# Prognostic Validity of Statistical Prediction Methods Used for Talent Identification in Youth Tennis Players Based on Motor Abilities

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## Abstract

**:**

_{♀}= 62 and n

_{♂}= 112) at the age of eight years (U9) were examined using five physical fitness tests and four motor competence tests. Based on the test results, four predictions regarding the individual future performance were made for each participant using a linear recommendation score, a logistic regression, a discriminant analysis, and a neural network. These forecasts were then compared with the athletes’ achieved performance success at least four years later (U13‒U18). (3) Results: All four prediction methods showed a medium-to-high prognostic validity with respect to their forecasts. Their values of relative improvement over chance ranged from 0.447 (logistic regression) to 0.654 (tennis recommendation score). (4) Conclusions: However, the best results are only obtained by combining the non-linear method (neural network) with one of the linear methods. Nevertheless, 18.75% of later high-performance tennis players could not be predicted using any of the methods.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. General Study Design

#### 2.2. Participants

_{♀}= 62 female and n

_{♂}= 112 male athletes. The mean age of the participants was 156 ± 16 months (min = 132, max = 206). All tennis players were club players who actively participated in club matches and tournaments.

#### 2.3. Tennis Success

_{♂}= 11, n

_{♀}= 5). In the group of low performers, 158 tennis players with only average performance were identified. These players were unable to perform beyond local and regional successes and at no time fulfilled the necessary requirements to obtain a national ranking. Finally, this group of low performers comprised n = 57 female tennis players and n = 101 male tennis players.

#### 2.4. Anthropometric Characteristics and Motor Abilities at U9

#### 2.4.1. 20 m Sprint (SP)

#### 2.4.2. Sideward Jumping (SJ)

#### 2.4.3. Balancing Backwards (BB)

#### 2.4.4. Standing Bend Forward (SBF)

#### 2.4.5. Push-Ups (PU)

#### 2.4.6. Sit-Ups (SU)

#### 2.4.7. Standing Long Jump (SLJ)

#### 2.4.8. Ball Throw (BT)

#### 2.4.9. Six min Endurance Run (ER)

_{general}= 0.85. The objectivity of the test battery is r

_{obj}= 0.95 (range: 0.87–0.99). However, the validity of the test procedures has not yet been sufficiently verified. While Bös et al. [37] have focused primarily on content-logical validity and mainly used expert ratings (expert rating: M = 1.83; with grades from 1 to 5), other authors have used correlations to check the criterion-related validity or confirmatory factor analyses to determine construct validity [40]. For most of the individual tests, sufficient to very good test validity can be attested to for the latter two validity categories (r

_{validity}= 0.69). Thus far, there are no major studies on prognostic validity.

#### 2.5. Statistical Analyses

#### 2.5.1. Prediction Methods

#### 2.5.2. Tennis-Specific Recommendation Score

_{TRS}is comparable to a normal z-value. Thus, also here, a value of z

_{TRS}= 0 indicates average suitability. In order not only to give a general tennis recommendation (z

_{TRS}> 0) but also to predict future top performers, it is necessary to define a suitable threshold value, above which a participant is assigned to the group of potential top performers. Sensitivity and specificity can thus be determined using the selected threshold value, e.g., z

_{TRS}= 1.3. In this example, the chosen z-value of z

_{TRS}= 1.3 corresponds to a selection rate of 10%, which is close to the observed percentage of top performers in this sample (16/174 = 10.875%). Thus, using this method, participants with z

_{TRS}≥ 1.3 were automatically predicted to be top performers, and participants with z

_{TRS}< 1.3 were predicted to be low performers.

#### 2.5.3. Binary Logistic Regression Analysis

_{cut}= 0.5 by default for these analyses. This means that, with an individual output value of u

_{cut}≥ 0.5, the participant was recommended as a top performer. In order to represent a valid and also practical result, the logistic regression was performed as a k-fold cross-validation (k = 5), and this procedure was repeated five times. The results of the 25 individual analyses were ultimately averaged.

#### 2.5.4. Discriminant Analysis

#### 2.5.5. Neural Network Analysis

#### 2.5.6. Prognostic Validity of the Analyses

_{RIOC}). This value determines the relative hit accuracy. In most analyses, a maximum hit rate of 100% cannot be achieved. This can lead to a misinterpretation of the validity parameters (e.g., phi or kappa; [34]). The RIOC index avoids this problem by calculating the actual hit rate in relation to the potential maximum hit rate (see Formula (10)).

_{RIOC}≤ 1, but it can also have negative values. With a value of x

_{RIOC}= 0.33, the classification is considered good. Above 0.66 is considered very good [53]. Using this calculation scheme, the four methods can be directly compared and evaluated independent of their actual selection rates. The real selection rate for talent diagnostics and, thus, also the maximum hit rate, always depends on the talent campaigns and support programs of the participating countries, and therefore, this selection rate can vary considerably in practice.

_{1}score were also ways to evaluate the predictive power of an analytical method (Formula (12)). The F

_{1}score is based on the harmonic mean, and its calculation is equally divided between sensitivity (recall) and positive predictive value (precision). It can take values between 0 and 1, where 1 stands for the maximum predictive strength. In contrast to Youden’s J, which includes sensitivity and specificity in equal measure, the focus here is on the predictive power of true-positive cases.

#### 2.5.7. Classification of Individual Tennis Players

## 3. Results

#### 3.1. Test Performance

#### 3.2. Test Quality Parameters of the Prediction Methods

#### 3.2.1. Tennis Recommendation Score

_{TRS}= 1.3, 12 of the 16 later top performers (75%) were true-positives (sensitivity). One hundred and thirty-one participants (82.9%) who did not reach the top level were also correctly classified as low performers, that is, true negatives (specificity). In total, 143 of 174 (82.2%) children could be correctly identified as later top or low performers via this linear method. If the talent forecasts with the same prediction rate (22.4%) were expressed at random, only 4, as compared with 12, of the top performers and 122, as compared with 131, of the low performers would be correctly predicted, and the overall prediction quality would only be 72.4%, as compared with the value of 82.2% described above. If the percentage values for sensitivity and specificity were considered in combination, the benefit is more obvious. With a cutoff limit value of z

_{TRS}= 1.3, the Youden Index amounts to a total of 157.9% (75% + 82.9%), thus representing a 57.9% improvement as compared with a random drawing. The Area Under ROC Curve was 0.852 (standard error = 0.048; 95% confidence interval: min = 0.759, max = 0.946).

#### 3.2.2. Logistic Regression

#### 3.2.3. Discriminant Analysis

#### 3.2.4. Neural Network Analysis

#### 3.3. Prognostic Validity of the Prediction Methods

_{1}= 0.437 in terms of the F

_{1}score, which is probably related to its low positive predictive value (30.8%). Among the four methods, the MLP performs best here, with F

_{1}= 0.462. This is not surprising because it has the highest sensitivity and also a high positive predictive value (33.3%). The RIOC values show values above 44% for all methods, with the MLP reaching the highest value of 68.1%. If, for example, a method would correctly predict the performance of another person, the RIOC value can increase between 1% and 8% depending on the performance group and method. Thus, another correct top performer prediction would increase the RIOC value of discriminant analysis from 58.8% to almost 67%.

_{1}score is very low at 42%, which is due to the low positive predictive value. Looking at the intersection of the predictions of the three classification methods, TRS, MLP, and DA (see also Figure 3), the sensitivity reaches a value of 68.8% and the specificity a value of 88.7%. Due to the higher positive predictive value (0.393), the F

_{1}score (0.5) is the highest among all analysis methods and combinations. Youden’s J reaches a value of 57.5%, and the RIOC value is 62.4%. A combination of the other analysis methods showed no significant improvements of the results.

#### 3.4. Classification of Individual Tennis Players

## 4. Discussion

_{1}score, and RIOC value [57]. All three variables provide a prediction of the validity of prognostic methods. However, the RIOC value has an advantage in that it measures the accuracy of the method used on the basis of the maximum possible accuracy. Thus, the selection rate has almost no influence on the calculation, and therefore, different methods with different selection rates can be better compared. It makes sense to not always consider a method only in relation to a random result (J = 0) but to also include the maximum possible result. In the example of logistic regression, the Youden Index reaches a theoretical maximum of J = 0.75. However, the TRS could reach a value of up to 85.4% with the existing selection rate. This is 10% above the maximum potential J for logistic regression. A direct comparison of the two values is therefore sometimes difficult.

_{RIOC}= 0.544 and J = 0.432, which are comparable with the results achieved here. Nevertheless, with the addition of the in-game performance (odds ratio = 12.5*) and familial support (odds ratio = 5.2*) survey parameters, a significantly higher prognostic validity is revealed for the predictions. Thus, in the study described [56], RIOC values could be significantly increased by about 20–35%, and Youden’s J could be increased by about 20‒30%.

_{1}score (0.5 for intersection of TRS, MLP, and DA) or the highest RIOC value (0.741 for the union set of TRS and MLP) among all analysis options.

_{TRS}= 1.0 versus z

_{TRS}= 1.3) to separate top and low performers makes a large difference in sensitivity and specificity. The summation of both values (overall benefit) varies between 100% (Youden’s J = 0) and 157.9% (Youden’s J = 0.579). The same applies to the separation parameters of the other three methods. Further studies are required to be able to make a more precise statement about this. Additionally, in the analyses, the selection rate fluctuates between 7.2% and 36.1%. Although this difference has no mathematical relevance for prognostic validity due to the use of the RIOC value, an approximation of the selection rate could provide more information about prediction calculations, and differences could then be shown on a classification map (Figure 3).

_{1}values of up to 0.729 were found. A comparison between random forests and classical methods or other neural network solutions (e.g., radial basis functions) would be interesting for future studies.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 2.**Discriminant analysis to predict later U13‒U17 tennis performance group based on initial performances (U9; each full symbol represents ten children).

Sex | Age | TP | Height | Weight | SP | SJ | BB | SBF | PU | SU | SLJ | BT | ER |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

1 | 97 | 1 | 132 | 27.3 | 4.21 | 33 | 38 | 4 | 17 | 23 | 153 | 19 | 1078 |

0 | 94 | 0 | 129 | 27.3 | 4.45 | 27 | 30 | –2 | 14 | 19 | 135 | 14 | 959 |

Predicted/Recommended | ||||
---|---|---|---|---|

Low Performer | Top Performer | ∑ | ||

Observed/Existing | Top Performer | C | A | A + C |

Low Performer | D | B | B + D | |

∑ | C + D | A + B | A + B + C + D |

**Table 3.**Descriptive statistics for the two anthropometric, five physical fitness, and four motor competence diagnostics of the U9 participants.

Variables | Groups | N | M | SD | SE | 95% CL | Min | Max | |
---|---|---|---|---|---|---|---|---|---|

LL | UL | ||||||||

Calendar age * (month) (Time of testing; U9) | LP | 158 | 93.8 | 5.0 | 0.39 | 93.0 | 94.6 | 83 | 110 |

TP | 16 | 97.5 | 6.4 | 1.60 | 94.1 | 100.9 | 88 | 112 | |

Test results | |||||||||

Body height * (cm) | LP | 158 | 129.1 | 5.7 | 0.45 | 128.2 | 130.0 | 117 | 145 |

TP | 16 | 132.3 | 4.5 | 1.13 | 129.8 | 134.7 | 127 | 143 | |

Body weight (kg) | LP | 158 | 27.2 | 4.1 | 0.33 | 26.6 | 27.9 | 20.0 | 39.3 |

TP | 16 | 27.3 | 1.9 | 0.48 | 26.3 | 28.3 | 23.4 | 30.6 | |

Sideward jumping ** (repeats) | LP | 157 | 27.3 | 6.1 | 0.49 | 26.3 | 28.2 | 6.5 | 40.5 |

TP | 16 | 33.0 | 5.1 | 1.27 | 30.3 | 35.7 | 27.0 | 45.0 | |

Balance backward ** (steps) | LP | 158 | 30.3 | 8.5 | 0.67 | 28.9 | 31.6 | 8 | 48 |

TP | 16 | 38.3 | 5.7 | 1.42 | 35.2 | 41.3 | 28 | 48 | |

Standing long jump ** (cm) | LP | 157 | 135.1 | 16.2 | 1.30 | 132.5 | 137.6 | 82 | 190 |

TP | 16 | 153.0 | 17.2 | 4.30 | 143.8 | 162.2 | 125 | 178 | |

20 m sprint * (s) | LP | 158 | 4.45 | 0.36 | 0.03 | 4.39 | 4.51 | 3.10 | 5.32 |

TP | 16 | 4.21 | 0.34 | 0.08 | 4.03 | 4.39 | 3.50 | 4.72 | |

Push-ups * (repeats) | LP | 158 | 14.6 | 3.6 | 0.28 | 14.0 | 15.1 | 4 | 24 |

TP | 16 | 17.1 | 5.2 | 1.30 | 14.3 | 19.9 | 9 | 25 | |

Sit-ups * (repeats) | LP | 158 | 19.2 | 5.1 | 0.40 | 18.4 | 20.0 | 2 | 30 |

TP | 16 | 23.4 | 4.1 | 1.02 | 21.3 | 25.6 | 15 | 29 | |

Bend forward (cm) | LP | 158 | 1.98 | 5.94 | 0.47 | 1.05 | 2.92 | −11 | 18 |

TP | 16 | 4.16 | 4.90 | 1.22 | 1.55 | 6.77 | −10 | 12 | |

6 min run ** (m) | LP | 154 | 959 | 130.8 | 10.5 | 938 | 979 | 545 | 1259 |

TP | 16 | 1078 | 80.7 | 20.2 | 1035 | 1121 | 891 | 1200 | |

Ball throw ** (m) | LP | 155 | 13.5 | 4.03 | 0.32 | 12.9 | 14.2 | 3.8 | 27.6 |

TP | 16 | 18.8 | 5.35 | 1.34 | 15.9 | 21.6 | 9.2 | 28.3 |

Tennis Recommendation Score (z _{TRS} = 1.3) | Predicted/Recommended | |||
---|---|---|---|---|

Low Performer | Top Performer | Percentage Correct | ||

Top Performer | 4 | 12 | 75% | |

Observed/Existing | Low Performer | 131 | 27 | 82.9% |

Percentage (total) | 77.6% | 22.4% | 82.2% |

(Binary) Logistic Regression ^{1} | Predicted/Recommended | |||
---|---|---|---|---|

Low Performer | Top Performer | Percentage Correct | ||

Top Performer | 10 | 6 | 37.5% | |

Observed/Existing | Low Performer ^{2} | 144 | 6 | 96% |

Percentage (total) | 92.8% | 7.2% | 90.4% |

^{1}A 5-fold cross-validation was performed a total of five times, and the results were averaged. For a better evaluation of the results, the average values were multiplied by five.

^{2}Eight children could not perform at least one test, so they were excluded from this analysis.

Multilayer Perceptron ^{1} | Predicted/Recommended | |||
---|---|---|---|---|

Low Performer | Top Performer | Percentage Correct | ||

Top Performer | 4 | 12 | 75% | |

Observed/Existing | Low Performer ^{2} | 126 | 24 | 84% |

Percentage (total) | 78.3% | 21.7% | 91% |

^{1}A 5-fold cross-validation was performed a total of five times, and the respective test results were averaged.

^{2}Eight children could not perform at least one test, so they were excluded from this analysis.

Recommendation Score | (Binary) Logistic Regression | Linear Discriminant Analysis | Multilayer Perceptron | |
---|---|---|---|---|

Sensitivity | 0.750 | 0.375 | 0.688 | 0.750 |

Specificity | 0.829 | 0.960 | 0.807 | 0.840 |

Selection Rate | 0.224 | 0.072 | 0.241 | 0.217 |

Positive Predictive Value | 0.308 | 0.500 | 0.275 | 0.333 |

Negative Predictive Value | 0.970 | 0.935 | 0.960 | 0.969 |

Random Hit Rate | 0.725 | 0.845 | 0.709 | 0.729 |

Hit Rate | 0.822 | 0.904 | 0.795 | 0.831 |

Maximum Hit Rat | 0.868 | 0.976 | 0.855 | 0.880 |

Youden’s J | 0.579 | 0.320 | 0.495 | 0.590 |

F_{1} score | 0.437 | 0.429 | 0.393 | 0.462 |

RIOC Value | 0.678 | 0.447 | 0.588 | 0.681 |

Probability of Being a Top Performer (%) | ||||
---|---|---|---|---|

Recommendation Score | Logistic Regression | Discriminant Analysis | Multilayer Perceptron | |

Top Performer 1 | 99 | 90 | 99 | 99 |

Top Performer 2 | 97 | 86 | 98 | 97 |

Top Performer 3 | 93 | 68 | 97 | 96 |

Top Performer 4 | 96 | 71 | 96 | 90 |

Top Performer 5 | 83 | 64 | 95 | 90 |

Top Performer 6 | 89 | 68 | 90 | 95 |

Top Performer 7 | 91 | 15 | 68 | 71 |

Top Performer 8 | 79 | 33 | 85 | 88 |

Top Performer 9 | 55 | 7 | 65 | 70 |

Top Performer 10 | 66 | 18 | 63 | 68 |

Top Performer 11 | 57 | 9 | 58 | 68 |

Top Performer 12 | 67 | 16 | 41 | 32 |

Top Performer 13 | 44 | 3 | 23 | 52 |

Top Performer 14 | 40 | 5 | 24 | 37 |

Top Performer 15 | 20 | 2 | 9 | 29 |

Top Performer 16 | 33 | 1 | 1 | 15 |

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## Share and Cite

**MDPI and ACS Style**

Siener, M.; Faber, I.; Hohmann, A. Prognostic Validity of Statistical Prediction Methods Used for Talent Identification in Youth Tennis Players Based on Motor Abilities. *Appl. Sci.* **2021**, *11*, 7051.
https://doi.org/10.3390/app11157051

**AMA Style**

Siener M, Faber I, Hohmann A. Prognostic Validity of Statistical Prediction Methods Used for Talent Identification in Youth Tennis Players Based on Motor Abilities. *Applied Sciences*. 2021; 11(15):7051.
https://doi.org/10.3390/app11157051

**Chicago/Turabian Style**

Siener, Maximilian, Irene Faber, and Andreas Hohmann. 2021. "Prognostic Validity of Statistical Prediction Methods Used for Talent Identification in Youth Tennis Players Based on Motor Abilities" *Applied Sciences* 11, no. 15: 7051.
https://doi.org/10.3390/app11157051