Most people hear this in one form or another at some point in their life, especially those kids who play basketball.
Even videos of white guys who have excellent jumping ability stress the fact that they are white — "A true white kid that can jump" (YouTube).
So is it really true? Scientifically speaking, on a bell curve of the vertical of all black people and all white people, would the peak of the curve be higher for black people than for white people?
According to Relationship between vertical jump and maximal power output of legs and arms: Effects of ethnicity and sport Scandinavian Journal of Medicine & Science in Sports Volume 25, April 2015, Pages e197–e207 :
The hypothesis that ethnicity and sport practice influence the relationship between maximal power in cycling (Pmax) and countermovement jump (CMJ) has been studied by relating CMJ and Pmax in two groups (volleyball players, VB, and physical education students, PES) including subjects with Caucasian (67 C) or West African (39 WA) origins.
...
Within WA, CMJ was significantly higher in VB (0.732 ± 0.057 m) than in PES (0.661 ± 0.082 m), although there was no difference in Pmax (14.7 ± 1.7 vs 14.7 ± 1.9 W/kg). CMJ was significantly higher in WA (0.69 ± 0.08 vs 0.65 ± 0.09 m in C, P = 0.002) .
In other words, the study is saying that West Africans jump, on average, 4 centimeters higher than Caucasians, and that this is a significant result.
Influence of ethnic origin on predictive parameters of performance in sprint running in prepubertal boys. International Journal of Sports Medicine 2005 Nov;26(9):798-802 finds that Afro-Caribbean boys jump vertically 36.77cm versus only 31.12 cm for Caucasians.
See also Leg muscle power in 12-year-old black and white Tunisian football players Research in Sports Medicine 2011 Apr; 19(2):103-17 :
A total of 113 children (white group (WG) = n = 56; black group (BG) = n = 57) participated in this investigation. ...jump and sprint performances of the BG were significantly higher than the WG
See also Racial/ethnic variation in the motor development and performance of American children Canadian Journal of Sports Sciences 1988 Jun;13(2):136-43:
Black children of school age, particularly boys, perform consistently better than White and Mexican-American children in running speed (dashes) and the vertical jump
African Americans in Sports: Contemporary Themes cites to the above reference and states:
In general the literature suggests that African American children, particularly males, perform better on average in sprinting and jumping tasked (vertical and broad jump) than do Caucasian children
This is a great article that goes through the truths & myths regarding African American athletes and their domination of many sports including football, basketball and more. It can be found on page 183 of the book "African Americans in sport: contemporary themes" By Gary Alan Sailes
Summary:
The African-American Athlete: Social Myths and Stereotypes by Gary A. Sailes, Indiana University
This essay notes the domination of African American athletes and discusses the attempts to explain the successes that have resulted in racial myths and stereotypes.
Again, the author reviews the history of African American participation in sport, this time adding the history of the “dumb jock” stereotype. The author also reviews two distinct stereotypes that have emerged regarding African American males—the “brute” and the “sambo.” The brute depicts the African American male as primitive, temperamental, overreactive, uncontrollable, violent and sexually powerful, intentionally separating the African American from intellectualism and mental abilities. The sambo depicts the African American male as benign, childish, immature, lazy, comical, fun-loving, impulsive, good-humored, inferior and loveable, a stereotype that the author says has its roots in American slavery. The author notes that the Harlem Globetrotters were criticized in the late 1970s for perpetuating the sambo stereotype.
The author discusses the belief, which was quite popular in mainstream media in the late 1980s, that African American athletes are physically superior to white athletes. The theory says that this superiority is genetic, giving Blacks an advantage over their white counterparts. The author then reviewed the common theories, dispelling each one as myth.
(emphasis added, source)
Google Book result in above link may or may not be available
The TV show The Nature of Things on CBC this week talked about man's (homo sapiens) evolutionary adaptations, which make us long-distance runners (able to run down animals until they have to stop from heat exhaustion - suggested we ought to be called 'homo cursor', "running man", instead).
Part of that show mentioned the first Ethiopian who won an Olympic gold medal for running: barefoot.
The show then took us to modern Ethiopia.
The people who do well (as runners) there come from similar backgrounds: really really poor (and, motivated). The fact that children of poor farmers don't wear shoes was asserted to be one of the reasons why they're stronger runners as adults.
If nature (e.g. 'black' or 'white' skin) might be a part of it, so might nurture.
Also this program wasn't talking about "the average": it was talking about athletes, and elite athletes at that.
This doesn't answer your question, which is explicitly about the average: but maybe that's the wrong question. "White men can't jump" might be more of a statement about elite athletes (e.g. the NBA) than about the average.
although there's nothing wrong with it scientificallywrong with it, scientifically, is the distinction of 2 colors - white and black - which doesn't fit. People aren't black, and less so white.