## 1 Introduction  
The anterior cruciate ligament (ACL) is the most frequently injured of all knee ligaments, with an incidence of 0.7 to 2.5 tears per 1000 athletic exposures in young and athletically active people [1]. The arthroscopic reconstruction of the ruptured ligament (ACLR) remains a gold standard of treatment, especially for patients with functional knee instability, as well as for those wishing to return to cutting and pivoting sports [2]. In the literature, there are a large number of standardized postoperative protocols after ACLR; however, there is still no consensus regarding postoperative physiotherapeutic procedure without the direct supervision of a physiotherapist; this procedure is called unsupervised or partially supervised physiotherapy [3; 4; 5; 6]. Since the 1990s, there has been a general assumption that unsupervised physiotherapy after ACLR produces results equal to those obtained with supervised physiotherapy [7; 8; 9; 10]; however, the assumption has been changing [11; 12].  
The vertical hop is a multi-joint movement task that is commonly used in the clinical environment, and is considered an important dynamic movement in physical activity [13; 14]. The current literature highlights the landing strategies analysis during standardized jump tasks as an interesting assessment tool, and several studies have reported an asymmetric landing pattern among patients after ACLR [15; 16; 17]. One of the qualitative methods for evaluating the lower limbs loading symmetry during landing is the measurement of the vertical compound of the ground reaction forces (vGRF) [18; 19]. The measurements are taken with the use of force plates and are useful for assessing some aspects of dynamic muscle function in clinical settings. This approach is commonly called jumping mechanography [20; 21]. The assessment of the symmetry of the lower limbs in ACL-reconstructed patients is commonly based on the analysis of the percentage difference between the lower limbs or on the basis of the so-called limb symmetry index (LSI). The value of the LSI is being used as one of the criteria for returning to sport activity after ACLR [22; 23]. An abnormal lower limb symmetry in ACL-reconstructed patients, which is characterized by asymmetries between the right and left legs, is defined by a between-limb percentage difference greater than 10% or an LSI lower than 90 [23; 24]. However, some authors suggest using diverse thresholds for different performance tasks [22]. In this context, it seems critical to establish the normative percentage difference and LSI values obtained by healthy individuals for the movement of the task being assessed. What is more, given that bilateral deficits are present after ACLR [25], which may result in a falsely high limb symmetry [26], the symmetry should be analyzed with caution, and the absolute values should be compared to the norm from the matched healthy controls.  
Short-term post-ACL reconstruction alterations in limb symmetry during double-leg vertical jump landing, dependent on postoperative physiotherapy supervision duration, have been reported [27]. The issue seems clinically important, as the altered loading of the knee joint may trigger the development of osteoarthritis, and therefore influence quality of life [13; 28]. Some studies have also suggested that abnormalities in the knee function during dynamic movements may increase the risk of subsequent ipsilateral and contralateral ACL injuries [29; 30; 31]. Nonetheless, it is hard to find any studies evaluating the influence of postoperative physiotherapy supervision on the vertical jump landing between-limb symmetry in a longer follow-up.  
This study investigated whether double-leg and single-leg vertical hop landing between-limb symmetry in males, an average of two years after ACLR, is associated with the duration of postoperative physiotherapy supervision.