PhD V.N. Pritykin
Omsk State Medical University, Omsk

Keywords: basketball, technique, bank shots, ball flight parameters, target/ rebound area parameters, shooting accuracy, teaching aids.

Introduction. Basketball shots to the ring may be classified as the backboard-free shots and bank ones [3]. When choosing an appropriate type of the shot, the shooter needs to have a clear vision the ball flight parameters and hittable target parameters, plus the target area coordinates for both types of basketball throws. The present study was made to follow up the previous study that was designed to find the optimal parameters of the backboard-free throws in basketball [4].

Different guiding methods are widely applied today by training systems in many sport disciplines [1, 2]. Point/ linear visual guides in gymnastics are known to often drive the gymnast to qualitative errors in landing performance, whilst a rectangular-shaped visual guide located on the floor or at specific height was found to help perform support-phase/ flight-phase/ landing-phase movement sequences with high quality [1].

It is the cross-point of the vertical axis and the mathematically calculated  targeting line that will comprise a targeting element within the frame of the target area coordinates calculation method we propose for the bank shots [6]. We completed studies to design new targeting guides in the form of areas to help improve the basketball shooting quality.

Objective of the study was to provide scientific substantiations for a mathematical ball flight modelling method and the relevant hittable target parameters for the bank shots.

Study results and discussion. The mathematical ball flight modelling process for the bank shots is based on calculations of the vertical coordinates of the target/ rebound points and regularities of the target/ rebound point coordinates depending on the shooter’s position on the court.

It is the target areas model for variably directed bank basketball shots that will comprise a product of the mathematical modelling process.

The mathematical modelling process will proceed from the assumption that the ball release point coordinates stay the same for a certain sequence of shots, whilst the ball release process parameters (starting speed, release/ course angles etc.) vary within a limited range to secure the ball coming to the hit target contour. As a result of the modelling process, we obtain a bunch of successful ball flight trajectories forming a curved cone with the ball release point on the top and the hoop-plane-located hit target in its base [4].

Having obtained the ball trajectories of the shooting sequence into the imaginary ring, we will apply the computer modelling tools to calculate the constellation of the successful ball trajectories contact points on the front plane of the backboard that will give us the target areas (see Figure 1).

Figure 1. Targeting guides for the bank shots

1. Interim target parameters:

Far rim area Clear target area within the hoop Near rim area Hit target area Hoop centre

2. Target/ rebound areas:

Rebound area Centre of the rebound area Overlap area Target area Centre of the target area

3. Evolution of the target/ rebound areas for Ek_min and attack angles of 90-15^o

4. Evolution of the target/ rebound areas for Ω_max and attack angles of 90-15^o

5. Evolution of the rebound areas for the attack angles of 90/ 40/ 15^o and the ball release angles of 37-75^o

6. Evolution of the target areas for the attack angles of 90/ 40/ 15^o and the ball release angles of 37-75^o

7. Targeting guides for the bank shots with the shooter’s positions on the arc at the same distance to the target

8. Targeting guides for the bank shots and for the shooter’s positions on the beam with the same attack angle

3, 4, 5, 6 are the cross-points of the coordinate axes with the contour line of the interim hit target on the backboard

Vertical targeting axis

Ω_max rebound areas

Ek_min  rebound areas

Summary

1. Bank shots are interpreted as the backboard-free shots to the imaginary ring with a vertical targeting axis in its centre serving as a main visual targeting guide.

2. Recommended range of the best ball trajectories is in between the economic trajectory Ek_min and the one with the maximum volume angle of the target Ω_max.

3. Contours of the near and far rim are variable as they depend on the shooter’s position coordinates on the court. It should be remembered that the off-the-far-rim shots are much more successful than that off the near rim.

4. Coordinates of the target points and rebound points on the backboard never match, and their constellations for successful shots represent the generally oval-shaped target/ rebound areas, the actual shape varying from a sharp-pointed to sub-circular (or elliptical).

5. Rebound area viewed as an interim hittable target is composed of 3 constituent areas: near rim, far rim and the clear target area within the hoop.

6. Drawn in the target/ rebound areas are the circles that show centres of the relevant areas.

7. The sharper is the shooting angle of the shooter to the backboard plane the higher are the horizontal and vertical coordinates (changed in a non-linear manner) of the target/ rebound areas from the backboard centre to its side, with the shape and size of each area changing.

8. When the shooter’s position on the court is the same, the higher is the ball release angle the more notable are the changes in shapes and sizes of the target/ rebound areas, with the areas positioned one above the other forming what may be called the target/ rebound columns.

9. The shooter will aim to the very centre of the target area, with the ball flight parameters being controlled by the rebound point coordinates that must be within the rebound area.

The same procedure will be applied to obtain constellations of the successful ball trajectory contact point coordinates on the backboard plane that will give us the rebound areas (see Figure 1.1).

The rebound areas may be obtained through the bunch of successful shots to the imaginary ring being crossed by the imaginary backboard plane with the resultant crosscut areas being projected to the front plane of the real backboard (see Figure 1).

Computer modelling tools will be applied to determine three constituent areas and coordinates of the hoop and hit target within the rebound/ target areas (see Figure 1.1). Having drawn the 4-cm circles inside the relevant centres of coordinates, we will obtain the centres of the rebound/ target areas (see Figure 1.2). As one can see on Figure 1, the rebound area covers relatively small portion of the target area.

Coordinates of the target/ rebound areas will depend on the shooter’s position angle to the backboard plan, i.e. the attack/ shooting angle. The sharper is the shooting angle the higher are the horizontal and vertical coordinates (changed in a nonlinear manner) of the target/ rebound areas from the backboard centre to its side, with the shapes and sizes of each area changing (see Figure 1.2, 1.4).

For these areas being used as a key target for the variably directed bank shots, we made an additional geometric plotting with the relevant modifications of the target/ rebound areas. Having selected the attack angle at first, we then will apply the computer modelling tools to calculate and plot the target/ rebound areas for the specific ball release point (for example, for α₀ = 51° (Ek_min), see Figure 1, Summary 2). Having obtained coordinates of the geometric centres of the hoop and hit target within the target area, we will place a 4-cm circle inside the constellation of these points to mark the centre of the target area. Let us then highlight the overlap area with violet colour (see Figure 1.2), followed by the lower contour of the target area being removed.

Then we will plot the target/ rebound areas for the same attack angle and the ball release angle of α₀ = 60° (Ω_max). The modified targets will be placed on the front plane of the backboard one above the other and then we will draw lines parallel to the backboard sides through the sides of the oval-shaped contours of the rebound areas (see Figure 1.8).

When the shooter’s position coordinates on the court are the same, the higher is the ball release angle the more notable are the changes in shapes and sizes of the target/ rebound areas, with the areas positioned one above the other forming a sort of target (see Figure 1.6) and rebound (see Figure 1.5) columns.

The targeting guides will be located on the front plane of the transparent backboard and applied together with the vertical targeting axis.

When special stations on the court are designed for the shooting skills mastering/ excelling by the basketball players, the following two approaches will be applied:

ü  The stations will be deployed on the panels of a movable shooting module [5] that offers a set of shooting positions evenly placed around the backboard, with the position distances to the hoop being the same (see Figure 1.7).

ü  Stations on the main panels will offer six directions for the shooter’s movement, with the shooting distance being varied whilst the attack angle stays the same (see Figure 1.8). Shot direction in this context will be defined as the vertical plane of the ball centre movement from the ball release point along the vertical targeting axis. We offer using special marks in the three-second rectangular zone to facilitate the ball throw direction being instantly selected in the training process and in game (see Figure 1.8).

Given hereunder is a graphical presentation of the case calculation and geometric plotting results for the Shooter’s Position #5 with the relevant optimal ball release range (see Figure 2a, 2b).

Conclusion. The mathematical modelling method in application to the successful ball flight trajectories gives the means to model a set of targeting guides to facilitate the bank shooting skills being mastered and excelled to improve the competitive game success rates of the players.

References

1. Kravchuk A.I. Metodika sovershenstvovaniya navykov prizemleniya (Landing skills development methods) / A.I. Kravchuk, G.D. Babushkin: Method. recombinations: Col. Inf. and method. materials of the Sports Committee of the RSFSR: Method. office), 1978, №56. -18 p.
2. Kravchuk A.I. Fizicheskoe vospitanie detey rannego i doshkol'nogo vozrasta (Physical education of infants and preschool / A.I. Kravchuk: Monograph. – V. 2,3. - Novosibirsk: NSPU pub. h-se, 1998. – P. 46.
3. Morozova N.S. Povyshenie tochnosti basketbol'nykh broskov s otrazheniem myacha ot shchita: dis.… kand. ped. nauk (Improving the accuracy of basketball backboard shots: PhD thesis). – Omsk, 2009. – 158 p.
4. Pritykin V.N. Basketbol'ny brosok bez otrazheniya myacha ot shchita (basketball backboard-free shot) // Teoriya i praktika fizicheskoy kultury. – 2015. – №11. – P. 69 – 72.
5. Pritykin V.N., Bokov I.S., Petrushov I.V. Metod opredeleniya koordinat tochek otrazheniya myacha ot basketbol'nogo shchita (Method of determination of backboard ball touch point coordinates) // Sovremennye problemy nauki i obrazovaniya. – 2015. – № 4; URL: www.science-education.ru/127-21160 (date of access: 09.09.2015).
6. Pritykin V.N. Organizatsionnaya struktura kompleksnykh metodik tekhniko-takticheskoy podgotovki v basketbole (Organizational structure of integrated technical and tactical training technologies in basketball) / V.N. Pritykin, N.S. Morozova, S.V. Sukharev // Teoriya i praktika fizicheskoy kultury. – 2009. – № 2. – P. 38–41.

Corresponding author: osma_fk@mail.ru

Abstract

The article presents results of a mathematical modelling of the ball shooting parameters intended to put together targeting guides for the bank shots. It was demonstrated by the study that the target point coordinates never match with those of the rebound points, with constellations of these points for successful shots forming oval-shaped target/ rebound areas, the actual shape varying from a sharp-pointed to sub-circular (or elliptical) depending on the ball release process parameters and the player’s position coordinates in relation to the backboard. The study also shows that the bank shots may be interpreted as the backboard-free shots in an imaginary ring with a vertical targeting axis in the centre serving as a main visual targeting guide for the shooter. The rebound areas duplicating the hit targets within the hoop plane are composed of three constituent areas: the near rim, far ream and the clear target area. The sharper is the shooting/ attack angle (of the shooter’s position to the backboard plane) the higher are the horizontal and vertical coordinates (changed in a nonlinear manner) of the target/ rebound areas from the backboard centre to its side, with the shape and size of each area changing. When the shooter’s position on the court is the same, the higher is the ball release angle the more notable are the changes in the shape and size of the target/ rebound areas, with the areas positioned one above the other forming what may be called the target/ rebound columns. The shooter will aim to the very centre of the target area, with the ball flight parameters being controlled by the rebound point coordinates that must be within the rebound area.