The combined paternity index (CPI) is a single number that expresses how many times more likely the DNA evidence is if the tested man is the biological father compared to a random, unrelated man. A CPI of 1,000, for example, means the genetic evidence is 1,000 times more likely if the alleged father is the true father than if a stranger chosen at random were. Most paternity tests produce a CPI in the millions or higher, which translates to a probability of paternity above 99.99%.
How the CPI Works as a Likelihood Ratio
At its core, the CPI is a likelihood ratio. The lab compares two scenarios: one where the tested man is the biological father, and one where an unrelated man from the same population is the father. For each genetic marker tested, the lab calculates a single-locus paternity index (PI) that captures how strongly that marker’s evidence supports the first scenario over the second.
The numerator of each PI is the probability of seeing the child’s DNA profile if the tested man is the real father. The denominator is the probability of seeing that same profile if a random man were the father instead. When the child carries a genetic variant that’s rare in the general population but matches the alleged father, the PI for that marker will be high. When the variant is common, it’s less informative, and the PI stays closer to 1.
The CPI is simply all of those individual PI values multiplied together across every marker tested. In one example from the National Institute of Justice, four genetic markers produced individual PI values of roughly 2.16, 1.03, 3.16, and 5.45. Multiplied together, those gave a CPI of about 38.4. That’s a small number because only four markers were used. Modern tests analyze 20 or more markers, which is why real-world CPI values climb into the hundreds of thousands or millions.
What Drives the Numbers Up or Down
Two main factors determine how large a CPI becomes: the number of genetic markers tested and how common the relevant gene variants are in the population.
Since 2017, the standard set of markers used in U.S. forensic and parentage databases includes 20 short tandem repeat (STR) locations spread across the genome. Each additional marker multiplies the CPI by its own PI value, so more markers generally produce a larger, more decisive number. Many commercial paternity tests now examine even more than 20 locations.
The frequency of each gene variant matters because the PI formula divides by the probability that a random man could have passed on the same variant. If only 5% of the population carries a particular variant, a match is far more meaningful than if 25% of the population carries it. This is why population databases are critical. Labs rely on allele frequency databases specific to the relevant ethnic or regional population. Using a database that doesn’t reflect the tested individual’s ancestry can skew results. Paraguay, for instance, long relied on a database from Colombia because no local database existed, prompting researchers to build one that better represents the Paraguayan population.
Converting CPI to a Percentage
Many paternity reports express results as a “probability of paternity” (POP) percentage rather than a raw CPI number. The conversion uses a formula that incorporates a prior probability, which represents the assumed likelihood of paternity before any DNA evidence is considered. Most labs set the prior probability at 0.5 (a neutral 50/50 starting point).
The formula is: POP = (CPI × prior probability) / [(CPI × prior probability) + (1 − prior probability)], then multiplied by 100 to express it as a percentage. With a prior of 0.5, a CPI of 1,000 translates to a probability of paternity of 99.9%. A CPI of 1,000,000 translates to 99.9999%. In practice, labs typically consider a CPI that produces a probability of paternity of 99% or higher as strong support for inclusion as the biological father.
When a Marker Doesn’t Match
Occasionally, one genetic marker shows a mismatch between the alleged father and the child even when all other markers match perfectly. This doesn’t automatically rule the man out. Small changes called mutations occur naturally when DNA is passed from parent to child, and they can cause a single marker to look different.
When a lab encounters an isolated mismatch, it adjusts the calculation for that marker by substituting the known mutation rate for that location in place of the usual allele frequency. Research from routine parentage testing in Zimbabwe confirmed that this approach, recommended by the American Association of Blood Banks, allows labs to account for mutations without discarding useful evidence from all the other matching markers. If multiple markers show mismatches, however, the case becomes much harder to explain by mutation alone, and exclusion becomes more likely.
Why Relatives Complicate Results
The standard CPI calculation assumes the alternative father is a random, unrelated man. That assumption breaks down when the alleged father has a close male relative, such as a brother or father, who could also be the biological father. Related men share a significant portion of their DNA, so the genetic evidence that distinguishes them is weaker.
In these situations, the lab can run a separate calculation that directly compares the two related men as competing candidates. The resulting CPI will be lower and more conservative than a standard calculation, because shared family DNA makes many markers less informative. Studies have also shown that when the alleged father and the child’s mother are themselves related (as in cases of incest), a modified formula is needed to avoid inflating the CPI. Without that correction, the overlapping genetics between the parents can make the evidence look stronger than it actually is.
Reading Your Paternity Report
A paternity report will typically list each genetic marker tested, the alleles found in the mother, child, and alleged father, and the individual PI for each marker. At the bottom, you’ll find the CPI (the product of all the individual PI values) and the probability of paternity percentage. A CPI in the hundreds of millions with a probability of paternity above 99.99% is a clear inclusion. A CPI below 1.0 means the evidence actually favors exclusion, because a random man would be more likely to produce the observed results than the tested man.
If the report shows a CPI of exactly 0 at any marker (a true exclusion at that location with no mutation adjustment), the man is excluded as the biological father. Reports that fall in a gray zone, with moderate CPI values or one to two mismatches, may prompt the lab to recommend additional testing with more markers to reach a definitive answer.