At the EuroBasket 1999, Alvertis seemed ready to lead Greece to its first medal since 1989. After leading the team in offense, with an average of 18.1 points per game in the qualifying round, everything seemed to indicate a great upcoming EuroBasket for the Greek star. Nevertheless, misfortune is part of the game of basketball. A few days before the tournament, Alvertis suffered a severe injury during practice. That injury caused him to not only miss the EuroBasket tournament, but also a major part of the 1999–00 club season. Without its offensive leader, and without key players Nikos Oikonomou and Efthimios Rentzias, who were also injured, Greece finished in an embarrassing sixteenth and last place at the tournament. They consequently failed to qualify for the 2000 Summer Olympics, and were doomed to two years of exclusion from every major tournament.