Asymptotically Optimum Estimation of a Probability in Inverse Binomial Sampling under General Loss Functions

The optimum quality that can be asymptotically achieved in the estimation of a probability p using inverse binomial sampling is addressed. A general definition of quality is used in terms of the risk associated with a loss function that satisfies certain assumptions. It is shown that the limit superior of the risk for p asymptotically small has a minimum over all (possibly randomized) estimators. This minimum is achieved by certain non-randomized estimators. The model includes commonly used quality criteria as particular cases. Applications to the non-asymptotic regime are discussed considering specific loss functions, for which minimax estimators are derived.

Automatic Categorization for Improving Spanish into Spanish Sign Language Machine Translation

This paper describes a preprocessing module for improving the performance of a Spanish into Spanish Sign Language (Lengua de Signos Espanola: LSE) translation system when dealing with sparse training data. This preprocessing module replaces Spanish words with associated tags. The list with Spanish words (vocabulary) and associated tags used by this module is computed automatically considering those signs that show the highest probability of being the translation of every Spanish word. This automatic tag extraction has been compared to a manual strategy achieving almost the same improvement. In this analysis, several alternatives for dealing with non-relevant words have been studied. Non-relevant words are Spanish words not assigned to any sign. The preprocessing module has been incorporated into two well-known statistical translation architectures: a phrase-based system and a Statistical Finite State Transducer (SFST). This system has been developed for a specific application domain: the renewal of Identity Documents and Driver's License. In order to evaluate the system a parallel corpus made up of 4080 Spanish sentences and their LSE translation has been used. The evaluation results revealed a significant performance improvement when including this preprocessing module. In the phrase-based system, the proposed module has given rise to an increase in BLEU (Bilingual Evaluation Understudy) from 73.8% to 81.0% and an increase in the human evaluation score from 0.64 to 0.83. In the case of SFST, BLEU increased from 70.6% to 78.4% and the human evaluation score from 0.65 to 0.82.

Optimized edge appearance probability for cooperative localization based on tree-reweighted nonparametric belief propagation

Nonparametric belief propagation (NBP) is a well-known particle-based method for distributed inference in wireless networks. NBP has a large number of applications, including cooperative localization. However, in loopy networks NBP suffers from similar problems as standard BP, such as over-confident beliefs and possible nonconvergence. Tree-reweighted NBP (TRW-NBP) can mitigate these problems, but does not easily lead to a distributed implementation due to the non-local nature of the required so-called edge appearance probabilities. In this paper, we propose a variation of TRWNBP, suitable for cooperative localization in wireless networks. Our algorithm uses a fixed edge appearance probability for every edge, and can outperform standard NBP in dense wireless networks.

Metabolic risk score indexes validation in overweight healthy people

The constellation of adverse cardiovascular disease (CVD) and metabolic risk factors, including elevated abdominal obesity, blood pressure (BP), glucose, and triglycerides (TG) and lowered high-density lipoprotein-cholesterol (HDL-C), has been termed the metabolic syndrome (MetSyn) [1]. A number of different definitions have been developed by the World Health Organization (WHO) [2], the National Cholesterol Education Program Adult Treatment Panel III (ATP III) [3], the European Group for the Study of Insulin Resistance (EGIR) [4] and, most recently, the International Diabetes Federation (IDF) [5]. Since there is no universal definition of the Metabolic Syndrome, several authors have derived different risk scores to represent the clustering of its components [6-11].

Score optimization and template updating in a biometric technique for authentication in mobiles based on gestures

This article focuses on the evaluation of a biometric technique based on the performance of an identifying gesture by holding a telephone with an embedded accelerometer in his/her hand. The acceleration signals obtained when users perform gestures are analyzed following a mathematical method based on global sequence alignment. In this article, eight different scores are proposed and evaluated in order to quantify the differences between gestures, obtaining an optimal EER result of 3.42% when analyzing a random set of 40 users of a database made up of 80 users with real attempts of falsification. Moreover, a temporal study of the technique is presented leeding to the need to update the template to adapt the manner in which users modify how they perform their identifying gesture over time. Six updating schemes have been assessed within a database of 22 users repeating their identifying gesture in 20 sessions over 4 months, concluding that the more often the template is updated the better and more stable performance the technique presents.

Estimation of a probability in inverse binomial sampling under normalized linear-linear and inverse-linear loss

Sequential estimation of the success probability p in inverse binomial sampling is considered in this paper. For any estimator pˆ , its quality is measured by the risk associated with normalized loss functions of linear-linear or inverse-linear form. These functions are possibly asymmetric, with arbitrary slope parameters a and b for pˆ

p , respectively. Interest in these functions is motivated by their significance and potential uses, which are briefly discussed. Estimators are given for which the risk has an asymptotic value as p→0, and which guarantee that, for any p∈(0,1), the risk is lower than its asymptotic value. This allows selecting the required number of successes, r, to meet a prescribed quality irrespective of the unknown p. In addition, the proposed estimators are shown to be approximately minimax when a/b does not deviate too much from 1, and asymptotically minimax as r→∞ when a=b.

Intermittency reinjection probability density function with and without noise effects.

Intermittency phenomenon is a continuous route from regular to chaotic behaviour. Intermittency is an occurrence of a signal that alternates chaotic bursts between quasi-regular periods called laminar phases, driven by the so called reinjection probability density function (RPD). In this paper is introduced a new technique to obtain the RPD for type-II and III intermittency. The new RPD is more general than the classical one and includes the classical RPD as a particular case. The probabilities of the laminar length, the average laminar lengths and the characteristic relations are determined with and without lower bound of the reinjection in agreement with numerical simulations. Finally, it is analyzed the noise effect in intermittency. A method to obtain the noisy RPD is developed extending the procedure used in the noiseless case. The analytical results show a good agreement with numerical simulations.

Estimation of a probability in inverse binomial sampling under normalized linear-linear and inverse-linear loss

Sequential estimation of the success probability $p$ in inverse binomial sampling is considered in this paper. For any estimator $\hatvap$, its quality is measured by the risk associated with normalized loss functions of linear-linear or inverse-linear form. These functions are possibly asymmetric, with arbitrary slope parameters $a$ and $b$ for $\hatvap < p$ and $\hatvap > p$ respectively. Interest in these functions is motivated by their significance and potential uses, which are briefly discussed. Estimators are given for which the risk has an asymptotic value as $p \rightarrow 0$, and which guarantee that, for any $p \in (0,1)$, the risk is lower than its asymptotic value. This allows selecting the required number of successes, $\nnum$, to meet a prescribed quality irrespective of the unknown $p$. In addition, the proposed estimators are shown to be approximately minimax when $a/b$ does not deviate too much from $1$, and asymptotically minimax as $\nnum \rightarrow \infty$ when $a=b$.

An interactive method of fuzzy probability elicitation in risk analysis

Expert knowledge is used to assign probabilities to events in many risk analysis models. However, experts sometimes find it hard to provide specific values for these probabilities, preferring to express vague or imprecise terms that are mapped using a previously defined fuzzy number scale. The rigidity of these scales generates bias in the probability elicitation process and does not allow experts to adequately express their probabilistic judgments. We present an interactive method for extracting a fuzzy number from experts that represents their probabilistic judgments for a given event, along with a quality measure of the probabilistic judgments, useful in a final information filtering and analysis sensitivity process.

Survival probability of round and tape tethers against debris impact

The current space environment, consisting of manmade debris and micrometeoroids, poses a risk to safe operations in space, and the situation is continuously deteriorating due to in-orbit debris collisions and to new satellite launches. Bare electrodynamic tethers can provide an efficient mechanism for rapid deorbiting of satellites from low Earth orbit at end of life. Because of its particular geometry (length very much larger than cross-sectional dimensions), a tether may have a relatively high risk of being severed by the single impact of small debris. The rates of fatal impact of orbital debris on round and tape tethers of equal length and mass, evaluated with an analytical approximation to debris flux modeled by NASA’s ORDEM2000, shows much higher survival probability for tapes. A comparative numerical analysis using debris flux model ORDEM2000 and ESA’s MASTER2005 validates the analytical result and shows that, for a given time in orbit, a tape has a probability of survival of about one and a half orders of magnitude higher than a round tether of equal mass and length. Because deorbiting from a given altitude is much faster for the tape due to its larger perimeter, its probability of survival in a practical sense is quite high.

Analysis of the influence of the different variables involved in a damage progression probability model

Motivated by these difficulties, Castillo et al. (2012) made some suggestions on how to build consistent stochastic models avoiding the selection of easy to use mathematical functions, which were replaced by those resulting from a set of properties to be satisfied by the model.

Effects of coaches' timeouts on basketball teams' offensive and defensive performances according to momentary differences in score and game period.

The aim of the present study was to assess the effects of game timeouts on basketball teams? offensive and defensive performances according to momentary differences in score and game period. The sample consisted of 144 timeouts registered during 18 basketball games randomly selected from the 2007 European Basketball Championship (Spain). For each timeout, five ball possessions were registered before (n?493) and after the timeout (n?475). The offensive and defensive efficiencies were registered across the first 35 min and last 5 min of games. A k-means cluster analysis classified the timeouts according to momentary score status as follows: losing ( ?10 to ?3 points), balanced ( ?2 to 3 points), and winning (4 to 10 points). Repeated-measures analysis of variance identified statistically significant main effects between pre and post timeout offensive and defensive values. Chi-square analysis of game period identified a higher percentage of timeouts called during the last 5 min of a game compared with the first 35 min (64.999.1% vs. 35.1910.3%; x ?5.4, PB0.05). Results showed higher post timeout offensive and defensive performances. No other effect or interaction was found for defensive performances. Offensive performances were better in the last 5 min of games, with the least differences when in balanced situations and greater differences when in winning situations. Results also showed one interaction between timeouts and momentary differences in score, with increased values when in losing and balanced situations but decreased values when in winning situations. Overall, the results suggest that coaches should examine offensive and defensive performances according to game period and differences in score when considering whether to call a timeout.

Type-I intermittency with discontinuous reinjection probability density in a truncation model of the derivative nonlinear Schrödinger equation

In previous papers, the type-I intermittent phenomenon with continuous reinjection probability density (RPD) has been extensively studied. However, in this paper type-I intermittency considering discontinuous RPD function in one-dimensional maps is analyzed. To carry out the present study the analytic approximation presented by del Río and Elaskar (Int. J. Bifurc. Chaos 20:1185-1191, 2010) and Elaskar et al. (Physica A. 390:2759-2768, 2011) is extended to consider discontinuous RPD functions. The results of this analysis show that the characteristic relation only depends on the position of the lower bound of reinjection (LBR), therefore for the LBR below the tangent point the relation {Mathematical expression}, where {Mathematical expression} is the control parameter, remains robust regardless the form of the RPD, although the average of the laminar phases {Mathematical expression} can change. Finally, the study of discontinuous RPD for type-I intermittency which occurs in a three-wave truncation model for the derivative nonlinear Schrodinger equation is presented. In all tests the theoretical results properly verify the numerical data

Evaluación del rendimiento de jugadores y equipos de fútbol de nivel de élite en diferentes contextos situacionales = Evaluation on Match Performances of Professional Football Players and Teams under Different Situational Conditions = 不同情境条件下高水平足球运动员和运动队的比赛表现分析

El análisis del rendimiento en deportes juega un papel esencial en el fútbol profesional. Aunque el estudio del análisis del juego en fútbol se ha utilizado desde diferentes ámbitos y situaciones, todavía existen diferentes aspectos y componentes del juego que siguen sin estar estudiados. En este sentido existen diferentes aspectos que deben de superar los estudios previos centrados en el componente descriptivo tales como el uso de variables/ indicadores de rendimiento que no se han definido ni estudiado, la validez de los métodos observaciones que no han sido testados con los softwares específicos en fútbol, la aplicación y utilidad de los resultados, así como las limitaciones del estudio de las variables situacionales/contextuales. Con el objetivo de cubrir las citadas limitaciones se han diseñado 6 estudios independientes e inter-relacionados que tratan de estudiar los aspectos anteriormente referidos. El primer estudio evalua la fiabilidad inter-observadores de las estadísticas de juego de la empresa privada OPTA Sportsdata, estos datos son la muestra de estudio de la presente tesis doctoral. Dos grupos de observadores experimentados se requieren para analizar un partido de la liga española de manera independiente. Los resultados muestran que los eventos de equipos y porteros codificados por los inter-operadores alcanzan un acuerdo muy bueno (valores kappa entre 0.86 y 0.94). La validez inter-observadores de las acciones de juego y los datos de jugadores individuales se evaluó con elevados niveles de acuerdo (valores del coeficiente de correlación intraclase entre 0.88 hasta 1.00, el error típico estandarizado variaba entre 0.00 hasta 0.37). Los resultados sugieren que las estadísticas de juego registradas por los operadores de la empresa OPTA Sportsdata están bien entrenados y son fiables. El segundo, tercer y cuarto estudio se centran en resaltar la aplicabilidad del análisis de rendimiento en el fútbol así como para explicar en profundidad las influencias de las variables situacionales. Utilizando la técnica de los perfiles de rendimiento de jugadores y equipos de fútbol se puede evaluar y comparar de manera gráfica, fácil y visual. Así mismo, mediante esta técnica se puede controlar el efecto de las variables situacionales (localización del partido, nivel del equipo y del oponente, y el resultado final del partido). Los perfiles de rendimiento de porteros (n = 46 porteros, 744 observaciones) y jugadores de campo (n = 409 jugadores, 5288 observaciones) de la primera division professional de fútbol Española (La Liga, temporada 2012-13), los equipos (n = 496 partidos, 992 observaciones) de la UEFA Champions League (temporadas 2009-10 a 2012-13) fueron analizados registrando la media, desviación típica, mediana, cuartiles superior e inferior y el recuento de valores de cada indicador de rendimiento y evento, los cuales se presentaron en su forma tipificada y normalizada. Los valores medios de los porteros de los equipos de diferentes niveles de La Liga y de los equipos de diferente nivel de la UEFA Champions League cuando jugaban en diferentes contextos de juego y situaciones (variables situacionales) fueron comparados utilizando el ANOVA de un factor y la prueba t para muestras independientes (localización del partido, diferencias entre casa y fuera), y fueron establecidos en los perfiles de red después de unificar todos los registros en la misma escala derivada con valores estandarizados. Mientras que las diferencias de rendimiento entre los jugadores de los mejores equipos (Top3) y los peores (Bottom3) fueron comparados mediante el uso de diferencias en la magnitud del tamaño del efecto. El quinto y el sexto estudio analizaban el rendimiento del fútbol desde un punto de vista de predicción del rendimiento. El modelo linear general y el modelo lineal general mixto fue empleado para analizar la magnitud de las relaciones de los indicadores y estadísticas de juego con el resultado final del partido en función del tipo de partido (partidos ajustados o todos los partidos) en la fase de grupos de la Copa del Mundo 2014 de Brasil (n = 48 partidos, 38 partidos ajustados) y La Liga 2012-13 (n = 320 partidos ajustados). Las relaciones fueron evaluadas mediante las inferencias en la magnitud de las diferencias y se expresaron como partidos extra ganados o perdidos por cada 10 partidos mediante la variable calculada en 2 desviaciones típicas. Los resultados mostraron que, para los 48 partidos de la fase de grupos de la Copa del Mundo 2014, nueve variables tuvieron un efecto positive en la probabilidad de ganar (tiros, tiros a puerta, tiros de contraataque, tiros dentro del área, posesión de balón, pases en corto, media de secuencia de pases, duelos aéreos y entradas), cuatro tuvieron efectos negativos (tiros bloqueados, centros, regates y tarjetas amarillas), y otras 12 variables tenían efectos triviales o poco claros. Mientras que los 38 partidos ajustados, el efecto de duelos aéreos y tarjetas amarillas fueron triviales y claramente negativos respectivamente. En la La Liga, existió un efecto moderado positive para cada equipo para los tiros a puerta (3.4 victorias extras por cada 10 partidos; 99% IC ±1.0), y un efecto positivo reducido para tiros totales (1.7 victorias extrsa; ±1.0). Los efectos de la mayoría de los eventos se han relacionado con la posesión del balón, la cual obtuvo efectos negativos entre equipos (1.2 derrotas extras; ±1.0) pero un efecto positivo pequeño entra equipos (1.7 victorias extras; ±1.4). La localización del partido mostró un efecto positive reducido dentro de los equipos (1.9 victorias extras; ±0.9). Los resultados obtenidos en los perfiles y el modelado del rendimiento permiten ofrecer una información detallada y avanzada para el entrenamiento, la preparación previa a los partidos, el control de la competición y el análisis post-partido, así como la evaluación e identificación del talento de los jugadores. ABSTRACT Match performance analysis plays an important role in the modern professional football. Although the research in football match analysis is well-developed, there are still some issues and problems remaining in this field, which mainly include the lack of operational definitions of variables, reliability issues, applicability of the findings, the lack of contextual/situational variables, and focusing too much on descriptive and comparative analysis. In order to address these issues, six independent but related studies were conducted in the current thesis. The first study evaluated the inter-operator reliability of football match statistics from OPTA Sportsdata Company which is the data resourse of the thesis. Two groups of experienced operators were required to analyse a Spanish league match independently in the experiment. Results showed that team events and goalkeeper actions coded by independent operators reached a very good agreement (kappa values between 0.86 and 0.94). The inter-operator reliability of match actions and events of individual outfield players was also tested to be at a high level (intra-class correlation coefficients ranged from 0.88 to 1.00, standardised typical error varied from 0.00 to 0.37). These results suggest that the football match statistics collected by well-trained operators from OPTA Sportsdata Company are reliable. The second, third and fourth study aims to enhance the applicability of football match performance analysis and to explore deeply the influences of situational variables. By using a profiling technique, technical and tactical performances of football players and teams can be interpreted, evaluated and compared more easily and straightforwardly, meanwhile, influences and effects from situational variables (match location, strength of team and opposition, and match outcome) on the performances can be properly incorporated. Performance profiles of goalkeepers (n = 46 goalkeepers, 744 full match observations) and outfield players (n = 409 players, 5288 full match observations) from the Spanish First Division Professional Football League (La Liga, season 2012-13), teams (n = 496 matches, 992 observations) from UEFA Champions League (seasons 2009-10 to 2012-13) were set up by presenting the mean, standard deviation, median, lower and upper quartiles of the count values of each performance-related match action and event to represent their typical performances and spreads. Means of goalkeeper from different levels of team in La Liga and teams of different strength in UEFA Champions League when playing under different situational conditions were compared by using one-way ANOVA and independent sample t test (for match location, home and away differences), and were plotted into the same radar charts after unifying all the event counts by standardised score. While differences between the performances of outfield players from Top3 and from Bottom3 teams were compared by magnitude-based inferences. The fifth and sixth study aims to move from the descriptive and comparative football match analysis to a more predictive one. Generalised linear modelling and generalised mixed linear modelling were undertaken to quantify relationships of the performance-related match events, actions and variables with the match outcome in different types of games (close games and all games) in the group stage of 2014 Brazil FIFA World Cup (n = 48 games, 38 close games) and La Liga 2012-13 (n = 320 close games). Relationships were evaluated with magnitude-based inferences and were expressed as extra matches won or lost per 10 matches for an increase of two standard deviations of a variable. Results showed that, for all the 48 games in the group stage of 2014 FIFA World Cup, nine variables had clearly positive effects on the probability of winning (shot, shot on target, shot from counter attack, shot from inside area, ball possession, short pass, average pass streak, aerial advantage, and tackle), four had clearly negative effects (shot blocked, cross, dribble and red card), other 12 variabless had either trivial or unclear effects. While for the 38 close games, the effects of aerial advantage and yellow card turned to trivial and clearly negative, respectively. In the La Liga, there was a moderate positive within-team effect from shots on target (3.4 extra wins per 10 matches; 99% confidence limits ±1.0), and a small positive within-team effect from total shots (1.7 extra wins; ±1.0). Effects of most other match events were related to ball possession, which had a small negative within-team effect (1.2 extra losses; ±1.0) but a small positive between-team effect (1.7 extra wins; ±1.4). Game location showed a small positive within-team effect (1.9 extra wins; ±0.9). Results from the established performance profiles and modelling can provide detailed and straightforward information for training, pre-match preparations, in-match tactical approaches and post-match evaluations, as well as for player identification and development. 摘要 比赛表现分析在现代足球中起着举足轻重的作用。尽管如今对足球比赛表现分析的研究已经相对完善，但仍有很多不足之处。这些不足主要体现在：研究中缺乏对研究变量的清晰定义、数据信效度缺失、研究结果的实用性受限、比赛情境因素缺失以及过于集中在描述性和对比性分析等。针对这些问题，本论文通过六个独立而又相互联系的研究，进一步对足球比赛表现分析进行完善。 第一个研究对本论文的数据源--OPTA Sportsdata公司的足球比赛数据的信效度进行了实验检验。实验中，两组数据收集人员被要求对同一场西班牙足球甲级联赛的比赛进行分析。研究结果显示，两组收集人员记录下的球队比赛事件和守门员比赛行为具有高度的一致性(卡帕系数介于0.86和0.94)。收集人员输出的外场球员的比赛行为和比赛事件也具有很高的组间一致性(ICC相关系数介于0.88和1.00，标准化典型误差介于0.00和0.37)。实验结果证明了OPTA Sportsdata公司收集的足球比赛数据具有足够高的信效度。 第二、三、四个研究旨在提升足球比赛表现分析研究结果的实用性以及深度探讨比赛情境因素对足球比赛表现的影响。通过对足球运动员和运动队的比赛技战术表现进行档案创建，可以对运动员和运动队的比赛表现进行简直接而直观的呈现、评价和对比，同时，情境变量(比赛场地、球队和对手实力、比赛结果)对比赛表现的影响也可以被整合到表现档案中。本部分对2012-13赛季西班牙足球甲级联赛的参赛守门员(n = 46球员人次，744比赛场次)和外场球员(n = 409球员人次, 5288比赛场次)以及2009-10至2012-13赛季欧洲足球冠军联赛的参赛球队(n = 496比赛场次)的比赛技战术表现进行了档案创建。在表现档案中，各项比赛技战术指标的均值、标准差、中位数和大小四分位数被用来展现守门员、外场球员和球队的普遍表现和表现浮动性。方差分析(ANOVA)被用来对西甲不同水平球队的守门员、欧冠中不同水平球队在不同比赛情境下的普遍表现(各项指标的均值)进行对比，独立样本t检验被用来对比主客场比赛普遍表现的差异。数据量级推断(magnitude-based inferences)的方法则被用来对西甲前三名和最后三名球队外场球员的普遍表现进行对比分析。所有来自不同水平球队的运动员和不同水平运动队的各项比赛指标皆被转换成了标准分数，从而能把他们在各种不同比赛情境下的普遍表现(各项比赛指标的均值)投到相同的雷达图中进行直观的对比。 第五和第六个研究目的在于进行预测性足球比赛表现分析，从而跨越之前固有的描述性和对比性分析。广义线性模型和广义混合线性模型被用来对2014年巴西世界杯小组赛(n = 48 比赛场次，38小分差场次)和2012-13赛季西甲联赛(n = 320小分差场次)的比赛中各表现相关比赛事件、行为和变量与比赛结果(胜、平、负)的关系进行建模。模型中的关系通过数据量级推断(magnitude-based inferences)的方法来界定，具体表现为某个变量增加两个标准差对比赛结果的影响(每10场比赛中额外取胜或失利的场数)。研究结果显示，在2014年巴西世界杯小组赛的所有48场比赛中，9个变量(射门、射正、反击中射门、禁区内射门、控球、短传、连续传球平均次数、高空球争抢成功率和抢断)与赢球概率有清晰的正相关关系，4个变量(射门被封堵、传中、过人和红牌)与赢球概率有清晰的负相关关系，其他12个被分析的变量与赢球概率的相关关系微小或不清晰。而在38场小分差比赛中，高空球争抢成功率由正相关变为微小关系，黄牌则由微小关系变为清晰的负相关。在西甲联赛中，每一支球队增加两个标准差的“射正球门”可以给每10场比赛带来3.4场额外胜利(99%置信区间±1.0场)，而所有球队作为一个整体，每增加两个标准差的“射正球门”可以给每10场比赛带来1.7场额外胜利(99%置信区间±1.0场)。其他大多数比赛相关事件与比赛结果的相关关系与“控球”相关联。每一支球队增加两个标准差的“控球”将会给每10场比赛带来1.2场额外失利(99%置信区间±1.0场)，而所有球队作为一个整体，每增加两个标准差的“控球”可以给每10场比赛带来1.7场额外胜利(99%置信区间±1.4场)。与客场比赛相对，主场能给球队带来1.9 /10场额外胜利(99%置信区间±0.9场)。 比赛表现档案和模型中得出的研究结果可以为俱乐部、足球队、教练组、表现分析师和运动员提供详细而直接的参考信息。这些信息可用于训练指导、赛前备战、赛中技战术调整和赛后技战术表现分析，也可运用于足球运动员选材、培养和发展。

Estudio del rendimiento bajo presión en los tiros libres en baloncesto, y su influencia sobre el porcentaje de acierto durante el último minuto de juego

El minuto final de un partido ajustado de baloncesto es un momento crítico que está sujeto a multitud de factores que influyen en su desarrollo. Así, el porcentaje de acierto en los tiros libres durante ese periodo de tiempo va a determinar, en muchas ocasiones, el resultado final del partido. La disminución de rendimiento (drop) en esta faceta de juego en condiciones de presión, puede estar relacionada con múltiples variables propias del contexto deportivo estudiado, como por ejemplo: los segundos restantes de posesión, la situación en el marcador (ir ganando, empatando o perdiendo), la localización del partido (jugar en casa o fuera), la fase de competición (fase regular o eliminatorias) o el nivel del equipo (mejores/peores equipos). Además, las características del jugador que realiza los lanzamientos tienen una gran importancia respecto a su edad y años de experiencia para afrontar los momentos críticos, así como el puesto de juego que ocupa en el equipo. En este sentido, la combinación de factores del contexto y del jugador, permiten interactuar en el rendimiento del lanzador en los momentos finales de partido durante sus lanzamientos de tiro libre. El presente trabajo de tesis doctoral tiene como objetivo encontrar aquellas variables más relacionadas con la disminución de rendimiento del jugador en los tiros libres durante el último minuto de juego, y la última serie de tiros libres en los partidos ajustados de baloncesto. Para alcanzar el objetivo del estudio se analizaron 124 partidos ajustados (diferencias iguales o inferiores a 2 puntos) de todas las competiciones (fase regular, playoff y copa del Rey) de la liga ACB durante las temporadas 2011-2012 a 2014-2015. Para el registro de variables se analizó el porcentaje de acierto en los tiros libres del lanzador en la liga regular, partido completo, último minuto y última serie. De este modo se trató de analizar qué variables del contexto y del jugador permitían explicar el rendimiento en los tiros libres durante el último minuto, y la última serie de tiros libres del partido. Por otro lado, se trató de conocer el grado de asociación entre el descenso del rendimiento (drop) en los momentos finales de partido, y las variables estudiadas del jugador: puesto de juego, edad, y años de experiencia profesional; mientras que las variables situacionales consideradas fueron: fase de competición, localización, clasificación, tiempo restante, y diferencia parcial en el marcador. Para el análisis de los datos se realizaron dos modelos estadísticos: 1º) un modelo de regresión lineal múltiple para conocer el efecto de las variables independientes en el porcentaje de aciertos del lanzador en el último minuto, y en la última serie de tiros libres del partido; y 2º) un análisis de regresión logística binomial para analizar la relación existente entre la probabilidad de tener un drop (disminución del rendimiento) y las características del lanzador, y las variables situacionales. Los resultados del modelo de regresión lineal múltiple mostraron efectos negativos significativos en el porcentaje de acierto en los tiros libres durante el último minuto, cuando los lanzadores son los pívots (-19,45%). Por otro lado, los resultados durante la última serie mostraron el efecto negativo significativo sobre la posición de pívot (- 19,30%) y la diferencia parcial en el marcador (-3,33%, para cada punto de diferencia en el marcador) en el porcentaje de acierto en los tiros libres. Las variables independientes edad, experiencia profesional, clasificación en la liga regular, fase de competición, localización, y tiempo restante, no revelaron efectos significativos en los modelos de regresión lineal. Los resultados de la regresión logística binomial revelaron que las variables experiencia profesional entre 13 y 18 años (OR = 4,63), jugar de alero (OR = 23,01), y jugar de base (OR = 10,68) están relacionadas con una baja probabilidad de disminuir el rendimiento durante el último minuto del partido; mientras que ir ganando, aumenta esta probabilidad (OR = 0,06). Además, los resultados de la última serie mostraron una menor disminución del rendimiento del jugador cuando tiene entre 13 y 18 años de experiencia (OR = 4,28), y juega de alero (OR = 8,06) o base (OR = 6,34). Por el contrario, las variables situacionales relacionadas con esa disminución del rendimiento del jugador son las fases eliminatorias (OR = 0,22) e ir ganando (OR = 0,04). Los resultados principales del estudio mostraron que existe una disminución del rendimiento del jugador en su porcentaje de acierto en los tiros libres durante el último minuto y en la última serie de lanzamientos del partido, y que está relacionada significativamente con la edad, experiencia profesional, puesto de juego del jugador, y diferencia parcial en el marcador. Encontrando relación también con la fase de competición, durante la última serie de tiros libres del partido. Esta información supone una valiosa información para el entrenador, y su aplicación en el ámbito competitivo real. En este sentido, la creación de simulaciones en el apartado de aplicaciones prácticas, permite predecir el porcentaje de acierto en los tiros libres de un jugador durante los momentos de mayor presión del partido, en base a su perfil de rendimiento. Lo que puede servir para realizar una toma de decisiones más idónea, con el objetivo de lograr el mejor resultado. Del mismo modo, orienta el tipo de proceso de entrenamiento que se ha de seguir, en relación a los jugadores más tendentes al drop, con el objetivo de minimizar el efecto de la presión sobre su capacidad para rendir adecuadamente en la ejecución de los tiros libres, y lograr de esta manera un rendimiento más homogéneo en todos los jugadores del equipo en esta faceta del juego, durante el momento crítico del final de partido. ABSTRACT. The final minute of a close game in basketball is a critical moment which is subject to many factors that influence its development. Thus, the success rate in free-throws during that period will determine, in many cases, the outcome of the game. Decrease of performance (drop) in this facet of play under pressure conditions, may be related to studied own multiple sports context variables, such as the remaining seconds of possession, the situation in the score (to be winning, drawing, or losing) the location of the match (playing at home or away), the competition phase (regular season or playoffs) or team level (best/worst teams). In addition, the characteristics of the player are very important related to his age and years of experience to face the critical moments, as well as his playing position into team. In this sense, the combination of factors in context and player, allows interact about performance of shooter in the final moments of the game during his free-throw shooting. The aim of this present doctoral thesis was find the most related variables to player´s drop in free throws in the last minute of the game and the last row of free-throws in closed games of basketball. To achieve the objective of the study, 124 closed games (less or equal than 2 points difference) were analyzed in every copetition in ACB league (regular season, playoff and cup) from 2011-2012 to 2014-2015 seasons. To record the variables, the percentage of success of the shooter in regular season, full game, last minute, and last row were analyzed. This way, it is tried to analyze which player and context variables explain the free-throw performance in last minute and last row of the game. On the other hand, it is tried to determine the degree of association between decrease of performance (drop) of the player in the final moments, and studied player variables: playing position, age, and years of professional experience; while considered situational variables considered were: competition phase, location, classification, remaining time, and score-line. For data analysis were performed two statistical models: 1) A multiple linear regression model to determine the effect of the independent variables in the succsess percentage of shooter at the last minute, and in the last row of free-throws in the game; and 2) A binomial logistic regression analysis to analyze the relationship between the probability of a drop (lower performance) and the characteristics of the shooter and situational variables. The results of multiple linear regression model showed significant negative effects on the free-throw percentage during last minute, when shooters are centers (-19.45%). On the other hand, results in the last series showed the significant negative effect on the center position (-19.30%) and score-line (-3.33% for each point difference in the score) in the free-throw percentage. The independent variables age, professional experience, ranking in the regular season, competition phase, location, and remaining time, revealed no significant effects on linear regression models. The results of the binomial logistic regression showed that the variables professional experience between 13 and 18 years (OR = 4.63), playing forward (OR = 23.01) and playing guard (OR = 10.68) are related to reduce the probability to decrease the performance during the last minute of the game. While wining, increases it (OR = 0.06). Furthermore, the results of the last row showed a reduction in performance degradation when player is between 13 and 18 years of experience (OR = 4.28), and playing forward (OR = 8.06) or guard (OR = 6.34). By contrast, the variables related to the decrease in performance of the player are the knockout phases (OR = 0.22) and wining (OR = 0.04). The main results of the study showed that there is a decrease in performance of the player in the percentage of success in free-throws in the last minute and last row of the game, and it is significantly associated with age, professional experience, and player position. Finding relationship with the competition phase, during last row of free-throws of the game too. This information is a valuable information for the coach, for applying in real competitive environment. In this sense, create simulations in the section of practical applications allows to predict the success rate of free-throw of a player during the most pressing moments of the game, based on their performance profile. What can be used to take more appropriate decisions in order to achieve the best result. Similarly, guides the type of training process must be followed in relation to the most favorable players to drop, in order to minimize the effect of pressure on their ability to perform properly in the execution of the free-throws. And to achieve, in this way, a more consistent performance in all team players in this facet of the game, during the critical moment in the final of the game.