WAIBI DISSECTION

 WHY wOBA AFFECTS BEST HITTERS AND FAVORS WORSE? THE SYNDROME OF AVERAGE & THE WAIBI PULSE

 

This article references:

• Why "The Book" is a Sabermetric’s masterpiece and an excellent reference book? 
• wOBA operation step by step. 
• Sport’s aleatority vs. Random’s aleatority. 
• Use vs overuse of averages in Sabermetrics.  Error-In in wOBA averages, step by step. 
• What really measures the Runs Value of wOBA?  
• Brief introduction to the calculation of Waibi Pulse.

Here’s the offensive component of WAR, possibly the most used sabermetric stats of recent times. El WAR calcula el aporte integral de un jugador a su equipo en relación al promedio de la liga, incluido el performance defensivo. WAR calculates the integral contribution from each player to his team, in relation to the league average, including defensive performance.  

El wOBA es el Weighted On Base Average (Promedio de embasado ponderado), y su fórmula es wOBA is On Base Weighted Average, and its formula is:

 

Siendo NIBB, las bases por bolas no intencionales, HBP los golpeados por lanzamientos, y RBOE las bases alcanzadas por error.Being NIBB, the unintentional bases on balls; HBP, hit by pitch; and RBOE, the bases reached by error. Si la comparamos con el OPS (OBP + SLG), veremos que los parámetros son muy similares, salvo por la inclusión de los errores.When we compare it with the OPS (OBP + SLG), we see that the parameters are very similar, except for the inclusion of errors. Para el espectador común, la inquietud mayor aflora de los constantes numéricas que anteceden cada parámetro en la fórmula, resultado ingenioso de sus creadores, Tom Tango, Mitchel Lichtman y Andrew Dolphin. For the common viewer, the biggest concern surfaces because of constant numbers preceding each parameter in the formula, ingenious result of its creators, Tom Tango, Mitchel Lichtman and Andrew Dolphin. Apareció por vez primera en “ The Book : Playing the Percentages in Baseball”. It first appeared in "The Book: Playing the Percentages in Baseball".  

Es realmente el algoritmo más completo y complejo de los que se utilizan en las estadísticas ofensivas.It’s truly the most complete and complex algorithm of those used in offensive statistics. O al menos de aquellas que sus creadores han hecho públicas. Or at least, of those which their creators have made public. ¿Cómo que públicas? Public? Pues sí, claro. Yes, of course. Debemos recordar que la interpretación estadística es un arte en el Béisbol, casi exacto a la Intelligence en una guerra. We must remember that the statistical interpretation is an art in Baseball, almost exactly to what  Intelligence is in a war. Un gran número de creadores de sistemas interpretativos, han sido contratados por equipos de Ligas Profesionales, una vez demostrada la utilidad de su método. Many interpretive systems creators, have been hired by  professional leagues teams, when they’ve demonstrated the usefulness of their method. Estos sistemas continúan desarrollándose, o al menos pueden convertirse en modelos superiores, al tener una serie de recursos e intereses concentrados, y poder mejorar la calidad de la información que procesan. These systems continue developing, or at least they can become more accurate, due to the access to new resources and interests, which improve the quality of processed information. Por esa razón, es altamente probable que el sistema actual usado por estos estadísticos, sea mucho más profundo que aquellas fórmulas explicadas para consumo del público. For this reason, it’s highly probable that the current system used by these analysts, is much deeper than those formulas explained for public use. Recordemos que casi cada equipo de MLB tiene un departamento estadístico de alta funcionalidad. Remember that almost every MLB team has a high functionality statistical department. Esta contratación no tendría lógica si se limitara solo a mostrar datos de una fórmula que es pública, y por tanto, cualquiera puede ejecutar y analizar. This contract wouldn’t have sense if it were limited only to a public formula that everyone can execute and analyze.

“The Book: Playing the Percentages in Baseball” es una obra maestra del análisis beisbolístico, con un alto nivel de objetividad y rigor. "The Book: Playing the Percentages in Baseball" is a masterpiece of analysis in Baseball, with a high level of objectivity and rigor. Es un libro que todo aficionado debería leer, y tratar de comprender. It’s a book that every fan should read and try to understand. Muchas apariencias, son desenmascaradas a través del método científico, echando por tierra esa subjetividad inevitable que nos genera lo que apreciamos en el terreno de juego. Many appearances are unmasked through the scientific method, shattering the unavoidable subjectivity that creates what we see in the field. En otro momento profundizaremos en esta maravilla. At another time, we’ll delve into this marvel. Ahora vamos a concentrarnos en la fórmula del wOBA, por ser la más acudida, al menos por los medios y los fans. Now let's concentrate on wOBA’s formula, the most used, at least by the media and fans.

In recent time, there’re different considerations to calculate wOBA. Its integration in the wRAA formula is another great intention to acchives more accuracy in the results. The web site Fan Graphs have publicated yearly the recent wOBA’s versions, where the coefficents, and the compensation changes each season. Even, they don´t includes the RBOE. Anyway, Waibi consider the principal problema it’s precisely, the “SINDROME of AVERAGE”, which still exists in the recent versions. So, in order to understand it better, let’s analyze it using wOBA’s foundations; so, the original fórmula.

Waibi Waibi Sabermetrics System considera esta interesantísima fórmula una herramienta útil para las estadísticas históricas, y para seleccionar a UN GRUPO de jugadores dentro de la liga.Sabermetrics System considers this interesting formula an useful tool for historical statistics, and to select A GROUP of players in the league. Nunca para una selección definitiva, es decir, elegir UN jugador dentro de un grupo (a menos que la diferencia entre él y el resto sea realmente aplastante). Never for a final selection, ie, it doesn’t allow to choose A PLAYER in a group, unless the difference between him and the rest is really overwhelming. El wOBA ayuda a dar una idea de la calidad global de los bateadores. wOBA helps to give us an idea of ​​the hitter’s overall quality. Por ejemplo, si necesitamos adquirir un slugger para nuestro equipo, nos dirá quienes NO son elegibles, pero al ser basada en promedios muy generales, nos deja matemáticamente a oscuras cuando debemos escoger UNO DENTRO DEL GRUPO preseleccionado. For example, if we need to acquire a slugger for our team, it will tell us which ones aren’t eligible. Being based on very broad averages, it leaves us mathematically in the dark when we must choose JUST ONE FROM A PRESELECTED GROUP.

 Veamos en primera instancia de donde se obtienen estos coeficientes: Let’s see, in the first instance, how these coefficients are obtained:

Cada número consta de dos partes: el número en sí mismo, y su compensación.Each number have two parts: the number itself, and its compensation. La compensación es una inclusión del 15 % del valor real, para que pueda ser leído e interpretado de la misma manera que el OBP. Compensation is an inclusion of 15% of the real value, so it can be readed and interpreted in the same way that the OBP. Así es más fácil familiarizarse. This makes it easier to understand it. Ahora, ¿cómo se obtuvo el valor de cada número? Now, how the value of each number was obtained?

Estos reconocidos sabermétricos se basaron en tres enfoques generales fundamentales:These recognized statheads were based on three main general approaches:

1. Estados base/outBase / Out States
2. Datos generales promedio de las temporadas 1999 a 2002 General Data from 1999 to 2002 seasons
3. Datos individuales de cada tipo de evento Individual data for each type of event

1. BASE / OUT STATES (B/O_State)

 Comprende todas las combinaciones de situaciones que aparecen en una entrada, respecto a los outs y los hombres en circulación.It includes all possible situations that appear on each inning regarding outs and runners on bases. También las transiciones entre estas. Also transitions between these. Por ejemplo: la que inicia siempre es “bases limpias sin outs”. For example: Every inning starts with "empty bases & no outs" state. Si el hombre se embasa por BB, sencillo, HBP u otros que permitan alcanzar la primera, este sería el estado “corredor en primera sin outs”. If a player gets on base by BB, single, HBP or another that achieves the first, this would be the "runner on first & no out" state. Si el hombre roba la segunda o se escapa la pelota, o el pitcher comete “Balk”, se pasa al estado de “corredor en segunda sin outs”. If he steals the second, or ball escapes by wild pitch or passed ball, or the pitcher commits "Balk", it have passed to "runner on second base & no outs" state. Si el bateador conecta un rolling, y el corredor es out en tercera, se pasa al estado de “corredor en primera con un out”. If the batter hits a ground-ball, and the runner is out at third, it have passed to "runner on first & one out" state. Así sucesivamente hasta que finalice el inning. So on until the end of the inning. En total son 24 estados prácticos. There are 24 states.

DATOS PROMEDIO

2. DATA AVERAGE 

 Tom Tango, Lichmann y Dolphin, tuvieron la brillante idea de contabilizar las carreras que se anotaron entre 1999 y 2002 desde cada Estado Base/Out específico hasta que finalizó el inning donde ocurrieron.Tango had the bright idea of ​​accounting all runs that were scored between 1999 and 2002 from each specific Base/Out State, until the end of the inning in which they occurred. Y tomaron estos resultados como modelo estándar, obteniendo la siguiente tabla de Carreras X Estado/Out (Carreras Esperadas):  He took these results as a standard model, obtaining the following  Runs/State table (Runs Expected):

GLOBAL BASE/OUTS_STATES
1B	2B	3B	0 Outs	1 Out	2 Outs
–	–	–	0,555	0,297	0,117
1B	–	–	0,953	0,573	0,251
–	2B	–	1,189	0,725	0,344
–	–	3B	1,482	0,983	0,387
1B	2B	–	1,573	0,971	0,466
1B	–	3B	1,904	1,243	0,538
–	2B	3B	2,052	1,467	0,634
1B	2B	3B	2,417	1,650	0,815

Explico brevemente: Cada vez que un equipo se encontró con “bases llenas sin outs”, anotó como promedio 2,417 carreras antes del tercer out, mientras cada vez que hubo “bases limpias sin outs”, se marcaron 0,555 como promedio.I’ll explain briefly: Each time a team founds "bases loaded & no outs", it scored 2,417 runs on average before the third out, as each time there was "bases empty & no outs", it scored 0,555 as average. Este es, a mi entender, el tercer aporte conceptual más importante de la historia de las estadísticas en el béisbol, después de su creación por Henry Chadwick, y el florecimiento de la Sabermetría de Billy James, en ese orden. El norteamericano Pete …. This is, in my personal point of view, the third most important conceptual contribution to the statistics in Baseball, after its creation by Henry Chadwick, and the flowering of Billy Jame’s Sabermetrics, in this order.

It’s fair to say that the american Pete Palmer, who wrote the foreword to the "The Book:  Playing the Percentages in Baseball", developed his first investigations basing  on the "Play by Play" notation, using the 1956-1960 World Series Data. These data were taken from the Sporting News Baseball Guides, because at that time this system wasn’t established on a large scale. No obstante, con su libro “The Hidden Game of Baseball”, Palmer fue pionero de una nueva estrada al desarrollo de la Sabermetría. However, with his book "The Hidden Game of Baseball" Palmer pioneered a new way for Sabermetric’s  development.

3. INDIVIDUAL EVENTS

De igual manera que con los Estados Base/Outs, contabilizaron lo sucedido con cada evento específico incluyendo las Carreras Esperadas de los estados inicial y final, y las Producidas específicamente en cada evento (hit, hr, error, bb, hbp, etc).They processed each specific event including initial and final Base/Out_State’s Run Expectancies, and run produced specifically  for each event (H, HR, E, BB, HBP, etc). Así, por ejemplo, un Thus, for example, aEstadode “hombre en tercera con un out” tiene una expectativa de carreras de 0,983. "runner on third &  one out" State has a Run Expectancy of 0.983. El bateador conecta un doble y el corredor de tercera anota. The batter hits a double and the runner on third scores. Se pasa al estado final de “hombre en segunda con un out”, que tiene una expectativa de 0,725. So, it pass to a final state of "runner on second & one out", which has an expectation of 0.725. Como se anotó una carrera, la operación sería: 1 + 0,725 – 0,983. As one run was scored, the operation would be: 1 + 0.725 - 0.983. Dando un 0,742 de Valor de Carrera para este doble específico. So, this double, have an specific Run Value of 0.742.

Siendo REFn la Expectativa de Carreras del EstadoBeing REFn, the final OBut Final, R las carreras, y REIn la Expectativa de Carreras delBase/Out_State’s Run Expectancies; R the runs, and REIn; the initial B/O_State’s Run Expectancies.

Tabla The Book, por evento, or estado/out

Concentrémonos en el comportamiento de los jonrones por Estados/Outs, en cuanto a Valor de Carreras.Let's concentrate on homers behavior by B/O_States, regarding Run Value. Usamos los jonrones como modelo, porque dentro de los parámetros ofensivos, es el menos complicado de manejar en una explicación corta. We’ll use homers as model, because within hitting parameters, it’s the least complicated to handle in a short explanation.

HOMERS RUN VALUE BY BASE/OUTS_STATES
1B	2B	3B	0 Outs	1 Out	2 Outs
–	–	–	1	1	1
1B	–	–	1,602	1,725	1,865
–	2B	–	1,367	1,573	1,772
–	–	3B	1,073	1,314	1,729
1B	2B	–	1,983	2,326	2,651
1B	–	3B	1,651	2,054	2,579
–	2B	3B	1,504	1,830	2,483
1B	2B	3B	2,139	2,647	3,302

Al promediar cada uno de estos datos, obtenidos a través de los 21 026 jonrones analizados porBy averaging each of these data, obtained through the 21 026 home runs analyzed by B/O_SEB/Otate, the chartado/out, nos dice que un jonrón promedio, produce 1,397 carreras, aproximadamente. tells us that an average homer produces 1,397 runs. En la tabla mostramos el valor promedio por evento. The next table shows the average value per event.

Event	RV	Event	RV
HR	1.397	BK	0.264
3B	1.070	NIBB	0.323
2B	0.776	IBB	0.179
RBOE	0.508	SB	0.175
INT	0.392	DI	0.120
SAC	-0.096	BUNT	0.042
PB	0.269	PK	-0.281
1B	0.475	OUT	-0.299
WP	0.266	K	-0.301
HBP	0.352	CS	-0.467

Uno de los puntos fuertes del análisis de Tango, Dolphin y Lietchmann, es sin dudas, el estudio de las Cadenas de Markov presentes en los sistemas aleatorios como el Béisbol.

One of the strengths of the analysis of Tango, Dolphin and Lietchmann, is undoubtedly the study of Markov’s Chains presents in random systems like Baseball. Este tipo de cadenas, describe un sistema de probabilidades consecutivas, donde el flujo de estas depende de cada acción anterior. This type of chain, describes a system of consecutive probabilities, where the flow of these depends on the previous action. Este tipo de This kind of techniques temastécnicasha sido ampliamente usado con éxito desde la meteorología y la física, hasta la epidemiología, economía y finanzas, o predicciones de juegos de azar y movimientos de mercado.as been widely  successfully used  from meteorology to physics, epidemiology, economics and finance, or predictions of gambling and market movements, among others. El manejo de estos datos les permitió hacer un estudio tan interesante como preciso, sobre la concepción del orden al bate. The management of these data allowed them to make an interesting as necessary study, on batting order conception. Su análisis pormenorizado rompió mitos tan arraigados como que el tercer puesto en el line up debe reservarse al mejor bateador del equipo. His detailed analysis broke so ingrained myths, like that the third turn in the line up should be reserved for the best hitter of the team.

EL VALOR DE CARRERASRUN VALUE

Habíamos visto que conceptualmente, si suprimimos las constantes numéricas, el cálculo del wOBA es muy similar al OBP, aunque añade los embasados por error, y elimina las bases intencionales.We had seen that conceptually, if we suppress the numerical constants, wOBA’s calculation is very similar to OBP, but adds the “on based by error”, and eliminates “intentional walks”. El OBP contabiliza como 1 todos las acciones en los que un jugador se embasa, y toma como 0, los outs. The OBP counts like “1” all the actions in which the player gets on base, and couts like “0” when he is out. To obtain the coefficients, we add to each value a number that allows to convert to “0”, the Run Value for the event "Out", which according to the table is -0,299. Es decir, habría que sumar +0.299 a cada evento. Es decir, habría que sumar +0.299 a cada evento. I mean, +0,299 ​​must be added to each event.

	RV INIC	PLUS 299	PLUS 15%	RV FINAL
HR	1,397	1,696	1,950	1,95
3B	1,070	1,369	1,574	1,56
2B	0,776	1,075	1,236	1,24
1B	0,475	0,774	0,890	0,90
RBOE	0,508	0,807	0,928	0,92
HBP	0,352	0,651	0,749	0,75
NIBB	0,323	0,622	0,715	0,72

 Como se aprecia, existen diferencias de algunas centésimas entre los números usados como coeficiente de la fórmula (en negro), y los de la columna “PLUSAs shown, there’re differences of few hundredths between the coefficient numbers used in the formula (in black), and the "PLUS 15" column. Esto sucede por el redondeo. This happens because of rounding. En algunas etapas del procesamiento de datos, se aplica para facilitar la manipulación. In some phases of data processing, it was applied to facilitate handling. En matemáticas, cada vez que recurrimos a esto, se introduce un pequeño error. In math, every time we turn to this, a small error is introduced. Lo ideal es no redondear jamás, pero si tenemos que hacerlo, es mejor esperar a la última operación. The best thing is not to round up, but if we have to, it’s better to wait until the last operation. Sobre todo en este caso, en que varios coeficientes son aplicados en una misma fórmula. Especially in this case, where various coefficients are applied in the same formula. TEl redondeo matemático se aplica “por defecto” o “por exceso”, por lo que en algunos casos, el valor real será mayor que el empleado, y en otros menor.he mathematical rounding applies by "default" or "excess", so in some cases, the actual value will be  greater than the used one, and in other ones less. Ese redondeo en direcciones opuesta, lógicamente aumenta el error aún más. This rounding in opposite directions, logically increases much more the Error-in.

USO vs SOBREUSO DEL PROMEDIO EN LA SABERMUSE VS OVERUSE OF AVERAGE IN SABERMETRICS. PROMEDIOS DEL wOBA. wOBA’s AVERAGES.

 He aquí el punto neurálgico del wOBA como estadística de SELECCIÓN.This is the neuralgic point of wOBA as a SELECTION stats. Es justo decir que el uso de los coeficientes derivados de promedios de bases de datos extensas es una excelente solución, ante la imposibilidad de conocer siempre los Estados B/O inicial y final, que comprenden cada evento de cada jugador específico. It’s fair to say that the use of average coefficents derived from large databases is an excellent solution, because of the impossibility of  knowing always the initial and final B/O_States, for each event of each specific player.Es sin dudas lo que Tango, Litchmann y Dolphin hubiesen preferido (o al menos era imposible para ellos en aquel momento) Aún sin esta condición ideal, lograron realmente que el wOBA haga una valoración sobre la calidad ofensiva de un jugador, más cercana a la realidad que con las otras estadísticas ofensivas. It’s undoubtedly what Tango, Litchmann and Dolphin would’ve preferred (or at least it was impossible for them at that time). Even without this ideal condition, they actually achieved  that wOBA dissects the offensive quality of a player, closer to the reality than other offensive statistics. De ahí la popularización de su empleo para elegir jugadores.Hence the popularity of its use for choosing players. Sin embargo, al igual que vimos en nuestro artículo sobre AVG, RBI, y el “Síndrome de Default” , aquí se manifiesta lo que Waibi define como el “Síndrome del Promedio”. However, as we saw in our article about AVG, RBI, and the "Default Syndrome", here it manifests what Waibi defines as the "AVERAGE SYNDROME". 

Vamos a ver: ¿Por qué nos interesa tanto lo que hace el grupo, si escogemos a un jugador y no al grupoLet's see: why do we care so much about what the group does, if we choose a player and not the whole group of players? Debería ser una cuestión comparativa informativa, no selectiva. It should be a comparative-informative matter, not a selective one. Con el aumento de la calidad del Béisbol mundial, los jugadores de las principales ligas se acercan cada vez más al jugador estándar, haciendo el sistema de promedios comparados, algo ineficiente para elegir a un pelotero sobre otro.With the increasing of Baseball’s quality in the world, the players from best leagues are getting closer to the standard player, making the system of compared averages, somewhat inefficient to select a player over another. Lo ideal sería procesar cada desempeño por sí mismo, en lugar de hacerlo en función del promedio, y aseguraríamos una disminución máxima del error permisible. The best thing is to process each performance by itself (I mean, individually), rather than depending on the average. Like this, we would ensure a maximum decrease of allowable errors. Waibi esgrime este principio como su Santo Grial: cada acción es particular, cada jugador un individuo, y cada momento una circunstancia. WAIBI wields this principle as his Holy Grail: every action is unique, each player an individual, and each moment a circumstance. El reto es llevarlo a números, tan ajustadamente a la realidad como sea posible.The challenge is to turn it in numbers, as closely to reality as possible. Es la misma diferencia, por ejemplo, entre describir a una persona de manera inespecífica: “…él es alto, delgado, lleva el pelo largo y es mayor de edad…”; It's the same difference, for example, between describing a person in a non specific way: "... he is tall, slim, wearing long hair and he is of greater age ..."; y otra persona descrita por su individualidad: “…1,84 de estatura, 70 kilos, pelo rizado negro brillante por la cintura atado en cola de caballo, aparenta unos 60 años, y además fuma y es alérgico a los mariscos…”. and another person described by his individuality: "... height 6.5, weight 70 kilos, curly black shiny hair tied in a ponytail, he’s 60 years old, and also smokes and is allergic to shellfish...". Es clara la diferencia de ajuste a la realidad objetiva, ¿no? The difference about the objective adjustment to reality is clear, right? Además, debemos recordar un principio básico: un equipo es un engranaje altamente funcional y complementado de jugadores, y no un “Todos Estrellas”, como piensan la mayoría de los fans. In addition, we must remember one basic principle: a team is a highly functional and complimented players gear, and not an "All Stars Team" as most of the fans think.

 

 EN GENERAL existe el error tremebundo de creer que la estadística debe ser comprensible y aplicable para todo el que se relaciona con el Béisbol, desde los aficionados hasta los directores de equiOVERALL, there’s the frightful misconception that statistics must be understandable and applicable for everyone related to Baseball, from the fans to the team managers. Comúnmente se han diseñado fórmulas que puedan ser usadas fácilmente, con un papel y un lápiz, o cuanto más, una buena calculadora. Commonly there’re designed formulas that can be easily used, with paper and pencil, or at the most, with a good calculator. Sin embargo, la complejidad matemática del juego y sus eventos es tal, que al intentar agrupar, reducir o sintetizar, estamos aumentando el margen de fallo de manera importante. However, the mathematical complexity of the game and its events are so great, that when we try to group, to reduce or to synthesize, we’re increasing significantly the margin of error. El Béisbol no puede ser analizado objetivamente por una herramienta tan arcaica como una calculadora… Sería cuando menos, como intentar hallar un logaritmo neperiano de alta complejidad, contando con los dedos.Baseball can not be objectively analyzed by an archaic tool such as a calculator ... It would be at least like trying to find a high complexity natural logarithm, counting on fingers. 

Al ser imposible (hasta hoy) esta especificación numérica de las acciones del juego, debemos por fuerza recurrir a los promedios.As it’s impossible (so far) this numerical specification of the game actions, we must apply averages. En ese caso, Waibi intenta no abusar de su uso.In that case, WAIBI tries not to abuse its use. O sea, utilizarlos solo si no encuentra un algoritmo más funcional matemáticamente.In other words, to use it only if there’s not a more functional mathematic algorithm. 

Veamos entonces los promedios del wOBA: Let’s see wOBA’s averages:

1. FIRST AVERAGE: It’s calculated on the Base/Outs_States. Como el objetivo es tener una idea de las carreras, partiendo de cada posible momento del inning, hacemos una operación lógica de promedio. As the objective is to have an idea of scoring, starting from each possible moment of the inning, we make a logical operation of average. Así sabremos medianamente nuestras probabilidades en cada situación. So, we’ll know our PROBABILITIES to score since each situation or state. Como la media se refiere al inning, se cuentan las acciones hasta que finalice. As this operation  regards the inning, we must to count until it’s finalized. But, bAl utilizar este sistema, aflora el gran conflicto que genera este síndrome: LA EXPECTATIVA PROMEDIO, POCAS VECES COINCIDE CON LA EXPECTATIVA DE LA SITUACIÓN ESPECÍFICA, PERO LAS DECISIONES SON TOMADAS COMO SI ASÍ FUESE SIEMPRE.y using this system,  flourishes the great conflict generated by this syndrome: AVERAGE EXPECTATION RARELY MATCHES WITH THE EXPECTATION OF THE SPECIFIC SITUATION, BUT DECISIONS ARE TAKEN AS IF THEY WERE ALWAYS SO.

Veamos un ejemplo “alocado”, pero ilustrativo: Si un hombre primitivo mirase un tablero de Ajedrez por primera vez desde una distancia suficientemente grande, vería seguramente un solo color, por ejemplo gris.Let’s consider this "crazy" but illustrative example:  if a primitive man would have seen up  a black & white chessboard for the first time, since a sufficiently large distance, surely he would’ve seen a single gray color. Ese sería el color promedio que nuestra retina alcanzaría a interpretar, pues en la distancia, el ojo humano no logra definir el objeto fielmente, e INTEGRA la información. That would be the average color that our retina achives to interpret. Why? Because of the distance, the human eye is unable to accurately define the object, so, it INTEGRATES the information. Al no conocer el diseño real, si quisiera copiarlo partiendo de la información visual que tiene, seguramente pintaría en la pared de su caverna un cuadrado monocolor gris. Not knowing the actual design, if he would have wanted to copy it, basing on the visual information he had, probably he would’ve painted  a monochrome gray square in the wall of his cave. ¡Nada más lejos de un tablero de Ajedrez!Nothing further from a chessboard! O sea, que aquello que miraba en la distancia tiene ocho columnas y ocho filas, que forman casillas que alternan colores blanco y negro, pero el promedio, es SOLO un cuadrado gris.Por tanto, su marca para la historia reflejará eso que creyó ver y no aquello que realmente era. Therefore, his mark in history  would have reflected what he thought he saw and not what it really was. Cuando milenios después sea descubierto este arte rupestre, los arqueólogos interpretarán el cuadrado gris en la caverna, como cualquier cosa, menos un tablero de Ajedrez. When some millennia later this rock art will be discovered, the archaeologists will interpret the gray square in the cave as anything except a chessboard.

Este paralelo algo pintoresco, es lo que ocurre en este tipo de estadísticas, como veremos más adelante.This somewhat picturesque parallel, is what happens in this type of statistics, as discussed below. En el béisbol, cada situación es específica, como cada casilla en el tablero de Ajedrez tiene una colocación y color específicos (particularidad), que el ojo en la distancia (generalidad) no logra distinguir. In baseball, every situation is specific, as each one of the 64 little squares in the chessboard has a specific placement and color (particularity), what the eye in the distance (generality, average) fails to distinguish.

El punto importante aquí, es que no hablamos de una cantidad concreta de carreras, ¡sino de PROBABILIDADES de realizarlas, según datos históricos!The sensitive point here is that we’re not talking about a specific number of runs, but about  the PROBABILITY to score them, according to historical data! Entonces, el primer escaño a franquear es la base de datos (1999-2002). Then, the first obstacle to overcome is the database (1999-2002). Este es un método elemental y recurrente dentro de los análisis estadísticos, cuando las muestras son lo suficientemente grandes, y las características las mismas en mayor o menor grado. This is a basic and recurrent method in the statistical analysis, when samples are large enough, and the characteristics are the same in greater or lesser degrees. Para entender más fácilmente qué sucede en las estadísticas del Béisbol, acudimos al ejemplo de los dados, el típico usado para explicar las probabilidades. To understand more easily what happen in baseball statistics, we turn to the example of the dices, the tipycal used to explain probabilities situations.

Un matemático llegaría a la conclusión de que, SI LOS DADOS NO ESTÁN “CARGADOS” O MANIPULADOS, la probabilidad de obtener determinado número, será siempre 1/6.A mathematician would conclude that IF THE DICE ARE NOT "LOADED" OR MANIPULATED, the probability of getting a determined number will always be 1/6. Un físico diría que es posible, SI LOS SEIS LADOS ESTÁN COMPENSADOS.A physicist would say that it’s possible, if THE SIX SIDES ARE COMPENSATED. Pero ¿no es la misma condición? But, is it not the same condition? Aparentemente sí, pero en realidad no. Apparently yes, but not really. La diferencia de enfoque define la aparición o no de un error entre el fenómeno real y su modelo teórico.The difference in approach defines the presence or the absence of an error between the actual phenomenon and its theoretical model. Una parte importante de los dados usados en el mundo, utilizan agujeros para representar el valor de cada cara. An important amount of the dices used in the world, use holes to represent the value of each side. De esta manera, se disminuye levemente el peso de las caras según la cifra correspondiente.So, the weight of each side slightly decreases as the corresponding figure. O sea, habría ligeramente una mayor probabilidad de obtener un 6 que un 1, debido al desplazamiento del centro de gravedad por la leve diferencia de masa entre las dos caras contrarias. Thus is, it will have slightly more chances to obtain a 6 rather than an 1, due to displacement of the center of gravity by the slight mass differences between two opposite faces. Como sucede en un tiovivo.Entre más cercanos sean los números opuestos, menos diferencias habrá entre sus probabilidades (4 y 3). While closer are the opposite numbers, there will be  less differences between their chances (4 and 3). Así, aunque teóricamente son iguales, en el sentido práctico, en los dados agujereados de masa homogénea, existe ligeramente una mayor posibilidad de obtener 6, 5 y 4, que 3, 2 y 1, en ese orden. So, although they’re theoretically equal (under Math’s point of view), in homogeneous mass leaky craps, there’s actually a slightly greater chance of getting 6, 5 and 4, than 3, 2 and 1, in this order. La discrepancia será mayor, cuanto mayor sea el tamaño de los orificios, concebidos por el diseñador. The discrepancy  will be greater, depending on the size of the holes, conceived by the dice’s designer.

Ahora, ¿cómo se compensan? So, how do they compensate?

A)   Si la unión de los volúmenes de los orificios en cada cara fuesen iguales (donde los seis agujeros pequeños equivalen al espacio del uno)If the union of the volumes of the holes on each side were equal (where the Six’s small holes were equivalent to the One’s hole volume)  

B)   Pintando los puntos y dejando las caras planas.Painting the numbers, so, the sides remain flatbed.

From this conditions, the mathematical approach assumes either, Desde estas condiciones, el enfoque matemático asumiría cualquiera de las dos, mientras el modelo físico solo la segunda. while the phisical model  just  the second. ¿Por qué? Why? Porque la forma y distribución distinta de los orificios harían actuar a las fuerzas de maneras particulares en cada cara, principalmente la de fricción, tanto en el aire como en la superficie. Because differents shape and distribution of the holes would make the physics forces act particularly on each side, mainly the friction, both in the air and on the board. Esto alteraría la paridad de las posibilidades. This would alter the parity of the possibilities. Por ello, los puntos deben estar pintados. Therefore, the dots must be painted. Solo de esta manera, cada cara tiene una expectativa real de 1/6 de aparecer en cada tiro.Only in this way, each side has a real expectation of 1/6 to appear in every shot. A pesar de esto, los dados con orificios son altamente utilizados y comercializados como dados balanceados. Despite this, the dices with holes are highly used and marketed as balanced dices.

Este fenómeno de las pequeñas diferencias específicas, es usual en muchos modelos matemáticos, pues siempre “infieren” la homogeneidad física de los elementos que intervienen, lo que en el mundo real no existe casi nunca.This phenomenon of small specific differences, is usual in many mathematical models, because  these always "infer" the physical homogeneity of the elements involved, which in the real world  hardly exist. El análisis combinado con modelos físicos, nos dan un mayor acercamiento a la realidad.The analysis combined with physical models, brings us closer to reality. Solo con un modelo matemático habría sido imposible llegar a la Luna, o poner un satélite artificial en órbita. Just with a mathematical model it would’ve been impossible to travel to the Moon, or put an artificial satellite into orbit.

 

Ahora, ¿Qué se entiende por “cargar” el dado?Now, what is meant by "load the dice”? Es cuando se altera la distribución de su peso para favorecer la probabilidad de una cara sobre otra. It is when the weight distribution is altered to favor the chance of a side over another. Pero ¿se puede aumentar dicha probabilidad sin recurrir al fraude?But,  can we increase this probability without resorting to fraud? Y dice la Física: ¡¡SÍ, DEFINITIVAMENTE!! And Physics says: YES, DEFINITELY !! Y aquí es donde se pone interesante!And here it’s where it gets interesting! La resistencia de las superficies, y la incidencia de la gravedad en el dado, tanto por el tamaño como por el peso, reducen relativamente características como el giro, el bote y el desplazamiento. The surface resistance and the impact of gravity on the dice, both the size and the weight, relatively reduce features like the twist, the rebound and displacement. Por lo tanto, podemos EJERCER CIERTO CONTROL sobre esas probabilidades “definitivas” esgrimidas por las matemáticas.Therefore, we can exercise some control over these "definitive" probabilities  put forward by the Maths.

Imaginemos que tenemos un dado de un kilogramo de peso, con superficie porosa, y lo lanzamos desde la misma altura y velocidad de un dado normal, en un suelo poco rígido (arena, por ejemplo).Imagine we have a dice with porous surfaces, one kilogram of weight, and five inches of measure in each edge. Let’s launch it from the same height and with similar speed of a normal dice, on a little stiff soil. The odds that always comes out the face we want, overwhelmingly increase, if we’re careful to put the craps in the same starting position, and throw it with the same movement and strength. That is to say, the mathematical odds on both dice are the same, but the possibilities to manipulate them LEGALLY, are extremely different. Esto es lo que DIFERENCIA UN DEPORTE DE UN JUEGO DE AZAR: ¡se puede “controlar” la aleatoriedad con cierto éxito, aunque las probabilidades matemáticas teóricas sigan siendo las mismas!This is what DISTINGUISHES SPORTS FROM GAMING: you can "control" the aleatority with some success, although the theoretical mathematical probabilities remain the same! Y esto establece un distanciamiento entre el FENÓMENO ESPECÍFICO y la ESTADISTICA PREDICTIVA obtenida por el COMPORTAMIENTO GENERAL DE FENÓMENOS SIMILARES. And this capacity sets A GREAT RIFT BETWEEN THE SPECIFIC SITUATION AND THE PREDICTIVE STATISTICS obtained by the general behavior of similar phenomena.

Es decir, las probabilidades matemáticas en ambos dados son las mismas, pero las posibilidades de manipularlos LEGALMENTE, son extremamente distintas.

Pero entonces, ¿cuál es la diferencia con los dados “cargados”?But then, what’s the difference with the "loaded" dices? En estos la distribución del peso no es equitativa. In this case, the weight distribution isn’t equitative. Esto nos alejará abrumadoramente de la realidad de la interpretación. So, you’ll get the same specific number (side), independently the way you execute the shot. Your ability is not what defines the result. This overwhelms us away from the reality of the performance. Entre más descompensados estén, mayor será el error de interpretación. More unbalanced they are, the interpretation error will be greater. Es lo que hace el DOPING en el deporte. IT’S WHAT MAKES DOPING IN SPORT. Pero andando más lejos aún, si usamos más de un dado ¿están igualmente “cargados”? But  going even further: if we use more than one dice:  are they equally "loaded"? Si así fuese, las probabilidades se alterarán proporcionalmente para todos los resultados. If so, the probabilities are altered proportionately  for all the results. Pero si cada dado tienen un nivel diferente de manipulación de su centro de gravedad, el error se introduce en “amalgama”, haciendo más inutilizables los datos de cada tirada para prever eventos futuros, debido a que ambos dados manejan el mismo código (1, 2, 3, 4, 5 y 6), y la anotación no distingue un dado de otro. But if each dice has a different level of manipulation of its center of gravity, the error is introduced like "amalgam", making more unusable the data to predict future events, because both craps have the same code (1, 2, 3, 4, 5 and 6), and the annotation doesn’t distinguish a dice from another. Solo sigue los resultados generales (estadística acumulativa). This just follow the overall results (cumulative statistics). Esto quiere decir que no es solo importante entender la condición, sino también la magnitud particular de la misma. So, we see it’s not only important to understand the condition but also the particular magnitude of it.

En resumen, EL DEPORTE TIENE UNA ALEATORIEDAD RELATIVA INTRÍNSECA, QUE EL AZAR EMULA, SOLO SI SE HACEN TRAMPAS.Summarizing, SPORT HAS A RELATIVE INTRINSIC ALEATORITY, THAT RANDOM EMULATES ONLY WHEN CHEATING.

Mirémoslo ahora en el Beisbol de MLB: ¿Qué sucedió de importante en estos años, que nos impide utilizarlos como muestra confiable para hallar nuestros promedios?Let's now look  at the Mayor Leagues Baseball: what happened significantly in these years, which prevent us from using them as reliable data to find our averages? Si miramos la progresión de jonrones de las últimas temporadas, salta a la vista algo importante: If we look at the home runs progression in recent seasons, jump to the view  something important:

	HRS
SEASON	MLB	AL	NL
2014	4 186	2 161	2 025
2013	4 661	2 504	2 157
2012	4 934	2 500	2 434
2011	4 552	2 271	2 281
2010	4 613	2 209	2 404
2009	5 042	2 560	2 482
2008	4 878	2 270	2 608
2007	4 957	2 252	2 705
2006	5 386	2 546	2 840
2005	5 017	2 437	2 580
2004	5 451	2 605	2 846
2003	5 207	2 499	2 708
2002	5 059	2 464	2 595
2001	5 458	2 506	2 952
2000	5 693	2 688	3 005
1999	5 528	2 635	2 893

Como se ve, la producción de cuatroesquinazos estaba sobrecargada en estos años, siendo ampliamente 1999, 2000 y 2001, los de mayor cantidad en los últimos quince años.

As shown, the production of homers was overloaded in these years, being widely 1999, 2000 and 2001 those with the  highest amount in the last fifteen seasons. En ocasiones hasta más de 1 000 unidades por encima de lo actual. Sometimes even more than 1000 units above the currents. En el año 2000 se conectaron 1 507 vuelacercas más, que en la temporada 2014. Esta fue una época muy crítica para los records en la MLB, debido al fantasma del dopaje. In 2000, 1507 more homers were hit than in the 2014 season. This was a very critical time for the MLB records, because of the shadow of doping.Los varios peloteros que recurrieron a este fraude para mejorar sus rendimientos, hacen de estas estadísticas una cantera dudosa para cualquier análisis. Several players who resorted to this fraud to improve their performances, made these statistics a dubious data for any analysis. Esto se debe a que no solo la producción de cuadrangulares se sobredimensiona, sino todos los parámetros ofensivos, incluso las bases por bolas intencionales, y hasta los HBP. This is because not only the Produced Runs are oversized, but all offensive parameters, including intentional walks, and even HBP. Todos recordamos la batalla por el record de bambinazos entre Sosa y McGwire (1998/66_70). We all remember the battle for the homer’s record between Sosa and McGwire (1998 / 66_70). Luego Barry Bonds (2001/73). Then Barry Bonds (2001/73). Sin embargo, en los últimos tiempos, son pocos los peloteros que rebasan la cifra de los cuarenta jonrones. However, in recent times, there’re few players who exceed the amount of forty home runs per season.

Existió además la teoría de las bolas trucadas.There was also the doctored balls theory. Algunos análisis no oficiales reportaron cambios del núcleo de corcho por otro de goma, o diferencias en el bote de pelotas fabricadas en 1999 y 2000. Esta teoría sin embargo, quedó “descartada” luego del escándalo de los esteroides. Some unofficial analysis reported changes in the ball rubber core by a cork core, or anomalies in rebounding of balls manufactured in 1999 and 2000. This theory, however, was "discarded" after the steroids scandal.

La situación estadística habría sido medianamente reparable, si todos los jugadores, de todos los equipos, en todas las temporadas hubieran hecho uso de esteroides;This statistical imbroglio would’ve been partially repairable, if all players of all teams, in all seasons would’ve ​​used steroids; o mejor aún, ninguno de ellos. or better yet, none of them. De esta manera, habría una proporción estadística utilizable en otros años. Thus, there would’ve been a statistical ratio usable in other years. Pero desgraciadamente, nunca sabremos cuántos jugadores consumieron esteroides ni por cuánto tiempo, lo que nos introduce un error “en amalgama”. But unfortunately, we’ll never know how many players used steroids or for how long, which introduces  amalgamated mathematical errors. NO sabemos en cuánto alteraron las estadísticas que se utilizaron para calcular los coeficientes. We don’t know how much they altered the statistics used to calculate wOBA’s coefficients.

Por otro lado, si hacemos un análisis superficial, pensaríamos que la disminución de los jonrones se debe, definitivamente, al mayor control sobre las sustancias prohibidas.On the other hand, if we make a superficial analysis, we would think that the decline in home runs is definitely due to a greater control over prohibited substances. Pero, otro elemento fundamental en nuestra lista de circunstancias, es que en estos años todavía la MLB no había concretado medidas determinantes para restablecer la zona de strike. But another key element in our list of circumstance is that in those years MLB still hasn’t materialized decisive actions to restore the strike zone. Existía cierta arbitrariedad en los conteos, lo que influye directamente sobre la generación o no de carreras. There was a great arbitrariness in the enforcement’s criterion, which directly influences the generation or not of runs. El contrato de QuesTech con MLB para desarrollar un sistema digital de monitoreo y evaluación del arbitraje en los conteos (2001), trajo consigo una variación notable de la zona de strike. The QuesTech and MLB contract to develop a digital system for monitoring and evaluating  count’s arbitration (2001), brought a remarkable change in the strike zone. Tal ajuste hizo inicialmente a los lanzadores más bateables, por lo que estos incorporaron nuevos tipos de lanzamientos, ángulos de salida y estrategias de picheo. Such adjustment initially made batting easier, but at the same time, it forced each pitcher to add new types of throws, release angles and pitching strategies, and to increase the throwing accuracy. Si volvemos a la tabla de jonrones por temporada, vemos que alrededor de 2006, la producción cae paulatinamente a menos de 5000. Probablemente corresponde al período de transición de la adaptación a la nueva zona de strike. If we return to the table of homers per season, we see that around 2006, the production gradually drops to less than 5 000. Probably, it corresponds to the transition period of adaptation to the new strike zone. Esto, y la ampliación del número de equipos que tributan a las Mayores, han aumentado ostensiblemente la calidad y especialización de los lanzadores.This, and the increasing of  the number of teams that nourish MLB, have greatly increased the pitchers quality and specialization. Por tanto, los bateadores de hoy enfrentan un pitcheo más difícil, en términos generales. Therefore, hitters today face in general a tougher pitching.Además, el cambio generacional y tecnológico, hace que los deportistas se comporten técnica y tácticamente de modo ligeramente mejor. Furthermore, generational and technological changes make players behave technically and tactically in a better way. Entonces, los datos serían útiles si esta situación no hubiese cambiado, como no cambian las proporciones entre las caras de uno a otro dado. Then, the data would be useful if this situations wouldn’t have changed, as haven’t changed the proportions between the sides of each dice.

Con todos estos elementos circunstanciales en nuestra balanza, veamos el cambio proporcional entre los años 2011-2014, en relación a 1999-2002.With all these circumstantial elements in our balance, let’s see the proportional change between the seasons 2011-2014, compared to those of 1999-2002.

Las barras rojas son los datos evaluados para obtener los coeficientes del wOBA, y las amarillas, la proporción de los mismos datos enThe red bars are the parameters proportions in the data evaluated to obtain the wOBA’s coefficients , and the yellow ones, are the proportion of the same parameters in the last four years. Se observa una disminución importante, pero equitativa, en RBI, R, HR y BB (aproximadamente -15%). Runs are the referential data between proportions. So, the comparison shows a significant but equitative decrease in RBI, R, HR and BB (approximately -15%). Los H, 2B, 3B y AVG, aunque también disminuyeron, lo hicieron apenas entre el 5 y el 8%. H, 2B, 3B and AVG, also decreased, but just  between 5 and 8%. Se robó cerca de 5% más por carrera, pero fueron capturados cerca de un 3% menos. The Stolen Bases are about 5% more per run, but about 3% less of runners were caught. Y los ponches se incrementaron en casi un 15%, a pesar de que el rescate de la verdadera zona de strike, favorece a los bateadores y no a los lanzadores. The Strike Outs increased by almost 15%, eventhough the real strike zone reestablishment, favors hitters and affects pitchers. Obviamente, los números modelo, tienen un comportamiento muy diferente y sobre todo, indistintamente desproporcionado, a los de las campañas actuales. Obviously,  the numbers used like model have a very different behavior and, above all, are indefinitely disproportionated to current campaigns. Por ejemplo, cuando vemos la cantidad de carreras, podríamos a groso modo, decir que un HR sigue teniendo aproximadamente el mismo coste que en 2002 . For example, when we see the number of runs, we could roughly say that a HR still have about the same cost as in 2002. Sin embargo, los dobles y triples descendieron su valor de modo visible, puesto que se necesita una mayor cantidad, para producir las mismas carreras, que es el dato referencial entre las proporciones. However, the value of doubles and triples decreased visibly, so, a greater amount is needed to produce the same Runs.

En resumen, este promedio nos dice cuál es nuestra probabilidad de anotar carreras, según el Estado Base/Out en que nos encontremos, pero el dato está afectado visiblemente de un período a otro.In brief, this average  tells us what is our chance of scoring, according to the Base / Out State where we are, but the data is visibly affected from one period to another. I mean, all real coefficient have changed. For this reason, nowaday the most important stathead groups, PROCESS EACH SEASON DATA INDEPENDENTLY, so, THE COEFFICIENTS IN THE FORMULA CHANGE EVERY YEAR. Despite this, a lot of fans and journalist continue to using the coefficients used in the first version of the formula. The web sites Fan Graph and Baseball References (among others) use his own wOBA’s versions to analyze the players performance. ALSO THE COMPENSATION NUMBER CHANGES.

2. SEGUNDO PROMEDIO: Es el realizado sobre los eventos, según su tipo. 2. SECOND AVERAGE: It’s calculated on each type of events. Acá existen dos introducciones de error entre las más importantes. Here there’re two introductions of errors among the most important. En primer lugar, a la hora de encarar el valor de las acciones específicas. First, when are distinguished the value of some specific actions. A nuestro entender es un error separar las situaciones que generan las mismas reacciones.As we understand, it’s a mistake to separate the situations that cause the same reactions. Es decir, NO HAY diferencias, ni desde la disposición defensiva, ni desde la estrategia ofensiva, si con bases limpias, un corredor arriba a la primera base por error, por hit , por base por bolas, golpeado por el lanzamiento, u otra que lo permita. I mean, there’re no differences, nor from the defensive disposition or from the offensive strategy, if with clean bases, a runner reaches the first base by error, hit,  base on balls, hit by pitch, or another one that permit it. El cambio, muy ligero, podría estar en la psiquis del pitcher, pero en la práctica, la mente de todos está enfocada en que hay un corredor en la inicial con determinada cantidad de outs, y no en cómo llegó a ella, más si hablamos de jugadores profesionales. A very light change could be in the psyche of the pitcher, but in practice, everyone's mind is focused in a “runner on first base” situation, with certain amount of outs, and not on how the runner got it, especially when we talk about professional players. Las probabilidades de anotar carreras son exactamente las mismas. The chances of scoring runs are exactly the same. Esta fragmentación innecesaria, introduce una diferencia de lectura en varios datos, que no existe.This unnecessary fragmentation  INTRODUCES A DIFFERENCE IN READING SOME PARAMETERS, THAT DOESN’T EXIST.

Así vemos en la fórmula final del wOBA, que un HBP tiene un valor de 0,75 y una BB 0,72.Thus, we see in the final wOBA’s formula, that a HBP has a Run Value of 0.75, and a BB  0.72. Esta diferencia, nos hace ponderar a un bateador sobre otro de la manera equivocada, si lo miramos como ESTADÍSTICA DE SELECCIÓN. This difference makes us ponder a batter above another in a wrong way, if we look at wOBA as a  STATISTICS FOR SELECTION. La desproporción de ocurrencia entre uno y otro introduce diferencias palpables. The occurrence disproportion between both parameters introduces palpable differences. Es similar al valor concedido al AVG cuando se tienen pocas veces al bate. It’s similar to AVG’s value when there’re just few at-bats. Por ello, lógicamente, el análisis del AVG se subordina a la cantidad de oportunidades, y no solo al porcentaje obtenido. Therefore, logically, the AVG analysis is subordinated to the number of opportunities, not only to the percentage obtained. Así, en las temporadas entre 1999 y 2002, se produjeron 68 180 BB, por solo 6 792 HBP, apenas un 9, 96%. Thus, in 1999 to 2002 seasons, there were produced 68180 BB,  for only 6 792 HBP, just a 9.96%.

Y aquí se manifiesta otra variante del “Síndrome de Default” .And here it manifests another variant of the "Default Syndrome" . Según la fórmula, un bateador que RECIBE 10 pelotazos, aporta más carreras que uno que OBTIENE 10 bases. According to the formula, a batter who receives 10 HBP, provides more runs than one who gets 10 BB. Sin embargo, el pelotazo es un error del pitcher, donde el bateador no tiene mérito alguno, mientras la base por bolas, es todo lo contrario. However, the HBP is A PITCHER’S MISTAKE, where the batter has no merit at all; meanwhile the BB it’s the opposite. Lo mismo sucede con el RBOE (embasado por error). The same applies to the RBOE (reached base by error). Este parámetro tiene más Valor de Carreras (0.92) que los hits de una sola base (0.90). This parameter has more Run Value (0.92) than single hits (0.90). La proporción de ocurrencia fue de 117 099 sencillos por solo 13 539 errores (11,56%). The proportion of occurrence was 117 099 singles, by only 13 539 bases reached by errors (11.56%).  Some wOBA’s recents version don’t use the RBOE. Anyway, each RBOE and HBP represent a runner on base, with a punctual incidence on scoring. So we can’t eliminate these parameters from the analysis, but we can’t count them  like hitter’s Positive Actions. Recent wOBA’s algorithms don’t achieve to manage this delicate situation.

Aquí vemos una causa más para valorar el wOBA como estadística histórica en lugar de selectiva.Here we see a cause more to assessing wOBA as an historical statistics rather than a selective one. Explico: Una estadística histórica lleva el performance Remember: A historical statistics register the global performancetotal, o sea, todo lo acontecido., I mean, everything that happened. Una estadística de selección, busca elegir a un jugador sobre otro, por su A selection stats, tries to choose a player above another, for their calidad capacidadindividualindividual capacities. Sin embargo, el algoritmo procesa dos variables que son errores del contrario. However, wOBA’s algorithm processes two variables that are opponent’s errors. Esto quiere decir, que no fueron responsabilidad de una Acción Positiva del bateador, pero aparece como tal, ocultándose en el resultado final. This means that even thought these parameters were not because of hitters Positive Actions, they’re counted as such, confounding the final result. Para más, se les otorga una dimensión mayor que a dos acciones fundamentales como el sencillo y la base por bolas. Further, they’ve technically more value (according to the formula) than two fundamental hitters Positive Actions, as Single and Walked. Recordemos el ejemplo absurdo del tablero de Recall the absurd example of the primitive man seeing the chessboardA. Cuando se integra esa información en el wOBA, no dice qué porciento pertenece a errores del contrario, ni cuáles a virtudes del bateador. When that information is integrated in wOBA’s formula, we can’t say what percentage belongs to opponent’s errors, or what to hitter’s virtues. Pero cuando comparamos utilizando esta estadística, interpretamos que el número obtenido, es producto de But when we compare using these statistics, we interpret (by Default) that the number obtained is a direct product of hitter’s quality, que es lo que nos interesa. which is what interest us. El mayor valor conferido a las Acciones Negativas The higher value given to the opponet’s Negative Actions takes usdel contrario , nos aleja del camino que pretendemos transitar, pero no nos damos cuenta.away from the answer we’re looking for, without us noticing it.

De manera objetiva, para elegir a un jugador sobre otro, no nos interesan los errores y golpeados por lanzamientos por ser de aleatoriedad total (si eliminamos la intencionalidadMoreover, objectively, to choose one player above another, we’re not interested on bases reached by errors and HBP because of its full wild randomness (if we eliminate the intentionality on any HBP). Son las únicas dos acciones en que ninguno de los dos contrarios tiene la intención legal de realizar dicha acción, principalmente en el error, donde fallan ambas partes. They’re the only two events that neither contrary has the legal intends to perform, mainly errors, where both teams fail. In order to understand: a batter with horrible reflexes, who get 100 HBP, and 100 errors on his in-play balls, would have a higher wOBA than Ichiro Suzuki in a campaign where he acchieves 182 hits in 200 appearances. Nothing more and nothing less than 910 AVG!!!! However, any runner on base represents a scoring posibility, and he could have influences on the rest of the inning, or even of the game. For that reason, Waibi designs the WAIBI PULSE.

We must insist on understanding something about the so revisited randomness: In baseball, the randomness is relative because of one important factor: The player. The player always tries to achieve an objective depending on his own abilities and those of his opponents. According concentration levels and technical and tactical training (among others) are taken seriously by the player, this randomness is "controlled" more frecuently by the most capables. Baseball is a probabilities game, but although there’s a Ramdom’s providential intervention in many circumstances, it’s above all things, a game of individual skills subordinated to a collective and a purpose. THIS ISOLATED INDIVIDUAL CAPACITY IS WHAT WE WANT TO EVALUATE IN A SELECTION STATS.

Ramdomness is conceptually opposite to the intentionality, if you have enough tools and abilities, as we saw earlier in the example of the dices. Nevertheless, both phenomena coexist in Sport. There’s a baseball phrase that says: "Homer just happens, you don’t look for  it." However, it’s possible to “look for” a home run, and it's not just about  swinging for the fences. Unfortunately, this is what’s believed. Likewise with a bunt-moving, this is about having an effective method which overcomes the opposite one to avoid it. If it was not so, how could some Circus’s performers hit repeatedly a small moving target with a knife? How could others cut a cigarette in three parts with a whip, while another person held it in the mouth, without hurting? And what about the horse archers, riding over a rough terrain with no other support than their legs, while shooting arrows with great accuracy? There’s a lot of ancient armies with this amazing soldiers (Mongols, Huns, Samurais, Sarmatians, Parthians and others). So, the human body is an amazing machine, in which most players operate only in a very physical level. So, when they’re  “looking for" a home run, this mean swinging at the ball as hard as possible, hoping for a homer. And that’s precisely what prevents, in most cases, that they achieve the target. In another article we’ll delve into this. We just add that THE KEY IS TO HIT THE BALL IN THE CENTER, with the right angle and a certain force. When we exceed that force, as happen most of the times, we affect the other two variables (point and angle of contact with the ball) ...  It’s in these conditions where Random, and not the sporting talent, does eventually match the three variables at the same time, and the homer happens. This doesn’t mean that the homer will always be achieved, but definitely will occur more often.

The second important error-in at this wOBA’s phase, occurs with events of the same type, in different B/O_State. Remember, we’re dissecting wOBA as a SELECTION STATS. So, let's analyze what happen with homers:

To implement the coefficients in the formula, we go through this procedure. Each specific data (HR, H, 2B, 3B, BB, HBP, etc), is processed according to each specific Base/Out_State. This will  give us the  Run Value  by event. In the specific case of homers  it’s very simple to understand it, because it’s a single action, which always ends in the same state of "bases empty".  In the graph, the first group of columns, is the Run Value when the initial state is also "bases  empty". The following three groups, are the states with a runner on circulation. The next three, with two on bases. The last one refers to the Grand Slams.

Here are shown behaviors  related to:

A. Amount of runners on bases.

B. Number of outs in the inning

C. Runners closeness to the plate.

Logically, home runs have more value, when find more runners on bases. But ... what about Homer’s Run Value variation in the same inning?:

1. The VALUE IS CONSTANT when the bases are empty.

2. With runners on bases, the VALUE INCREASES as more outs in the inning.

3. With runners on bases, the VALUE DECREASES as more the runners advance.

Does it make any sense? Why this behavior? When trying to find out how many runs more than expected produces a hitter, the formula directly relate a SPECIFIC VALUE with a PROBABILITY. In fact, what’s being measured is "how much the TEAM has exceeded the scoring expectations for that specific situation." And then, "how much are the TEAM’s new scoring expectations, after THIS HITTER’S intervention." It lacks of a comparative analytical value, because in the generalization of the formula, the relativity of the datum is canceled, notwithstanding is precisely this relativity what gives it relevance. To make you understand: a batter who hits a home run with bases loaded with no outs, generates a Run Value of 2,139; but doing so with two outs, the value is 3,302. However, the real value of runs, in both cases, is the same (4), which is what really matters. Therefore, when we use wOBA as a selection stats, the relativity of data favors batters that hit homers with more outs in the inning. That is, the RUN VALUE IS MORE ASSOCIATED TO CONDITIONS  THE BATTER CAN’T CONTROL, which  are completely random (like in which order occur his At_Bat in the inning, or how advanced were the runners, among others.)  THAN TO THOSE DETERMINED BY HIS DIRECT ACTION (relative randomness); precisely what we want to evaluate.

This moment’s evaluation (related to outs in the inning) may have some sense in sports like Long Jump and High Jump, and others where it’s important who gets first to the result. The most important point is that in these sports, all attempts are executed by the same athlete. I mean, each athlete is a team. In baseball this is meaningless, because the actions are performed by different batters that must be evaluated under the same conditions, as much as possible. Thus, the leadoff of each line up, are more likely to be favored by these situations (from their second appearance), because he’s preceded by the weakest hitters in the line-up (8th & 9th). Furthermore, they bat at least once in each game, with no outs on the board (first appearance). Thus, two batters with similar qualities, will have different data depending on the offensive characteristics of their respective team, and not necessarily on themselves.

Regarding the advance of the runners, we wonder why the Run Value decreases, as they are closer to the plate. The same. This means that there’re greater chances of scoring. When we subtrack  the PROBABILITY from the SPECIFIC DATA, we’re favoring the batter who hit the home run with runners furthest from the plate, because they've less probabilities to score before the end of the inning. However, the actual value of the homer is still the same. Thus, those players in slower line ups, with less base_stealers, or with more deficiencies when running  bases, will be more favored.

THIRD AVERAGE: As it was extremely difficult to know the initial and final states of each event separately, the creators of wOBA decided to average each event by B/O_State, and leave it in a number.  Logically, this greatly facilitates the calculation. This number (plus its15%) is the coefficient used in the formula for each parameter. By resorting to this method, is implemented a system whose functionality is very similar to Slugging. Except that instead of using integer numbers relating to run bases, it uses decimal numbers concerning to scoring probabilities, plus some additional parameters. By including the generated runs, and not just the dimensions of the hit, it introduces an important perception error. In wOBA, all hits of the same type, have the same Run Value,  just as in the Sluging the same kind of hit has the same run distance value. The conceptual problem here is that SLUGGING IS RELATED ON EACH SINGLE  AND SPECIFIC ACTION, while RUN’S PRODUCTION IS DUE TO A COMBINATION OF CONSECUTIVE ACTIONS. Thus, a player who hit a triple or a double with bases loaded, provides, just with this action, three times more runs, than another that produces a homer with empty bases. However, using its coefficients, wOBA confers 1.56 and 1.95 respectively (with 15% compensation) regardless of the actual contribution. So, THE SLUGGING ALWAYS REPRODUCES THE EXACT REALITY, WHILE THE wOBA ALMOST NEVER.

Summarizing, in this system of averages, and with the final calculations, a solo homer always gets a 70% extra bonus, while a triple with the bases loaded, is penalized with 54.78% less than the real value. Ironically, wOBA aims to determine who are the more productive hitters, but by using the system of averages, it ends affecting them, and favoring those whose production is actually lower than the average

In order to understand: using the above two examples, imagine that two batters produce 10 hits in 20 at bats distributed in 10 situations of "bases empty" and 10 of "bases loaded". The batter “A” hits 10 homers, but always with "bases empty"; and the batter “B”, hits 10 triples, but always with "bases loaded". Both have an AVG of .500. But wOBA favors the first (10 x 1.95 / 20 = 0.975) instead of the second one (10 x 1.56 / 20 = 0.780). However, the batter “A” concretely  produces 10 runs and the “B” generates 30. That is three times more!!! So, who would be chosen for you?

If we did a superficial  analysis of the CONTEXT, as in wOBA’s final formula, we’d assume as an irrefutable truth (by Default), that the batter “A” hasn’t had the luck to find too many runners on bases, as happened to “B”. That’s due to the fail in specific opportunities are not recorded in almost any Baseball formula (cumulative statistics) before Waibi System (progressive statistics). Thus, by applying the "Average" coeficient, WE FOCUS OUR INTEREST ON ISOLATED HIT AND NOT ON THE CIRCUMSTANCES. However, when we scrutinize the at-bats, it shows that both had similar opportunities. The following chart supports the claim that randomness in baseball  is not as absolute as the WOBA mathematical model suggests, but relative:

The chart shows the homers  percentage distribution by B/O_State, according to the outs in the inning, in the data processed to create wOBA’s foundations. Why this particular behavior? Although it may seem exorbitant, the answer is quite simple. When the inning is beginning, most pitchers search for "reconnecting" with the strike zone, especially if the offensive chance of their teams has delayed more time than usual. The most effective pitchers can start the inning directly with more difficult throws and hitting the corners, but generally they begin with more hittable pitches. Moreover, pitchers with longer performances, as starters and long releavers, dose their resources to avoid arm’s early fatigue, and hitters adjustment. So, this kind of pitchers don’t constantly resort to the maximum speed, or to their most dominant throws when the bases are empty (as occurs in the case of closer pitchers), but they use their entire repertoire, looking for advance the game holding the batters in check. Therefore, specialization has helped to reduce the number of home runs when there’re no outs, as there’re at least two innings, in which pitchers are working at full. (Eighth and ninth innings).

As shown in the graph, the situation dramatically changes when there’re runners on bases without outs. Here the pitcher cares much more to prevent an opposing rally, and he uses most often  his “star” throws and speed, registering a peak in the administration of his best resources.

Another curious thing is that with runners on bases, most home runs are allowed, when  there’re more outs. To our understanding, for the same reasons. The pitcher uses his best technical arsenal with runners on bases and no outs, besides being fresher after resting in the interinning (just like whith batches in body building). Also, the batter didn’t  had time to make his individual adjustment for this specific situation. When there’re more outs, the batter in turn, together with the batting coach, has more time to study the pitcher AT THAT PARTICULAR MOMENT (inning); besides a higher physical recovery, if he were a fielder, mainly those positions with greater physical wear (catcher, shortstop, center fielder, or pitcher in the league without designated hitter). Therefore, the hitter’s adjustment is greater, the later in the inning they consume his at-bat.

	State 1	State 2	State 3	State 4	State 5	State 6	State 7	State 8
0 outs	5518	1195	292	42	305	120	59	78
1 out	3498	1401	535	193	544	230	133	230
2 outs	3023	1394	661	273	588	312	155	247

This is the distribution of all 21 026 homers in the seasons of 1999-2002, used to obtain the numeric constants applied today.

To understand more easily, let's see it in percent:

	State 1	State 2	State 3	State 4	State 5	State 6	State 7	State 8
0 outs	26,24	5,68	1,39	0,20	1,45	0,57	0,28	0,37
1 out	16,64	6,66	2,54	0,92	2,59	1,09	0,63	1,09
2 outs	14,38	6,63	3,14	1,30	2,80	1,48	0,74	1,17
totales	57,26	18,98	7,08	2,42	6,83	3,15	1,65	2,64

In the state 1, that is "bases empty", occur the 57.26% of homers !! To wOBA, without the compensation of 15% to match up to the OBP, a home run should value approximately 1.70 runs. But actually, according to used data, the 57.26% of homers produce a single run, and the 28.48% produces 2. Only 2.64% of the homers produce an ammount of 4 runs, which give a special value to the hitters included in this group. 

 

But why in the State 7 (runners on second and thirth) the pitchers allow lest homers than with bases loaded? The reason is that in the State 7, the first base is empty. So, the pitchers aren’t required to hit the strike zone, like in the State 8.

 As the algorithm used by wOBA is based on the concept of the averages, to be realistic it requires at least that:  

1. Each pitcher acts in the same way in any situation, in any inning, with any score, against any hitter. 
2.  All League’s pitchers have the same quality. 
3. All League’s hitters have the same quality. 
4. The situations occur in proportion to the number of runs they produce. That is, a B/O_State of “bases empty" should occur four times more  than a state of "bases loaded". 
5.  All hole places have the same opportunities. 
6.  All parks have the same characterístics 

As the sides of the dice. That way, the graphic obtained should show this:

That’s to say, to make sense to use the same Run Value for all homers, the frequency of opportunities should be of 100 "bases loaded” at-bats for every 133 with "two on base", 200 with "one on base" and 400 with "bases empty". Or what it’s the same, one Grand Slam opportunity every 8.33 appearances. In addition, the frequency of opportunity, must be the same for the whole line up. As we saw in RBI’s article, hitters with more offensive responsibility will find a greater number of runners on base, resulting in a greater chance of producing runs for each homer.

Actually, proportions are very different from the model. If the  ideal conditions were met, an average run should be worth 2.5 runs. Registering 1.70, the first thought is that B/O_States with more runners on base occur less frequently (in every innings there’re at least a situation of "bases empty", but rarely a "bases loaded" one). But not only  it occurs less frequently, but is also MORE DIFFICULT TO SUCCEED, because the pitcher works at his full  capacity. For these reasons,  Grand Slams are usually hitted by great hitters, or in winning streak. The average however, understands that homers not only produce the same amount of runs, but also have the same difficulty level, favoring those batters who hit homers in less complex situations, and therefore, with more possibilities to succeed. This is precisely the opposite of what wOBA’s concept claims . For example: in the formula, if facing pitchers of equal quality, a player hits 10 home runs with empty bases , and another one 10 Grand Slams, both with no outs, they have the same Run Value of 1.95 per homer. The second one, however, is a much better hitter, because he faces pitcher performing at 100% capacity.

Let's make a visual comparison between the behavior of Homer’s Run Value posed by the coefficients of wOBA’s model, and what really happen on the data that were processed to obtain them:

The first group of columns shows the proportion of RBI by homer, and the second, the frequency of these ones to achieve such behavior; namely, that hypothetically all homers have the same actual value like wOBA suggests. Yellow represents the home runs with empty bases, and descends to red, showing the homers with the bases loaded. This is the necessary distribution to wOBA be 99.99% reliable. Recall that when the same value is given to all homers (always multiply by 1.95) it means that everyone has about the same level of difficulty, and that opportunities are presented in a compensatory sequence, among other parities seen before.

The third group of columns shows the distribution of RBIs for home runs, in the seasons analized to create wOBA ('99 -'02) ; and fourth, the homers by runners found in circulation. As clearly seen, the Grand Slams of average model (employed by wOBA) occur 3.7 times more than in a real game. It’s enough to say there were 666 244 at-bats, with a frequency of one homer every 31.69. However, the Grand Slams, which according to the modeling scheme  must occur each 264 AB, in the real game, they occur each 1 200.

Let's see how it has been in recent times:

SEASON	TOTAL GS	LEADERS		GS HITERS
2014	83	2 (3) David Mesoraco		73
2013	96	2(3) Mike Napoli		84
2012	125	(3) Nick Swisher		104
2011	115	(3) R. Canó		102
2010	144	3(3) Y. Betancourt		120
2009	143	(5) Albert Pujols		115

As the table shows, there has been a significant drop in Grand Slam production in the recent seasons, going down about 42% in the most recent five. In 2014 only 73 batters homered with the bases loaded. Only two connected 3, but Mesoraco did it in less at-bats. This progressive decrease is mainly due to the general increase in the pitching quality. The frecuency was 1 per 2 436 plate appearances!

BRIEF INTRODUCTION TO WAIBI’S OFFENSIVE PULSE   

As we conclude that:  

A.   One thing is TEAM’S Run Expectation (where is very important the amount of outs) and another is the Specific Value of those Runs Produced by the BATTER, where it doesn’t  matter how many outs exist, but  just the runs scored because of his performance with some runners on base.

B.   The Runs Value in wOBA is completely situational. This means that it doesn’t evaluate the performance of a player compared to the average. It evaluates the performance of a player compared to the average IN A PARTICULAR SITUATION. As all players don’t go through the same situations or in equal proportion, by using the single average coefficient (for each event analysis), that situational relativity disappears, wrongly equating all circumstances. This ignores  that the difficulty level of success varies in correspondence also with the specific management of the resources by each pitcher. Therefore, the most capable hitters are the most affected, while the less skilled are more favored.

C.   The model differentiates a small group of more quality players, of all those involved in the league, but it doesn’t differentiate one player in a small group with similar quality.

D.   The aleatority of the system is more related to the analysis of general fenomena, and therefore its useful application is also in general situations (to know what kind of hitter should occupy each hole place, when to go to bunt, which group of hitters not to hire for a certain function, etc.). However, even though it’s true that Baseball is a game of probabilities, each specific player in each specific situation, potentially makes the difference between the exception (personal performance) and the rule (average yield), especially if he's a great hitter .

For these reasons Waibi Sabermetrics System redefines the use of the B/O_States in evaluating hitters, and replaces with the OFFENSIVE PULSE, whose calculation is one of the cornerstones of its functionality. The Offensive Pulse will be explained on the Waibi’s Web Site. Suffice to say that it evaluates the passive, active or mixed contribute  of each player, from the moment he starts his at-bat until he comes out of circulation, whether by scoring, out, ending of the inning or of the game.

Waibi’s coefficients, contrary to those of wOBA, emphasize not only on the performance of batter, but also on the difficulty to achieve it, and the importance it generates for the team. Being based on Play By Play annotation, it allows to go through each situation particularities, achieving to differentiate numerically, not just situational yields against the same kind of pitcher, but also to distinguish  between a specific pitcher and another. As we saw  in the article about AVG and AVQ, is not the same thing to hit a homer against the worst pitcher of the tournament, and do it facing the best. 

The calculation of Waibi Offensive Pulse is quite complex, so, to use a  calculator makes it very cumbersome. Obviously, it’s a computerized and automatic calculation. Thus supports the intention of Waibi System to open the way to the PROGRESSIVE STATISTICS in Baseball, to replace the merely CUMULATIVE, where undoubtedly wOBA is the most complex, complete and efficient.