All Data Users Need to Know, Chapter 7, Understanding Error and Determining Statistical Significance. Data period 2020. https://www.census.gov/content/dam/Census/library/publications/2020/acs/acs_general_handbook_2020_ch07.pdf (retrieved 2026-11-11).
  27. U.S. Census Bureau. Understanding and Using American Community Survey Data: What All Data Users Need to Know, Chapter 7, Understanding Error and Determining Statistical Significance. Data period 2020. https://www.census.gov/content/dam/Census/library/publications/2020/acs/acs_general_handbook_2020_ch07.pdf (retrieved 2026-11-11).
  28. U.S. Census Bureau. Understanding and Using American Community Survey Data: What All Data Users Need to Know, Chapter 7, Understanding Error and Determining Statistical Significance. Data period 2020. https://www.census.gov/content/dam/Census/library/publications/2020/acs/acs_general_handbook_2020_ch07.pdf (retrieved 2026-11-11).
  29. U.S. Census Bureau. Understanding and Using American Community Survey Data: What All Data Users Need to Know, Chapter 7, Understanding Error and Determining Statistical Significance. Data period 2020. https://www.census.gov/content/dam/Census/library/publications/2020/acs/acs_general_handbook_2020_ch07.pdf (retrieved 2026-11-11).
  30. Loan Analytics loan dataset, analytics-loan-data freeze-3 (commit 360c856), cell SA-AZ-C02 (AZ, Car wash, 7(a) and 504, approvals FY2017 to FY2026). Source: U.S. Small Business Administration, 7(a) and 504 FOIA loan files as of 2026-09-30 (data.sba.gov), as compiled by Loan Analytics. Data as of 2026-09-30; cell computed 2026-11-11.
  31. National Center for Health Statistics, Centers for Disease Control and Prevention. National Center for Health Statistics Data Presentation Standards for Proportions, Vital and Health Statistics Series 2, Number 175. Data period August 2017. https://www.cdc.gov/nchs/data/series/sr_02/sr02_175.pdf (retrieved 2026-11-11).
  32. Loan Analytics loan dataset, analytics-loan-data freeze-3 (commit 360c856), threshold table THRESHOLDS (docs/THRESHOLDS.csv): candidate and qualifying cells by kind and loan threshold. Source: U.S. Small Business Administration, 7(a) and 504 FOIA loan files as of 2026-09-30 (data.sba.gov), as compiled by Loan Analytics. Data as of 2026-09-30; THRESHOLDS computed 2026-11-11, with the cells.
  33. Loan Analytics loan dataset, analytics-loan-data freeze-3 (commit 360c856), cell SAP-AZ-C02-7A (AZ, Car wash, 7(a), approvals FY2017 to FY2026). Source: U.S. Small Business Administration, 7(a) and 504 FOIA loan files as of 2026-09-30 (data.sba.gov), as compiled by Loan Analytics. Data as of 2026-09-30; cell computed 2026-11-11.
  34. National Center for Health Statistics, Centers for Disease Control and Prevention. National Center for Health Statistics Data Presentation Standards for Proportions, Vital and Health Statistics Series 2, Number 175. Data period August 2017. https://www.cdc.gov/nchs/data/series/sr_02/sr02_175.pdf (retrieved 2026-11-11).
  35. National Center for Health Statistics, Centers for Disease Control and Prevention. National Center for Health Statistics Data Presentation Standards for Proportions, Vital and Health Statistics Series 2, Number 175. Data period August 2017. https://www.cdc.gov/nchs/data/series/sr_02/sr02_175.pdf (retrieved 2026-11-11).
  36. U.S. Census Bureau. Understanding and Using American Community Survey Data: What All Data Users Need to Know, Chapter 7, Understanding Error and Determining Statistical Significance. Data period 2020. https://www.census.gov/content/dam/Census/library/publications/2020/acs/acs_general_handbook_2020_ch07.pdf (retrieved 2026-11-11).
  37. Loan Analytics loan dataset, analytics-loan-data freeze-3 (commit 360c856), cell PA-C02-504 (all states, Car wash, 504, approvals FY2017 to FY2026). Source: U.S. Small Business Administration, 7(a) and 504 FOIA loan files as of 2026-09-30 (data.sba.gov), as compiled by Loan Analytics. Data as of 2026-09-30; cell computed 2026-11-11.
  38. U.S. Government Publishing Office (govinfo), Code of Federal Regulations. 13 CFR Part 120, Business Loans (2026 edition), 120.150 What are SBA's lending criteria?. Data period 2026 edition. https://www.govinfo.gov/content/pkg/CFR-2026-title13-vol1/pdf/CFR-2026-title13-vol1-part120.pdf (retrieved 2026-11-10).
  39. U.S. Government Publishing Office (govinfo), Code of Federal Regulations. 13 CFR Part 120, Business Loans (2026 edition), 120.150 What are SBA's lending criteria?. Data period 2026 edition. https://www.govinfo.gov/content/pkg/CFR-2026-title13-vol1/pdf/CFR-2026-title13-vol1-part120.pdf (retrieved 2026-11-10).
  40. U.S. Small Business Administration, 13 CFR part 120 (1-1-26 edition), via GPO govinfo. 13 CFR 120.160(b). https://www.govinfo.gov/content/pkg/CFR-2026-title13-vol1/pdf/CFR-2026-title13-vol1-part120.pdf (retrieved 2026-11-10).
  41. U.S. Census Bureau. Understanding and Using American Community Survey Data: What All Data Users Need to Know, Chapter 7, Understanding Error and Determining Statistical Significance. Data period 2020. https://www.census.gov/content/dam/Census/library/publications/2020/acs/acs_general_handbook_2020_ch07.pdf (retrieved 2026-11-11).