Batting Order Research Articles

50, 100 & 150 Years: Best baseball batting order; mummies demystified.

50, 100 & 150 Years: Best baseball batting order; mummies demystified.

No expectation bias in elite-level cricket umpires’ leg-before-wicket (LBW) decisions according to batting order position

ObjectivesPrevious studies have shown that sport officials’ decisions can be impacted by biases associated with expectations. The aim of this study was to determine whether elite cricket umpires’ decisions are also influenced by expectations associated with batter skill. MethodsLBW decisions (n = 5578) from actual elite level cricket matches in Australia between 2009 and 2016 were analysed in a multi-level binomial logistic regression paradigm. In our first model, we predicted the likelihood that an umpire will answer ‘out’ for batters in the top order (1–4), middle order (5–7), and low order (8-11). In our second model, we controlled for the correctness of a decision. ResultsUmpires were more likely to respond ‘out’ as the batting order progressed, however this did not appear to be due to biased decision-making. Instead, as batting order progressed, batters were more likely to actually be ‘out’. ConclusionsCricket umpires do not seem to be impacted by expectation bias associated with batting order. This study highlights the importance of controlling for the correctness of a decision when exploring bias in sport officials’ decisions.

Further application of the generalized matching law to multialternative sports contexts.

Cox et al. (2017) successfully applied the multialternative version of the generalized matching law (GML) to pitch selection among a sample of Major League Baseball (MLB) pitchers. The purpose of the present study was to replicate and extend these findings by fitting the multialternative GML to pitch data among a sample of MLB pitchers with varying levels of success in the major leagues. We also examined how matching parameters changed as a function of novel antecedent game contexts such as the infield shift, game location, and number of times the pitcher faced the batters in the batting order. These results replicate the findings from Cox et al. and suggest the multialternative GML is a robust descriptor of pitch selection among MLB pitchers. Together, these findings further extend the generality of the multialternative GML to naturalistic, nonlaboratory environments.

Best’11 strategy in cricket using MCDM, rough matrix and assignment model

In 1982, Pawlak set up a fresh approach to deal with uncertainties namely rough set theory, Multiple-Criteria Decision Making (MCDM) first traced by Benjamin Franklin in 17th century. Several researchers did significant contribution to MCDM thereafter. An assignment problem involves what happens to the effective function when each of a number of sources is associated with the same number of destinations. Using MCDM, Rough matrices and Assignment model we are inducing an idea to pick Best’11 in all three formats (Test, One Day Internationals (ODI), Twenty20 International matches (T20I)) in the game of cricket with players from two nationals. Using the existing data, we are providing best batting position for any player to maximize team’s run. In addition, based on the preprocessing of informations, we are bringing some new indices to pick Indian squad for the 2019 World Cup cricket held in England from May 2019 to July 2019. After making a selection from our framework, we will compare the list of selected players by Board of Cricket Control Board in India (BCCI) and giveaway the percentage of similarity between the our selection against BCCI’s selection. We pick 11 players after selecting 15 players from 24 players to formulate the assignment model and offer the best batting order to optimize team’s run.

A sequential principal component-based algorithm for optimal lineup and batting order selection in one day international cricket for Bangladesh

ABSTRACTDetermining the optimal lineup and batting order have ever been a challenge in ODI cricket for the Bangladesh team management. Over the years, we have seen them trying different batsmen in various positions and the process is still going on. While a stable batting order is crucial for long-term success in the game, this is understandably a difficult problem to decide because there are so many determinants that a team needs to consider. These determinants are usually correlated and optimally mapping them into a single dimension can help us make the problem easier and comment about what’s best on statistical grounds. In this article, we propose a sequential principal component-based algorithm to evaluate the players’ performances in batting and bowling, and to order the batting positions of the recent Bangladesh national cricket team players to find the best squad. In particular, the first principal component explains a substantial portion of the variation in a linear combination of some commonly used measures of cricket prowess. The algorithm focuses on obtaining the best batting line-up using successive principal components for each position. We also layout different strategies of team formation based on the bowling performances for different conditions and pitches.

A DYNAMIC PROGRAMMING ALGORITHM FOR OPTIMIZING BASEBALL STRATEGIES

In this paper, baseball is formulated as a finite Markov game with approximately 6.45 million states. We give an effective dynamic programming algorithm which computes Markov perfect equilibria and the value functions of the game for both teams in 2 second per game. Optimal decision making can be found depending on the situation—for example, for the batting team, whether batting for a hit, stealing a base or sacrifice bunting will maximize their win percentage, or for the fielding team, whether to pitch to or intentionally walk a batter, yields optimal results. In addition, our algorithm makes it possible to compute the optimal batting order, in consideration of strategy optimization such as a sacrifice bunt or a stolen base. The authors believe that this baseball model is also useful as a benchmark instance for evaluating the performances of (multi-agent) Reinforcement Learning methods.

Survival ability of Indian and overseas batsmen on the cricket pitch in Indian premier league

Twenty20 format of cricket is a fast track ball game compared to the other formats of cricket viz. Test and One-day International (50-over a side). The Indian Premier League (IPL) is a national franchise based Twenty20 cricket tournament initiated by Board of Control for Cricket in India (BCCI). In this format, each batsman tries to score maximum runs in minimum balls. This fact increases the probability of dismissal of a batsman. As fall of wickets leads to the loss of resources of the batting side, thus it has an impact on the result of the game. This study tries to examine the survival ability of Indian and overseas batsmen in IPL 2012 season using a probabilistic model. The proposed model can be used to forecast the survival rate of the batsmen on the pitch in other format of cricket also, while the game is in progress. The findings of the study can be used to arrange the batting order of a team in Twenty20 cricket based on the match situation.

Batting Order Setup in One Day International Cricket

In the professional sport of cricket, batting order assignment is of significant interest and importance to coaches, players, and fans as an influencing parameter on the game outcome. The impact of batting order on scoring runs is widely known and managers are often judged based on their perceived weakness or strength in setting the batting order. In practice, a combination of experts’ intuitions plus a few descriptive and sometimes conflicting performance statistics are used to assign an order to the batters in a team line-up before the games and in player replacement due to injuries during the games. In this paper, we propose the use of learning methods in automatic line-up order assignment based on several measures of performance and historical data. We discuss the importance of this problem in designing a winning strategy for cricket teams and the challenges this application introduces to the community and the currently existing approaches in AI.

Using Analytics To Challenge Conventional Baseball Wisdom

Baseball, like most other sports, has a set of tenets that began early and have survived virtually unquestioned. Modern analytics gives us an opportunity to examine some of these long-held tenets to see if they were founded on solid evidence. This research examines some common baseball wisdom through an initial study utilizing simulation. In particular, the profiles of several baseball teams are constructed and various factors are examined by simulating ten baseball seasons under various configurations with the different teams. Contrary to conventional wisdom, a batting order where high-average hitters bat third in a lineup and the team’s best power hitter bats cleanup (fourth), for example, does not necessarily generate the most runs per game over the long run. Moreover, high-average hitters with less power can generate more runs per game than power hitters with lesser averages. Finally, it appears that hitters who perform well with runners in scoring position are more influential in helping their team score more runs than even more powerful or higher average hitters who do not produce as frequently in such cases. Players with lower star profiles, but who rise to the occasion with runners in scoring position, can often be purchased by baseball clubs that have a more constrained payroll; teams that are less well-off financially may thus purchase or trade for these hitters and still field a team with a competitive level of high run production.

Optimal batting orders in run-limit-rule baseball: a Markov chain approach

Amateur baseball contests, particularly those involving young players, often feature a run limit, which establishes a maximum number of runs that may be scored in a half-inning of play. Although conventional wisdom can be used for designing the batting order under standard baseball rules, the composition of the optimal lineup under run limit is still unclear, and the best batting order could differ significantly from the traditional ordering. In this paper, we consider the impact of run limits on the design of the optimal batting order, by developing a Markov chain model for calculating the expected number of runs scored (ENRS) under 3- and 5-run limits. We apply this model to both a high-quality and a lower-quality team, using the data from the 2011 Little League World Series, and illustrate the effect of run limit on the ENRS and the optimal batting order.

Various applications to a more realistic baseball simulator

This paper develops a simulator for matches in Major League Baseball (MLB). Aspects of the approach that are studied include the introduction of base-running probabilities which were obtained through a large data set, and the simulation of nine possible outcomes for each at-bat. Various applications to the simulator are investigated, such as the definition of a measure of the ability of a batter/pitcher, in-play strategy and the determination of the optimal batting order for a given team.

You're Hurting My Game: Lineup Protection and Injuries in Major League Baseball

Does lineup protection exist? Observers of baseball frequently invoke the idea of lineup protection in which a batter will walk less and hit for more power if he is followed in the batting order by a high-quality hitter. Previous attempts to measure protection in Major League Baseball have sometimes found evidence of lower walk rates but never an impact on power hitting. I argue that these efforts fail to uncover such evidence because lineups are selectively chosen by managers, introducing endogeneity bias into ordinary linear regression and batting split comparisons. To remedy this problem, I use injuries to batters’ “protectors” as a natural experiment that quasi-randomly changes the level of protection received by batters. Using this approach, I find evidence that protected batters hit for more power, hitting 9.7 percent more extra-base hits if the protector’s OPS is 100 points higher. These effects are strongest among 3rd hitters, who hit 26 percent more extra-base hits under the same scenario. Supporting the previous literature, I find that batters walk more, especially intentionally, when left unprotected.

Reconsideration of the Best Batting Order in Baseball: Is the Order to Maximize the Expected Number of Runs Really the Best?

In previous studies for analyzing the batting order of baseball games, the order is evaluated by its expected number of runs scored in a game, under the Markov chain model on the D’Esopo and Lefkowitz runner advancement model. However, the order to maximize the expected number of runs may not be the best order in the sense that it may not get more than 0.5 in probability of winning the game against other possible batting orders. In this sense, the best batting order is reconsidered, and it is tried to find better orders than the order which maximizes the expected number of runs. In this paper, the existence of such orders and the difference between the best orders and the order to maximize the expected number of runs are concretely shown by taking into account of not only the expected number of runs but also the standard deviation of runs, based on the data of Major League teams.

Getting to Know Your Students

Your class walks out to the field for the first day of a softball unit. A few students sprint ahead with their gloves, eager to play the game. Others talk among themselves and slowly make their way to the field. When it is time for game play, some students rush out to play shortstop, first base, and pitch, while others try to hide in the outfield, particularly to the right. On offense, these same students try to hit in the bottom of the batting order or get another student to bat for them. Based on your observations, do you perceive these students as not interested in physical education, disengaged, or resistant to your instruction? Have you ever asked yourself why these students want to play defensive positions where the ball is least likely to be hit to them, or do not want to come to bat? Getting to know students and understanding their background and experi­ ences are primary goals of effective teachers. But how can physical educators accomplish this? This article discusses how teachers can get to know their students by incorpo­ rating various formative assessment methods within their instruction to foster self-confidence and a positive self-image, while enhancing students' valuation and enjoyment of physical activity.

Optimal batting orders in cricket

Cricket teams are usually listed on the scoreboard in expected batting order, andalthough captains can choose to send in any of the remaining batsmen when awicket falls, they rarely depart from the usual batting order. By optimizing asimplified model using dynamic programming, this paper shows that in all formsof cricket significant increases in expected score result if captains allow avariable batting order and base their decision on the state of the game, ratherthan using a set batting order.

Mathematics in games, sports, and gambling: the games people play

Basic Probability Introduction Of Dice and Men Probability The Laws That Govern Us Poker Hands versus Batting Orders Let's Play for Money! Is That Fair? The Odds Are against Us Things Vary Conditional Expectation The Game's Afoot Applications to Games Counting and Probability in Poker Hands Roulette Craps Let's Make a Deal - The Monty Hall Problem Carnival Games Other Casino Games Backgammon Repeated Play Introduction Binomial Coefficients The Binomial Distribution The Poisson Distribution Streaks-Are They Real? Betting Strategies The Gambler's Ruin Card Tricks and More Introduction The Five-Card Trick The Two-Deck Matching Game More Tricks The Paintball Wars Dealing with Data Introduction Batting Averages and Simpson's Paradox NFL Passer Ratings Viewing Data - Simple Graphs Confidence in Our Estimates Measuring Differences in Performance Testing and Relationships Introduction Suzuki versus Pujols I'll Decide If I Believe That Are the Old Adages True? How Good Are Certain Measurements? Arguing over Outstanding Performances A Last Look at Comparisons Games and Puzzles Introduction Number Arrays The Tower of Hanoi Instant Insanity Lights Out Peg Games Puzzles on the Chessboard Guarini's Problem Martin Gardner's No 3-in-a-Line Problem The Knight's Tour Domination and Independence Attacking Placements and Independence Combinatorial Games Introduction to Combinatorial Games Subtraction Games Nim Games as Digraphs Blue-Red Hackenbush Green Hackenbush Games as Numbers More about Nimbers Appendix Review of Elementary Set Theory Relations and Functions Standard Normal Distribution Table Student's t-Distribution Solutions to Problems Solutions to Selected Exercises Bibliography Index

Electric Scoreboards, Bulletin Boards, and Mimic Diamonds

These days, fans who cannot visit their favorite ball yard need not fret. They can relax at home in a comfortable chair, watching countless games on television with an assortment of snack food at hand. Announcers describe the play-by-play, filling them in on the ins and outs of the contest. A nonstop array of graphics informs them of everything from scores and pitch counts to batting statistics and runners' positions on the bases.Similarly, a visit to a 21st century big-league ballpark is akin to attending a hightech three-ring circus, or setting forth on a family vacation to Disneyworld. Booming heavy metal or salsa cascade through the air as players saunter up to home plate, more music blasts between innings, costumed mascots prance through the stands, and fireworks light up the center-field sky after home runs. Full-color, high-definition scoreboards display oversized player head shots, in-game and season statistics, pitch counts and speeds, and endless streams of factoids of varying relevance (In his last five games at [insert corporation name here] Field, Joe Jones has 11 hits, including eight singles, in 19 at-bats.)This contemporary way of watching baseball is the result of a physical phenomenon that impacts all our lives, but which often is underappreciated: electricity. Starting at the tail end of the 19th century and segueing into the first decade of the 20th, electricity became a major component in how the game was experienced-both in ballparks and outside them.Originally, scoreboards in ballparks were rudimentary, hand-operated contraptions which served a lone purpose: to allow fans attending a game to follow the score inningby- inning. But they were not incorporated into the first ball yards that featured professional games. During the 19th century, fans were encouraged to plunk down a few pennies for scorecards and to record statistics on their own. Back then, club owners were reluctant to offer fans access to game information, preferring that they pay for scorecards. Only in the early 1900's did manual scoreboards become a familiar part of ballpark landscapes.One notable early scoreboard was in Shibe Park, home of the Philadelphia Athletics, which opened in 1909. It first was located down the third-base line, on the left edge of the left-field wall; it only offered data on the game being played, including the names of the players and their positions on the field and in the batting order. In 1913, when bleachers were added to this location, a larger scoreboard was constructed in right-center field. This one offered statistics for both A's and Phillies games. According to Philadelphia Athletics historian Bob Warrington, the scorekeeperstood at the base of the scoreboard during the game and used a ladder and poles to update developments. [A] photo, taken during a game in progress between the A's and White Sox, clearly shows a person at the base of the scoreboard with a ladder and poles leaning against a corner of the scoreboard.... Standing on the field of play, the scoreboard operator had to pay particular attention to the game in order to stay clear of any balls hit to deep centerfield and to avoid interfering with the play of outfielders, especially the centerfielder.Other scoreboards were wooden and rectangular in shape, consisting of a series of portholes, with scorekeepers sitting behind the board and updating a game's run, hit, and error totals by placing numbered panels in the appropriate portholes. Depending upon their design, each ballpark required the scorekeeper to perform a different function. For example, in Fenway Park, the scoreboard, located at field level in left field, was set into the wall that is fondly known as the Green Monster. In order to update the game's numbers, the scorekeeper had to climb up a wooden stepladder. This scoreboard is arguably the most celebrated of its type. It stayed in operation even after the team added its first electric scoreboard in 1975, and remains a cherished throwback to an earlier era. …

Dynamic programming in cricket: optimizing batting order for a sticky wicket

In cricket, a rain-affected pitch can make batting more difficult than normal. Several other conditions such as poor light or an initially lively pitch, may also result in difficulties for the batsmen. In this note, we refer to all of them as ‘sticky wickets’. On sticky wickets, lower order batsmen are often sent into ‘hold the fort’ until conditions improve. In this paper, a stochastic dynamic programming model is used to examine the appropriateness of this policy. The model suggests that the tactic is often optimal when the sticky wicket persists until the end of the day's play, but not often when the sticky wicket is transitory. In some circumstances, it is worthwhile, on a normal wicket near the end of the day, to send in a lower order batsman to hold the fort (a night watchman): when the wicket is sticky, this tactic is even more worthwhile.

Pigou at the Plate

Past studies estimating the marginal revenue products of baseball players have assumed individual players' hitting performances to be independent of teammate spillovers. However, the baseball community's widely held belief in “protection”—that a good (bad) player can improve (diminish) the hit probability of the batter who precedes him in the batting order—violates the assumption of the independence of batting outcomes. In this paper, the authors identify two possible hitting externalities in baseball. Using play-by-play data the authors find evidence contrary to the protection hypothesis—the quality of the on-deck hitter negatively impacts the preceding hitter—though the magnitude of the effect is very small.

An optimisation model to determine batting order in baseball

Baseball teams face the problem of choosing a set of nine players to start in each game and of determining a sequence in which these nine players bat. The objective is typically to maximise the offensive capability of the team. In baseball, the payoffs associated with a slight statistical advantage can be huge. While these are difficult to quantify exactly, the multimillion dollar contracts with the players and the managers suggest that even a few more wins every year are significant. We model this problem of choosing the players and of determining their batting order as a problem of finding the longest simple cycle in a graph and demonstrate our methodology by proposing batting orders for the Florida Marlins. We also explain how our model can also be useful in quantifying the benefits of trading players and for predicting the outcome.