OPINION
KETHLEDGE, Circuit Judge.
The Plaintiffs in this case — now only two organizations that represent migrant farm-workers — claim that the United States Border Patrol allows agents at its San-dusky Bay, Ohio station to target persons of Hispanic appearance for questioning. After a bench trial, the district court found that the Plaintiffs had not proved their claim. We affirm.
I.
The Border Patrol’s mission includes enforcing the Nation’s immigration laws, as well as preventing terrorism and combat-ting border-related crimes like human smuggling and sex trafficking. The agency’s Sandusky Bay Station lies near Lake Erie, about an hour west of Cleveland. Agents from Sandusky Bay patrol a roughly 30-mile swath of land along 150 miles of the Ohio shoreline of Lake Erie, including Interstates 80 and 90 and the rest areas there. In the course of their duties, agents often initiate consensual conversations with people they encounter. Sometimes those conversations lead to information that gives an agent probable cause to think that a person is present in the United States illegally, in which case the person is arrested. The Station records all arrests in an “apprehension log,” which includes information about each arrestee’s nationality and specifies whether the Border Patrol or [444]*444some other law-enforcement agency originally approached or stopped the person.
The Plaintiff organizations — the Ohio Immigrant Worker Project and the Farm Labor Organizing Committee (collectively, “Plaintiffs”) — brought this lawsuit in 2009, claiming among other things that the Border Patrol’s policy at its Sandusky Bay Station was to allow its agents to target persons of Hispanic appearance when deciding whom to approach during the agents’ patrols. Eventually the district court held a two-week bench trial on that claim,.after which it found that the Plaintiffs had not shown that the Border Patrol had such a policy. The district court therefore entered judgment in favor of the Border Patrol. This appeal followed..
II.
After a bench trial, “we review a district court’s factual findings for clear error and its legal conclusions de novo.” Calloway v. Caraco Pharm. Labs., Ltd., 800 F.3d 244, 251 (6th Cir. 2015).
We first engage in some analytical housekeeping, of which there is, plenty to do here. The only remaining defendant is •the United.States Border Patrol, and the Plaintiffs’ only remaining claim is one for injunctive relief. The parties assume, that, for the Plaintiffs to succeed on that claim, they must show, that the Border Patrol itself has a policy that allows agents to use race in some unconstitutional manner. See generally United States v. Avery, 137 F.3d 343, 355 (6th Cir. 1997); Ellis v. District of Columbia, 84 F.3d 1413, 1424 (D.C. Cir. 1996). They further assume that; to show the existence of such a policy, the Plaintiffs must satisfy the standard used in cases brought against municipalities under 42 U.S.C. § 1983. See Monell v. Dep’t of Soc. Servs. of N.Y., 436 U.S. 658, 690-91, 98 S.Ct. 2018, 56 L.Ed.2d 611 (1978). We will likewise assume, without deciding, that the Monell standard applies in determining whether the Plaintiffs can prevail against the Border Patrol here.
Couched in terms of Monell, the Plaintiffs’ argument is that the Border Patrol has a policy that allows agents at its San-dusky Bay Station to use race in a manner that violates the. Constitution’s guarantee of equal protection as applied to the federal government. See generally Washington v. Davis, 426 U.S. 229, 239, 96 S.Ct. 2040, 48 L.Ed.2d 597 (1976). That means the Plaintiffs must show two things: first, that the Border Patrol has a policy that allows consideration of race in determining whom to approach; and second, that such a policy is unconstitutional.
We begin and end with the first point. A plaintiff can prove the existence of an agency policy in several ways. One is to show the existence of an “official policy” that expressly permits the conduct at issue. D’Ambrosio v. Marino, 747 F.3d 378, 386 (6th Cir. 2014). The Plaintiffs do not contend that the Border Patrol has any such policy here. (For good reason: the Border Patrol’s official policy expressly “prohibit[s] the consideration of race or ethnicity in [agents’] daily law enforcement activities in all but the most exceptional instances ... • [and only] when a compelling governmental interest is present[.]”) Another way is to show the existence of an informal policy that causes the constitutional violation. To that end a plaintiff can show- that the agency has “a policy of inadequate training or supervision,” which in turn causes agency personnel to act in ways that are unconstitutional, Id. But the Plaintiffs make no such argument here. (Again for good reason: the.Border Patrol trains its agents to follow the official policy described above- and to avoid racial profiling.)
[445]*445That leaves two other ways to show the existence of an informal policy. One is to prove that an agency “official with final decision[-]making authority ratified illegal actions”; another is to prove that the agency has a custom of tolerating violations of federal law. Id. Here the Plaintiffs say they have done both — that they have proof of both ratification and custom, to show that the Border Patrol allows agents at its Sandusky Bay Station to consider race as a factor in determining whom to approach.
As to ratification, the Plaintiffs contend that “[tjestimony by high-ranking supervisors” at Sandusky Bay shows that the Border Patrol maintains a policy of racial profiling there. But Corey Bammer, the Sandusky Station Chief from -2008-12, testified unequivocally that race “cari’t be any basis for a stop whatsoever[.]” He added that “I feel confident that I would be able to see in a report if somebody had used race as a [ ] basis of making a stop;” The current Station Chief at Sandusky Bay, Robert Simon, likewise testified that he would not “tolerate racial profiling [at his] station,” and that Mario Martinez, the Border Patrol’s Sector Chief for the area encompassing Sandusky, “[absolutely” would not tolerate racial profiling “in the Sandusky Bay Station or anywhere in the sector[.]” And Martinez himself testified that he would not “tolerate racial profiling at the stations” in his sector and that he would “know about it if it was going on[.]”
The Plaintiffs elide all this testimony and instead focus upon the testimony of two deputies at Sandusky Bay. One of them, David York, testified that race “could be one of many factors, but it shouldn’t be the sole factor” in deciding whom to approach.
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OPINION
KETHLEDGE, Circuit Judge.
The Plaintiffs in this case — now only two organizations that represent migrant farm-workers — claim that the United States Border Patrol allows agents at its San-dusky Bay, Ohio station to target persons of Hispanic appearance for questioning. After a bench trial, the district court found that the Plaintiffs had not proved their claim. We affirm.
I.
The Border Patrol’s mission includes enforcing the Nation’s immigration laws, as well as preventing terrorism and combat-ting border-related crimes like human smuggling and sex trafficking. The agency’s Sandusky Bay Station lies near Lake Erie, about an hour west of Cleveland. Agents from Sandusky Bay patrol a roughly 30-mile swath of land along 150 miles of the Ohio shoreline of Lake Erie, including Interstates 80 and 90 and the rest areas there. In the course of their duties, agents often initiate consensual conversations with people they encounter. Sometimes those conversations lead to information that gives an agent probable cause to think that a person is present in the United States illegally, in which case the person is arrested. The Station records all arrests in an “apprehension log,” which includes information about each arrestee’s nationality and specifies whether the Border Patrol or [444]*444some other law-enforcement agency originally approached or stopped the person.
The Plaintiff organizations — the Ohio Immigrant Worker Project and the Farm Labor Organizing Committee (collectively, “Plaintiffs”) — brought this lawsuit in 2009, claiming among other things that the Border Patrol’s policy at its Sandusky Bay Station was to allow its agents to target persons of Hispanic appearance when deciding whom to approach during the agents’ patrols. Eventually the district court held a two-week bench trial on that claim,.after which it found that the Plaintiffs had not shown that the Border Patrol had such a policy. The district court therefore entered judgment in favor of the Border Patrol. This appeal followed..
II.
After a bench trial, “we review a district court’s factual findings for clear error and its legal conclusions de novo.” Calloway v. Caraco Pharm. Labs., Ltd., 800 F.3d 244, 251 (6th Cir. 2015).
We first engage in some analytical housekeeping, of which there is, plenty to do here. The only remaining defendant is •the United.States Border Patrol, and the Plaintiffs’ only remaining claim is one for injunctive relief. The parties assume, that, for the Plaintiffs to succeed on that claim, they must show, that the Border Patrol itself has a policy that allows agents to use race in some unconstitutional manner. See generally United States v. Avery, 137 F.3d 343, 355 (6th Cir. 1997); Ellis v. District of Columbia, 84 F.3d 1413, 1424 (D.C. Cir. 1996). They further assume that; to show the existence of such a policy, the Plaintiffs must satisfy the standard used in cases brought against municipalities under 42 U.S.C. § 1983. See Monell v. Dep’t of Soc. Servs. of N.Y., 436 U.S. 658, 690-91, 98 S.Ct. 2018, 56 L.Ed.2d 611 (1978). We will likewise assume, without deciding, that the Monell standard applies in determining whether the Plaintiffs can prevail against the Border Patrol here.
Couched in terms of Monell, the Plaintiffs’ argument is that the Border Patrol has a policy that allows agents at its San-dusky Bay Station to use race in a manner that violates the. Constitution’s guarantee of equal protection as applied to the federal government. See generally Washington v. Davis, 426 U.S. 229, 239, 96 S.Ct. 2040, 48 L.Ed.2d 597 (1976). That means the Plaintiffs must show two things: first, that the Border Patrol has a policy that allows consideration of race in determining whom to approach; and second, that such a policy is unconstitutional.
We begin and end with the first point. A plaintiff can prove the existence of an agency policy in several ways. One is to show the existence of an “official policy” that expressly permits the conduct at issue. D’Ambrosio v. Marino, 747 F.3d 378, 386 (6th Cir. 2014). The Plaintiffs do not contend that the Border Patrol has any such policy here. (For good reason: the Border Patrol’s official policy expressly “prohibit[s] the consideration of race or ethnicity in [agents’] daily law enforcement activities in all but the most exceptional instances ... • [and only] when a compelling governmental interest is present[.]”) Another way is to show the existence of an informal policy that causes the constitutional violation. To that end a plaintiff can show- that the agency has “a policy of inadequate training or supervision,” which in turn causes agency personnel to act in ways that are unconstitutional, Id. But the Plaintiffs make no such argument here. (Again for good reason: the.Border Patrol trains its agents to follow the official policy described above- and to avoid racial profiling.)
[445]*445That leaves two other ways to show the existence of an informal policy. One is to prove that an agency “official with final decision[-]making authority ratified illegal actions”; another is to prove that the agency has a custom of tolerating violations of federal law. Id. Here the Plaintiffs say they have done both — that they have proof of both ratification and custom, to show that the Border Patrol allows agents at its Sandusky Bay Station to consider race as a factor in determining whom to approach.
As to ratification, the Plaintiffs contend that “[tjestimony by high-ranking supervisors” at Sandusky Bay shows that the Border Patrol maintains a policy of racial profiling there. But Corey Bammer, the Sandusky Station Chief from -2008-12, testified unequivocally that race “cari’t be any basis for a stop whatsoever[.]” He added that “I feel confident that I would be able to see in a report if somebody had used race as a [ ] basis of making a stop;” The current Station Chief at Sandusky Bay, Robert Simon, likewise testified that he would not “tolerate racial profiling [at his] station,” and that Mario Martinez, the Border Patrol’s Sector Chief for the area encompassing Sandusky, “[absolutely” would not tolerate racial profiling “in the Sandusky Bay Station or anywhere in the sector[.]” And Martinez himself testified that he would not “tolerate racial profiling at the stations” in his sector and that he would “know about it if it was going on[.]”
The Plaintiffs elide all this testimony and instead focus upon the testimony of two deputies at Sandusky Bay. One of them, David York, testified that race “could be one of many factors, but it shouldn’t be the sole factor” in deciding whom to approach. The other, Matthew Richardson, testified that, he thought race could be “an articulable fact” in determining whom to approach, but that “you can’t base your sole stop on race.” Neither of these agents, however, .testified that he ratified anyone else’s use of race as a factor in determining whom to approach. And neither of them has served at San-dusky Bay as the sort of “final dedsion-maker” whose ratification could .create an informal policy in the first place. See Feliciano v. City of Cleveland, 988 F.2d 649, 655 (6th Cir. 1993). The Plaintiffs therefore did not prove the existence of a ratification-based policy of racial targeting at San-dusky Bay.
That leaves the Plaintiffs’ evidence of custom, which' takes three forms. First, the Plaintiffs say that four encounters in particular demonstrate that agents from Sandusky Bay routinely target people of Hispanic appearance for questioning. After observing the testimony of the agents who initiated these encounters, however, the district court flatly disagreed. In one encounter, the agent observed a young man driving a 2001 Dodge Ram with tinted windows, a young woman in the passenger seat, and a passenger door hanging open— all in an area of North Toledo known for sex trafficking, and all of which (excepting perhaps the open door) fit the profile of a vehicle used in sex trafficking. (The woman turned out to be the driver’s sister, and the agent promptly sent the driver on his way — the agent testified that the entire encounter lasted “[t]hree or four minutes max.”) In another encounter, Agent. Thomas Payne approached the driver of a vehicle only after determining that it was “hob-plated,” ie., that the registration associated with the license plate did not match the vehicle. In a third encounter, Agent Bradley Shaver began a conversation with the driver of a pickup truck at a gas station near the Phio Turnpike, in an area known as a corridor for- drug - trafficking. The truck had decals with the. words “Durango Durango,”, which is a state in Mexico known for drug trafficking. The decals also [446]*446had silver scorpions, which Shaver testified is a symbol used by Mexican drug cartels. And the pickup had flared stepboards, which the agent testified are often used to conceal narcotics. In the fourth encounter, Agent Alexander Chavez was patrolling on foot at a plaza along the Ohio Turnpike, looking for indications of human smuggling. He walked past several Hispanic men who seemed evasive when he greeted them, but Chavez notably did not approach them then. Instead he walked out to the parking lot, where he eventually saw a large SUV with tinted windows and temporary license tags, all of which fit the profile for a vehicle used in human smuggling. At that point, the men Chavez had seen in the plaza came to him — because the SUV he was looking at was theirs. Only then did Chavez begin questioning them. Thus, the district court did not clearly err in finding that, in each instance, the agent initiated the encounter for reasons other than race.
The Plaintiffs next point to the testimony of their expert, Dr. Kara Joyner, as proof of racial targeting. Joyner analyzed the Sandusky Bay Station’s “apprehension log” for 2008-14, which in her view showed that persons arrested by Sandusky Bay agents were disproportionately citizens of Mexico or of countries in Central and South America. And from that statistical disparity, standing alone, Joyner opined that agents from Sandusky Bay were targeting persons of Hispanic appearance.
The district court found that Joyner’s analysis was unreliable, again for good reason. Joyner’s analysis involved both a numerator and a denominator. The numerator comprised the persons whose arrests were reflected on the apprehension log. About 90 percent of those persons, Joyner said, came from primarily Hispanic countries. The denominator purportedly comprised the “at-risk” population — which Joyner rather vaguely described as “the group that’s likely to elicit reasonable suspicion” from the Border Patrol — in the area of Northern Ohio patrolled by agents from the Sandusky Bay Station. Perhaps one-third of that population, Joyner estimated, was Mexican or Hispanic. Hence Joyner said that Hispanics were overrepresented in the apprehension log.
As the district court explained, however, Joyner’s numerator and denominator alike were seriously flawed. To begin, the numerator measured activity at the wrong point in time. The Plaintiffs claim that Sandusky Bay agents use race in determining whom to approach for an encounter. The apprehension log, in contrast, identifies whom the agents arrested. And for all the record shows here, the proportion of Hispanics approached might have been quite different from the proportion arrested. Joyner’s statistics thus contained precisely the same flaw as the statistical evidence in United States v. Travis, 62 F.3d 170 (6th Cir. 1995). There Travis argued, much like the Plaintiffs do here, that “the ‘incident reports’ compiled by the Airport Police Task [FJorce reveal that officers in the airport have interviewed a disproportionate number of minorities.” Id. at 175. There, we held that “the methodology used to compile these numbers is deeply flawed — so much so that the numbers do not reliably report any data that could give rise to an inference of racial discrimination.” Id. Specifically, we explained, “the ‘incidents’ do not include all consensual encounters between officers and passengers. Officers only report those incidents in which a passenger has been arrested” or where the officer otherwise believed that the person interviewed “was involved with drugs in some capacity.” Id. Nearly the same thing is true here. “Consequently,” we said in Travis, “the statistics do not give a representative picture of the people whom the airport police approach for interviews.” Id. Change “airport [447]*447police” to “Border Patrol,” and again the same is true here. See also Avery, 137 F.3d at 357 (rejecting statistical evidence based on law-enforcement activity at the wrong point in time).
Joyner’s numerator also suffers from a more obvious flaw: her analysis in effect holds the Border Patrol responsible for stops initiated by “Other Agencies.” Specifically, many of the arrests recorded in the apprehension log came after a different law-enforcement agency — say, the local police — initiated the stop and then called the Border Patrol for assistance. Those encounters are plainly irrelevant here, because the Border Patrol did not initiate them. Yet Joyner included them in calculating her “90 percent” figure.
Joyner’s denominator, for its part, is little more than a guess. As an initial matter, and to some extent in Joyner’s defense, the number of undocumented persons present in a particular area is un-disputedly very hard to measure. Here, Joyner cited national and statewide estimates — some purporting to measure the undocumented population, others purporting to measure the “foreign-born” — and then produced an estimate of the “at-risk” population in the swath of Northern Ohio patrolled by agents from Sandusky Bay. But Joyner offered little explanation as to why those national or statewide estimates afforded her a reliable basis to estimate the “at-risk” population in the comparative sliver of territory at issue here. Joyner also overlooked the presence in that territory of large corporate farms that make heavy use of migrant labor. And she overlooked that agents from Sandusky Bay do focus disproportionately on one group: the transient population on Interstates 80 and 90 and at the rest areas along the way, who undisputedly get intensive attention from the Border Patrol — but who got little or none from Dr. Joyner. The district court was correct to discount her testimony as unreliable.
Finally, as evidence of a custom or widespread practice of targeting Hispanics, the Plaintiffs point to testimony and several emails showing that in years past (though as recently as eight years ago) Border Patrol agents at Sandusky Bay and elsewhere used the terms “wets” and “tonks” to refer to persons present in the United States illegally. “Wets,” in particular, is an odious term, being derived from an epithet directed against Mexicans. But at trial all of the agents — including Latino agents— testified that Border Patrol agents used these words as terms of art to refer to undocumented persons generally, rather than Hispanics specifically. And as the Plaintiffs themselves point out, the Border Patrol has acted aggressively, and it appears successfully, to end the usage of these terms by its agents. That the agents used these terms in the past, therefore, is no reason to award injunctive relief now.
Thus, the district court did not clearly err in finding that the Border Patrol did not have the policy alleged here.
* * *
The district court’s judgment is affirmed.
CONCURRENCE