## What does Ra Rd Rs mean in baseball?

RS stands for Runs Scored. RA stands for Runs Allowed. DIFF is an abbreviation for Run Differential. RS/G is an abbreviation for Runs Scored per Game. As well as this, what does the letter RA imply in baseball? This information comes from Wikipedia, the free encyclopedia. Run average (RA) is a term used in baseball statistics to describe the rate at which runs are allowed or scored by a team. For pitchers, the run average is the amount of runs allowed per nine innings, whether they are earned or unearned.

Despite the fact that run differential is a valuable measure, it is not without its limitations and can be misled by a fluke over the course of 42 games.

Ground-ball Percentage (GB percent ) It is the proportion of balls that are hit into the field of play that are classified as ground balls that is measured.

According to Bill James’ sports analytics method, Pythagorean expectation estimates the percentage of games that a baseball club “should” have won based on the number of runs they scored and the number of runs they allowed.

## Why is a home run not an earned run?

When the leadoff batter comes up to bat and hits a home run, the run is considered legitimate. That one is straightforward, as are the unearned runs that are simple. Whenever a batter hits a ground ball to shortstop, he or she gets two outs. It seems unfair that the two runs were scored when a mistake should have resulted in the third out of the inning.

## Can a runner go back to first after touching second?

(a) If a batter hits a ball out of the park or hits a ground rule double and misses first base (ball is dead), he may return to first base to correct his mistake before reaching second base; however, if he reaches second base, he may not return to first, and if the defensive team appeals, he is declared out at first. (b) If a batter hits a ball out of the park or hits a ground rule double and misses first base

## What does BF mean in baseball?

Definition. Batters faced is essentially a tally of the total number of plate appearances made against a specific pitcher or club in a given season. A pitcher will record 27 batters faced if he or she pitches a perfect game with 27 outs. Batters faced may frequently be used as a reference for in-game tactics while analyzing a game.

## Is it better to have a higher or lower run differential?

The total number of runs scored by the team in all games; however, the maximum number of runs scored in one game is limited by the Max Differential parameter. Generally speaking, the larger the number, the better.

## What does RF mean in baseball?

Range Factors are calculated by dividing the sum of a fielder’s putouts and assists by the total number of defensive games in which the fielder has participated in.

## What does RBI mean in baseball?

Runs batted in (RBI) | Glossary | Major League Baseball.com

## What does G mean in baseball?

Games that have been played (G) Grand Slam is a series of victories in a single sport (GSH) Toss The Ball Into Double Play (GIDP) The Groundout-to-Airout Ratio (GO/AO) is the ratio of groundout to airout. Pitch-for-pitch (HBP)

## What does P mean in baseball?

Participated in games (G) Double-double in double-doubles in double-doubles in double-doubles (GSH) A Double Play Is Created (GIDP) Ratio of groundout to airout is referred to as Groundout-to-Airout Ratio (GO/AO) in aviation terminology. ‘Pitch by pitch’ refers to the way a baseball pitch is delivered (HBP)

## What are POS in baseball?

The position of the player.

## How is Pythagorean Theorem used in baseball?

This Bill James’s invention relates the number of runs a team has scored and surrendered to its actual winning percentage. The theory is based on the idea that the number of runs scored relative to the number of runs allowed is a better indicator of a team’s (future) performance than the team’s actual winning percentage.

## How is Pythagorean Theorem used in soccer?

Soccer and the Pythagorean theorem are connected in a number of ways. During a throw-in during a soccer game, the ball is thrown directly above the heads of the players at one point. … The distance between the player who throws the ball and the player who receives the ball is represented by side B of the triangle. The trajectory of the ball is represented by Leg C of the triangle.

## How is the Pythagorean Theorem used in sports?

Several aspects of soccer are similar to those found in the Pythagorean theorem. It is possible that the ball will pass right over the players’ heads as they are thrown in during a soccer match. … Side B of the triangle measures the distance between the player who throws the ball and the player who receives the ball. The ball’s trajectory is represented by Leg C of the triangle.

## Are passed balls earned runs?

The passing of a ball is not recorded as an error, but when a run scores as a consequence of a passed ball, it is not counted as an earned run against the pitcher. If a runner advances to second base as a result of a passed ball, he is not given credit for a stolen base.

## Can you purposely get hit by a pitch?

The vast majority of hit-by-pitches are inadvertent. A pitcher, on the other hand, may throw at a hitter on purpose as a form of retaliation from time to time. if the home-plate umpire has reasonable grounds to believe this is the case, he or she has the authority to dismiss the pitcher (as well as the pitching team’s manager) from the game

## Can two runners touch the same base?

It is not permitted for two runners to share the same starting point. If two runners get within touching distance of the same base, the lead runner is awarded the base. When two runners are occupying the same base, most coaches will instruct their defensive players to tag both runners at the same time.

## Can a batter-runner run backwards?

There is no penalty for sprinting backwards to avoid being tagged, but once the batter-runner reaches home plate, he is OUT regardless of whether or not he was tagged in the process.

## Can a baserunner go backwards?

When there is a tag play between home plate and first base, a batter-runner may retreat toward home plate in order to dodge a tag, but he or she is ruled out if he or she touches or passes home plate, or if the batter-runner or first baseman crosses the base line. The ball is still in play. As a result, a runner has the option of backing up to just before touching home plate.

## What does BB mean?

Bareback.

The abbreviation BB is frequently used on online dating services, as well as in text messages and in chat forums, with the meaning “Bareback,” to allude to engaging in sexual activity without the use of a condom.

## RS Meaning in Baseball – What does RS mean in Baseball? RS Definition

There are three different definitions for the termRSis Run Support, which can be found at the bottom of this page. The termRSis Run Support is used in baseball terminology and has three different meanings. All of the meanings associated with the RS acronym are found solely within the context of baseball terminology, and no additional meanings are discovered. If you’d like to view more definitions, please visit the RS definitions section. As a result, you will be sent to a website that contains all of the meanings of RS.

## RS Meaning in Baseball

There are also additional sites where you may learn about RS meaning for Baseball.

- MoreRS definition may be found at Acronym24.com. To read about RS on Wikipedia, simply click on the link. Last but not least, searchRS Baseball in Google over and over again

## What does RS stand for Baseball?

On Acronym24.com, you can learn more about RS. Visit Wikipedia and look up RS. Finally, search for RS Baseball in Google over and over again.

### What does RS meaning stand for Baseball?

- MoreRS definition may be found at Acronym24.com
- Click here to read about RS on Wikipedia
- Finally, searchRS Baseball on Google over and again

#### What is RS definition?

The meanings of the RS abbreviation in baseball are not the only things that can be found on this website. Yes, we are aware that your primary goal is to provide an explanation of the RS abbreviation in baseball. However, we believed that, in addition to the meaning of the RS meanings in Baseball, you might be interested in the astrological information associated with the RS acronym in Astrology. It is for this reason that the astrological interpretation of each word in each RS abbreviation is also supplied.

##### RS Abbreviation in Astrology

- RS RS RS RS RS RS RS RS RS RS RS (letter R) Individual who doesn’t waste time and is focused on getting things done. You need someone who can keep up with you and who is on an intellectual par with you
- The smarter they are, the better it is for you. You are more easily turned on by a brilliant intellect than you are by a terrific physique. Physical appearance, on the other hand, is extremely essential to you. You have to be pleased with your partner’s accomplishments. You are really hot in private, but you do not gloat about it, and you are willing to serve as a teacher. You may be a highly demanding playmate, and you place a high value on sexuality. If your name begins with the letter S, you are reserved, self-contained, and timid. Despite the fact that you are extremely seductive, sensuous, and passionate, you keep it a secret. This aspect of your nature will only be shown in the most intimate of settings. When it comes down to the nitty-gritty, you are the consummate professional. You are well-versed in all of the nuances of the trade, are capable of taking on any role or participating in any game, and are really serious about your love life. You don’t play games with your life. You have the patience to be patient and wait for the appropriate person to show up

## Run Differential

The run differential of a team is calculated by subtracting the total number of runs (earned and unearned) that it has allowed from the total number of runs that it has scored throughout the season.

### Example

A total of 808 runs were scored and 556 runs were allowed by the 2016 Chicago Cubs during the regular season, resulting in a run difference of +252. The 2018 Baltimore Orioles, on the other hand, scored 622 runs as a team while allowing 892 runs to score against them. Their run difference was a negative 270 runs.

### Why it’s useful

It is possible to tell the difference between teams who are overachieving and those that are underachieving by looking at their run differential. In the past, there have been teams who had a winning record but a negative run differential – or vice versa – but such teams were statistical oddities compared to other teams. When evaluating a team’s run differential early in the season, it can be helpful in determining whether or not a team is capable of maintaining a “hot” start or of reversing a bad start.

It is not always the case that the team with the highest run differential will win the World Series.

All three teams were victorious in their respective categories.

A team’s pythagorean winning percentage – another statistic that seeks to offer a more accurate picture of a team’s talent than raw winning percentage – is similarly strongly linked to their winning percentage.

## Baseball Abbreviations

Tony Gwynn had another outstanding season in 1997, with 592 at-bats and 220 strikeouts, and an avg of.372, which was the best in the National League. Which of these abbreviations do all of these letters stand for? The Baseball Almanac is glad to give a standard collection of acronyms that are seen and used in print on a regular basis in the sport of baseball.

## Baseball Stats

Baseball Abbreviations 101Offensive Abbreviations for Statistics | |

ABBBAVGCS2BGIDP GRSLHBPHHRRHRIBBISO LOB OBPOPSRRBISFSHSSLGSB%SBRSBSOTB3B | At BatsBases on Balls (Walks)Batting AverageCaught StealingDoublesGround into Double Plays Grand SlamsHit by PitchHitsHome Run RatioHome RunsIntentionalBasesonBalls(Walks)Isolated Power Left on Base On-Base PercentageOn-Base Plus SluggingRunsRuns Batted InSacrifice FliesSacrifice Hits (Bunts)SinglesSlugging PercentageStolen Base PercentageStolen Base RunsStolen BasesStrikeoutsTotal BasesTriples |

Pitching Abbreviations for Statistics | |

AOBB BFPBKCBOCGCGLERERAGFGOGOAOGPGSHHBPHRIBBIPIRAIPSLMB9OBAPARRPFRWS/SHOSOSVSVOTBWWP | Fly Outs (Air)Walks (Bases on Balls) Batters Facing PitcherBalksCombined ShutoutComplete GamesComplete Game LossesEarned RunsEarned Run AverageGames FinishedGround OutsGround Outs / Fly Outs RatioGames PlayedGames StartedHitsHit BattersHome RunsIntentional WalksInnings PitchedInherited Runs AllowedInnings Per StartLossesBaserunners Per 9 InningsOpponents’ Batting AveragePlate AppearancesRunsRelief FailuresRelief WinsShutoutsStrikeoutsSavesSave OpportunitiesTotal BasesWinsWild Pitches |

Defensive Abbreviations for Statistics | |

ACSDPEGPOFAPBPKPOSBTCTP | AssistsCaught StealingDouble PlaysErrorsGames PlayedOutfield AssistsPassed BallsPickoffsPutoutsStolen Bases Total ChancesTriple Plays |

Miscellaneous Abbreviations for Statistics | |

ML SER | Major League Service |

Baseball Stats Abbreviations 101 |

The “common” set has several variations (DO Doubles, TR Triples, etc.), but these are the ones that are regarded “official” and are the ones that are used here at Baseball Almanac, among other places. Did you know that the National Association (a non-official league that gave rise to the National Leagueofficial )’s statistics were destroyed in a fire in the early 1900’s? Major League Baseball organized a Special Baseball Records Committee in the 1960s to examine the irregular records that had been kept previous to the 1920 season.

## Baseball: Pythagorean Method

Ben Vollmayr-Lee is a writer and editor based in New York City. (For those familiar with Baseball Primer, this is a Fanhome post from sometime around the spring of 2002.) Although the formatting isn’t perfect, it should still be readable. ) It is in quotes because I want to discuss more broadly about the concept of taking RS (runs scored) and RA (runs allowed) and forecasting the winning percentage of an individual team. My belief is that concepts are more essential than formulae, and the relative effectiveness of different formulas may reveal a lot about the concepts they are intended to represent.

- Let’s take this as a starting point and ask: how much does the winning percentage grow as the number of runs scored increases?
- We already know that p=1/2 for x=1/2.
- If we wanted to match this data in a certain way, we might use a formula like as11.
- Listed below is a valuable rule of thumb to memorize and maintain in your brain at all times: Multiplying the proportion of runs scored by two gives you the fraction of runs scored in excess of one-half, which is the fraction of runs scored in excess of one-half of the winning percentage.
- What is the significance of a factor of two?
- As a result, there is no straightforward way to get this slope, however it is intriguing to isolate different elements and see what influence they have on it.
- What does this have to do with Pythagoras, you might wonder.
- That second step may not be immediately apparent, but dividing the top and bottom of the original formula by (RS + RA)n will allow you to deduce it.
- Plenty.

1 In the words of Pythagoras, p = – + n (x -) – (x —)3 +.2232 p = – + n (x —) It turns out that only odd powers of x-1/2 are found, which is owing to symmetry in the pythagorean (or any valid) formula, which states that a team scoring 55 percent of the runs and a team scoring 45 percent of the runs should have winning percentages that add up to one (1).

- The cubic term is negative, and it reflects a sort of declining returns in winning percentages as a function of the variable x.
- What is the relationship between Pythagoras and the basic linear formula?
- By calculating the root mean square error in their expected victories per 162 games, I can compare their accuracy to that of the data going back as far as 1901.
- So, yes, the declining returns did make pyth better, but only marginally better (so that rule of thumb is a pretty useful thing to remember – the single most important thing to know about this business in my opinion, along with the scale of rms error being about 4 wins).
- We may expect to do better if we let the data to choose the cubic coefficient on its own behalf.
- What I discover is that the fit yields an rms of 4.213, which is just marginally better than pythagoras’s result.

However, it appears that accuracy in the leading cubic section of the declining returns is more essential. Let’s take a step back and review the principles we’ve discussed so far:

- Excess wpct is mainly linear in terms of the number of runs scored
- Pythagoras works well since it is mostly linear as well, plus it incorporates some diminishing returns into the equation. A fit to the law of diminishing returns performs just marginally better
- The difference between all of the alternatives is modest (making the first item on the list all the more relevant)
- Non-linearity in the form of decreasing returns is distinct from behavior in the x to 0 or 1 limits, and it is more critical for season wpct accuracy than either of those limitations.

Okay, so far we haven’t taken into account the average number of runs scored per game. As many of you are aware, the severity of the transgression can have an impact on the pythagorean exponent. So let’s take a closer look at this. First, let’s take a look at Pete Palmer’s formula (which can be found in Clay Davenport’s piece). It is possible to express this as 131 Palmer: using some algebra. p = – +- sqrt(r) where p = – +- sqrt(r) (x – -) 252 where is the same as previously and r is the average number of runs scored by a team every game: RS plus RA r = – G is the reciprocal of r.

- If I fit this, I obtain an rms error of 4.220, which is an improvement above the constant coefficient we had previously.
- Despite this, there was nothing particularly noteworthy about the square root of r.
- 4.192a is obtained by multiplying a and b ln(r).
- It is important to note that all of these formulae, which are linear in x and do not have diminishing returns built in, perform better than any formula we can devise that does not take r into consideration.
- So here’s another crucial aspect to consider:

- We haven’t taken into account the average number of runs scored per game up to now. Pythagorean exponents can be affected by the severity of a transgression, as many of you are aware. In any case, let’s go ahead and investigate this. Before anything further, let’s have a look at Pete Palmer’s formula (as presented in Clay Davenport’s piece). With a little math, you can express this as131 Palmer: Palmer: p = – +- sqrt(r) where p = – +- sqrt(r) (x – -) 252 This is the same as previously and r is the average number of runs scored by a team every game + RA = R + R the negative of G is denoted by r Please keep in mind that Palmer’s technique turns out to be nothing more than a modified version of our linear fit, except that the slope is now dependent on r. This has an rms error of 4.220 when I fit it, which is an improvement than the constant coefficient we had. However, there was no underlying concept behind the number 3/5, so what if I use Palmer’s approach and leave the coefficient as a fitting parameter? 11 + a sqrt(r) = – + a sqrt(p) for Palmer and fit:p (x – -) 22 Now I obtain 4.204 (with a=0.617403), which is a huge improvement over all of the calculations that did not take r dependency into account previously. Despite this, the square root of r did not possess any unique characteristics. In lieu of a*sqrt(r), I might substitute any of the following functions: A + b r = 4.193 (with a=1.262 and b=0.06408) when a and b are both equal to 1. This is obtained by multiplying a and b by ln(r). Rb produces a result of 4.192. Given that it doesn’t make much of a difference which one we choose, if I want to add run dependency, I go with the first option listed above because it’s the easiest one. It is important to note that all of these formulae, which are linear in x and do not have any diminishing returns built in, perform better than any formula we can devise that does not take r into consideration. Pythagoras was a great thinker, for example. As a result, here’s another crucial concept:

Okay, thus far, we haven’t taken into account the average number of runs scored per game. As many of you are aware, the degree of offense can have an impact on the pythagorean exponent. So let’s take a look at this a little more closely. Before anything further, let’s have a look at Pete Palmer’s formula (as presented in Clay Davenport’s paper). This may be written as 131 Palmer: p = – +- sqrt(r) p = – +- sqrt(r) (x – -) 252 where x is the same as previously and r is the average total number of runs scored each game as follows: RS + RA =?

Take note that Palmer’s technique turns out to be nothing more than a linear fit with a slope that depends on r, as opposed to our linear fit.

However, there was no theory behind the number 3/5, so what if I use Palmer’s approach and leave the coefficient as a fitting parameter: 11 Palmer + fit:p = – + a sqrt(r) Palmer + fit:p (x – -) 22 Now I obtain 4.204 (with a=0.617403), which is a huge improvement above all of the formulae that did not incorporate r dependency.

In place of a*sqrt(r), I might use any of the following functions: A + b r = 4.193 (with a=1.262 and b=0.06408) when a and b are both equal.

rb produces a result of 4.192 Given that it doesn’t make much of a difference which one we choose, if I want to add run dependency, I go with the first option listed above because it’s the simplest.

It is important to note that all of these formulae, which are linear in x and do not have diminishing returns built in, perform better than any formula we can devise that does not take into account r. Pythagoras was a great mathematician. So, here’s another crucial topic to consider:

## Baseball Acronyms – Abbreviations

To be successful in handicap games, you must be familiar with the jargon and abbreviations used in the industry. In the list below, you’ll discover a collection of baseball acronyms that you’re likely to see on stat sheets and in box scores. USE YOUR VISA CARD TO DEPOSIT AT ATSPORTS AND PLACE A BET ON MLB GAMES BETTINGAB:At bats is a good bet. ADP is an abbreviation for Average Draft Position. AL stands for American League. A:Assists Batting average (BA): BA A:Batting average versus the opposition BB:Base on balls is an abbreviation for Base on Balls (walk) BF:Batters were up against it BK:Balk BS:Blown opportunity CG: The game has been completed.

- ERA is an abbreviation for earned run average.
- GB stands for ground ball.
- G/F: The ratio of ground balls to fly balls.
- HP:Home plate is spelled with a capital letter.
- LOB:Left over on the field Major League Baseball (MLB) is a type of baseball played in the United States.
- OF:Outfield OBP is an abbreviation for on base percentage.
- PB: The ball was passed to me.
- R:Run was successful.
- RISK:Runners in scoring position are at risk.
- SHO:Shutout SP: The pitcher who will start the game.
- Wild pitch is the name of the game.

## Hillsborough Little League – Standings

Standings The Upper Division team standings for the season you chose are listed below.

Majors Baseball | ||||||||||||||

GP | W | L | T | PCT | GB | RF | RA | RD | H2H | L5 | Streak | HRs | ||

1 | Majors Athletics | 0.000 | – | 0-0-0 | – | |||||||||

1 | Majors Braves | 0.000 | – | 0-0-0 | – | |||||||||

1 | Majors Cubs | 0.000 | – | 0-0-0 | – | |||||||||

1 | Majors Giants | 0.000 | – | 0-0-0 | – | |||||||||

1 | Majors Padres | 0.000 | – | 0-0-0 | – | |||||||||

1 | Majors White Sox | 0.000 | – | 0-0-0 | – | |||||||||

1 | Majors Yankees | 0.000 | – | 0-0-0 | – |

Minors Baseball | ||||||||||||||

GP | W | L | T | PCT | GB | RF | RA | RD | H2H | L5 | Streak | HRs | ||

1 | Minors Brewers | 0.000 | – | 0-0-0 | – | |||||||||

1 | Minors Cubs | 0.000 | – | 0-0-0 | – | |||||||||

1 | Minors Giants | 0.000 | – | 0-0-0 | – | |||||||||

1 | Minors Pirates | 0.000 | – | 0-0-0 | – | |||||||||

1 | Minors Red Sox | 0.000 | – | 0-0-0 | – | |||||||||

1 | Minors Yankees | 0.000 | – | 0-0-0 | – |

AAA Baseball | ||||||||||||||

GP | W | L | T | PCT | GB | RF | RA | RD | H2H | L5 | Streak | HRs | ||

1 | AAA Athletics | 0.000 | – | 0-0-0 | – | |||||||||

1 | AAA Brewers | 0.000 | – | 0-0-0 | – | |||||||||

1 | AAA Cubs | 0.000 | – | 0-0-0 | – | |||||||||

1 | AAA Giants | 0.000 | – | 0-0-0 | – | |||||||||

1 | AAA Nationals | 0.000 | – | 0-0-0 | – | |||||||||

1 | AAA Phillies | 0.000 | – | 0-0-0 | – | |||||||||

1 | AAA Pirates | 0.000 | – | 0-0-0 | – | |||||||||

1 | AAA White Sox | 0.000 | – | 0-0-0 | – |

54-80 Division | ||||||||||||||

GP | W | L | T | PCT | GB | RF | RA | RD | H2H | L5 | Streak | HRs | ||

1 | HLL Hawks Blue | 0.000 | – | 0-0-0 | – | |||||||||

1 | HLL Hawks Gray | 0.000 | – | 0-0-0 | – |

The following factors are used to determine standings: PCT, GB, H2H, RA, and coin toss.

Abbreviations: | |||

GP | Games played | RF | Runs scored for this team |

W | Wins | RA | Runs scored against this team |

L | Losses | RD | Run differential (RF – RA) |

T | Ties | H2H | Head-to-head wins among teams with same win percentage |

PCT | Win percentage | L5 | W-L-T record over the last five games |

GB | Games behind 1st place | Streak | Current win / loss streak |

HRs | Total home runs hit by this team |

## A New Formula to Predict a Team’s Winning Percentage – Society for American Baseball Research

As part of his groundbreaking work, Bill James devised a method for projecting an expected winning % for big league baseball teams based on the amount of runs scored and allowed. Empirically, this formula has a good correlation with a team’s observed (actual) winning percentage, denoted by the letter W percent. The following is what is known as the “Pythagorean” formula for baseball: EXP(W percent) = EXP(W percent) (RS) The projected winning percentage created by the method is denoted as 2/EXP(W percent), RS is the number of runs scored by a team, and RA is the number of runs allowed by a side.

- James’s choice of the exponent 2 appears to offer a reasonable estimate of the value.
- A team’s future success is more accurately predicted by the number of runs they score relative to the number of runs they allow, according to James, than by their win-loss record at a given point in time (assuming the team is far enough into the season for significance).
- Consider the following scenario: a club is 45-37 at the halfway point of the season, yet their EXP(W percent) is at or below 0.500 according to James’s method.
- Why not just use the quantity (RS – RA) to calculate EXP(W percent) instead of the percentage (RS – RA)?
- EXP(W percent) = m*(RS – RA) + b.
- The year 1998 was chosen as the starting point since it was the first year in which there were 30 Major League Baseball clubs.
- This constant would function in the same way as the exponent “2” functions for each year in James’s calculation.

Finally, a comparison is made between the Pythagorean Formula and our new Linear Formula, which was introduced in 2013.

For the NFL, m = 0.001538 and b = 0.50, whereas for the NBA, m = 0.000351 and b = 0.50 are the values to use.

Instead, the difference between their records will be understood as the difference between their respective teams’ records.

A simple linear regression model to predict the winning percentage of an MLB team using (RS – RA) is shown.

To calculate the expected winning percentage EXP(W percent) for each team, divide the difference between their runs scored and runs allowed by the number of runs scored (x = RS – RA).

For each year from 1998 through 2012, let W be the total number of victories achieved by a Major League Baseball team.

It is straightforward to see: (1) x = (RS – RA) = 0 when RS = RA (2) y = W percent = (1/T)*W = (1/T)*(n/2) y = W percent = (1/T)*W T = n/2 = 15 T = n/2 = 15 (3) xy = x*W percent = (RS – RA) xy = x*W percent W percentage of the total When the coefficients “m” and “b” in Equation 1 are replaced with (n/2), x with 0, and xy with (RS – RA)W percent, the following results: (4) b =/ b = 0.50 b =/ b = 0.50 (5) the product of (RS + RA) and the product of m =/ W percent divided by (RS – RA) 2 For each team throughout the period 1998-2012, Equation 1 is transformed into Equation 2.

- y′ = EXP(W percent) =*(RS – RA) + 0.50 = EXP(W percent) It is assumed that each club completed its scheduled T = 162 games in order to get the results in Equation 2.
- In some cases, such as in 2009 and 2013, this can occur when a rainout game is not made up because the game has little impact on the standings, or when an additional game is forced by a tie for a playoff place, as happened in 2009 and 2013.
- In 2009, the value of b in (4) will be 0.5001, and in 2013, the value of b in (4) will be 0.5002.
- In this case, it is clear that y′ is essentially unaffected.
- The scatter diagram, the regression line, the linear regression equation, and the coefficient of determination, r 2, for Major League Baseball in 2012 are depicted in Figure 1.
- Let x = (RS – RA)W percent, y = (RS – RA) 2, and y′ = EXP(RS – RA) 2, the expected yearly RS – RA 2.
- Table 2(click image to enlarge or see below) displays the x and y values, as well as the slope “m,” for each year from 1998 through 2012.
- Using the years 1998-2012 as an example, Figure 2 depicts the linear regression equation, the graph of the regression line, and the coefficient of determination, r 2, for each year.
- The coefficient for the linear regression equation, r 2, is given as Equation 3.
- EXP(W percent) = [EXP(W percent) = 0.50 times the product (RS – RA).
- As shown in Table 2, 1464.4(RS – RA)W percent is greater than 212,418.5 percent for each year, which is a significant amount greater than the value of 32,710 in Equation 4.

EXP(W percent) =*(RS – RA) + 0.50= (1/1464.4)*(RS – RA) + 0.50= 0.000683(RS – RA) + 0.50= 0.000683(RS – RA) + 0.50= 0.000683(RS – RA) + 0.50= 0.000683(RS – RA) + 0.50= 0.000683(RS – RA) + 0.50= The Linear Formula Is Applied To Baseball In Equation 5 It would take an increase in the difference (RS-RA) of approximately 14.64 runs (0.01/0.000683) for a team to increase its winning percentage for an entire year by one percentage point.

If a team won 81 games last year (50 percent of its games), and we believe that if a team wins 90 games (winning 55.56 percent of its games), they will have a good chance of making the playoffs, the yearly difference (RS-RA) should increase by 14.64*5.55 = 81.25 runs, the RS-RA should increase by 81.25 runs.

- Using Linear and Pythagorean Formulas to Make Comparisons The Pythagorean formula and my Linear Formula for Baseball will be compared in this comparison, which will be based on the 2013 regular season.
- Table 3 shows the expected win totals for each Major League Baseball team in 2013 based on the Linear Formula.
- The Linear Formula has a chi-square sum of 5.76, while the Pythagorean Formula has a chi-square sum of 5.87.
- They are both greater than 0.90 for the p-values (the probability of these two small chi-square sums occurring strictly by chance if we believe the two formulas to be accurate) to occur strictly by chance (using 29 degrees of freedom).
- In Table 3(click image for larger view or see below), you can see that, using the Linear Formula, the top 11 expected winning percentages belong to the 10 teams who qualified for the postseason in 2013.
- Extending the Linear Formula for Baseball to the National Football League and the National Basketball Association For the National Football League and the National Basketball Association, we will use the same techniques to develop Equations 2, 3, 4, and 5 using the same methodology.
- Take note that PS and PA are used in place of RS and RA, but have the same meaning.
- T and n may differ between leagues, but this had no effect on the final results for “m” and “b,” which were the same regardless of the league.
- y′ = EXP(W percent) =*(PS – PA) + 0.50 y′ = EXP(W percent) y′ = EXP(W percent) y′ = EXP(W percent) y′ = EXP(W percent) y′ = EXP(W percent) In contrast to Major League Baseball, Item (2) above is always true in the NBA and NFL.
- Equation 3 for the NFL is shown here, as is Equation 3 for the NBA (see Tables 6 and 7 along with Figures 3 and 4).
- In the NBA, y′ = EXP((PS – PA) 2) = 2850 is the value of y′.

We may use 650.36(PS – PA)W percent – 39,803 (from Equation 3) to replace (PS – PA) 2 in Equation 2 for the NFL, and 2850.8(PS – PA)W percent – 673,540 (from Equation 3) to replace (PS – PA) 2 in Equation 2 for the NBA, resulting in a new Equation 4 for the NFL and a new Equation 4 for the NBA.

(Equation 4)In the NBA, EXP (W percent) equals [*(PS – PA) + 0.50 for each team (Equation 4) Due to the fact that 650.36(PS – PA)W percent is greater than 270,722.1 for each year of the NFL (see Table 6), which is significantly greater than 39,803, and 2850.8(PS – PA)W percent is greater than 3,311,685 for each year of the NBA (see Table 7) which is significantly greater than 673,540, we can replace 39,803 with 0 in Equation 4 for the NFL and 673,540 with 0 in Equ In the NFL, EXP (W percent) =*(PS – PA) + 0.50= (1/650.36)*(PS – PA) + 0.50 = 0.001538(PS – PA) + 0.50.

- In the NBA, EXP (W percent) =*(PS – PA) + 0.50= 0.001538(PS – PA) + 0.50.
- (See also Equation 5) As a result, these are the final versions: The Linear Formula for NFL Football is EXP (W percent) = 0.001538(PS – PA) + 0.50, where EXP (W percent) = 0.001538(PS – PA).
- Using the formula 0.01 divided by 0.001538, we can calculate that each increase of 6.5 points for (PS – PA) will result in an increase of one percentage point in an NFL team’s winning %.
- Conclusion We demonstrated that the Linear Formula and the Pythagorean Formula were both effective in forecasting the actual win totals for the 2013 Major League Baseball season using the Chi-Square Goodness-of-Fit Test for both formulas.
- For a general manager, the Linear Formula has several advantages over the Pythagorean Formula, the most significant of which is that it is simpler to grasp and apply.
- A general manager might intend to improve his team’s performance by increasing the gap between runs scored and runs allowed in the previous season as a starting point for the current season.
- Enhancing the roster with players who have unappreciated run-producing statistics but reduced salary demands is one method of increasing the RS component of (RS – RA) without paying too much money to acquire players with glitzier numbers.

As a second advantage, the Linear Formula can be applied to other sports leagues, such as the NBA and the NFL, and the same team-building advantages that were gained from developing it for baseball can be gained from applying it to other sports leagues.

Why is there such a high positive association between (RS – RA) 2 and W percent (RS – RA) in the Major League Baseball, the National Football League, and the NBA?

How many games must be played in a season for the Linear Formula to be an effective tool for predicting winning percentages in these leagues?

In the fall of 1970 he joined the Quinnipiac University faculty as an Assistant Professor of Mathematics.

He headed the mathematics department at Quinnipiac from 1992 until 2010.

His book “Sandlot Stats: Learning Statistics with Baseball” was released by Johns Hopkins University Press in September 2012 and is available online.

In addition to the West Point Military Academy and California State University in Los Angeles, he has lectured at a number of other campuses.

Some of his study areas include the likelihood of a player reaching particular hitting streaks, the likelihood of having another.400 hitter, and the significance of minorities in baseball.

Additional considerations: 1.

As a result, this is not a significant issue because the maximum value for (RS – RA) for the years 1998 to 2012 is 300.

If PS – PA325 is the linear formula for football, 0.001538(PS – PA) + 0.50 may provide an EXP(W percent) of 100 percent, then PS – PA325 is the linear formula for basketball.

If PS – PA1425 is the linear formula for basketball, 0.000351(PS – PA) + 0.50 may result in an EXP(W percent)100 percent, then PS – PA1425 is the linear formula for baseball.

On ESPN.com, under the heading MLB and subheading Standings, you can find the scoring information you need for the discussion that follows Equation 2 as well as for the figures 3 and 4.

If you go to the subtopic Standings, you can get the statistics for (PS – PA), (RS – RA), and W percent, among other things. Sources Wikipedia. “Pythagorean Expectation.” In baseball, this is known as “The Pythagorean Theorem.” Retrosheet. Click on any image below to enlarge:

## How Baseball Works (a guide to the game of Baseball)

Statistics In baseball, there is just one statistic that is truly significant. How many runs did you put on the board? And was it a larger sum than the opposing team’s total? Although baseball is a game of chance, it is a sport that lends itself to a variety of hitting, pitching (and, to a lesser degree, fielding) statistics, and many of them are given below, along with the codes that are frequently associated with them, for your convenience. However, it should be noted that numerous “percentages” are used in baseball, but the values are not stated as percentages, but rather as decimal fractions in practice.

Aspects of the Hitting Statistics The number of games in which the batter has actually appeared is denoted by the letter G.

Plate appearances that resulted in a “walk,” at which a hitter was hit by a pitch, or at which a batter was given first base due to interference, as well as “sacrifices,” are not included (appearances where he intentionally sacrificed his chances of getting on base to allow base runners to advance).

Hits (H)-The total number of base hits recorded by a player, excluding baserunners who reached base as a result of an error or a “fielder’s choice.” Total Bases (TB)-The total number of bases reached by a player when he or she hits a baseball (singles count one, doubles count two, triples count three and home runs count four).

- Triples (3B) are the amount of base hits that a player receives that allows him to advance to third base on a single play.
- Base hits, sacrifice bunts, walks, and other such actions result in runs being scored by the other team.
- A base hit by the batter allows a runner from third base to cross the plate, and the runner is given credit for the run while the batter is given credit for the RBI (runs batted in).
- It is possible that a run is scored but no RBI is awarded in this situation.
- Hit by Pitch (HBP)- The number of times a hitter has been awarded first base as a result of getting hit by a pitch in a given season.
- Sacrifice Bunt (SB) is a bunt that will generally advance a runner on first or second base.
- Although a sacrifice does not qualify as an at bat, the batter may be “credited” with an RBI if he or she hits a home run (so a hitter can be credited with a sacrifice and an RBI, but has no base hit and no at bat recorded).
- In the case of a runner who is caught in the act of attempted base theft, he is charged with the crime of “caught stealing” and faces a fine.
- It is widely agreed that an effective base stealer must have a success rate of around 70% or higher.

This is not the same as a strike out when a hitter “flies out” or “grounds out.” The term “fielding error” refers to a fielder’s failure to complete a play that stops a batter or runner from being put out (drops a catch, fumbles a pick-up, throws to the wrong base, etc.) or allows him to advance a base or bases after making a play.

- Batting appearances that result in a Base on Ball or a Sacrifice are not counted toward the total.
- On Base Percentage (OBP)- On Base Percentage is similar to batting average in that it includes appearances that resulted in walks and times a hitter was hit by a pitch.
- When you add up the base hits, bases on balls, and hits by pitches, and divide the total by the amount of at bats, bases on balls, hits by pitches, and sacrifices, you get the batting average.
- In the end, it doesn’t matter how a runner gets to second base; what matters is that he does!
- A player’s Slugging Percentage (SLG) is computed by dividing the number of total bases by the number of at bats during the season.
- The typical metric of a hitter’s “power” is his or her slugging percentage.
- The on-base percentage (OPS) is the newest “statistic” and is often regarded as the most accurate indicator of a hitter’s abilities, as it takes into account both his ability to get on base and his “power numbers.” Anything with a score of above 800 is considered excellent.

Statistics on the field When a fielder retires a hitter (for example, by collecting a fly ball or tagging out an infield runner), he is awarded with a putout (also known as an out).

if the shortstop fields the ball and throws to first base where a runner is tagged out then the shortstop is credited with an assist and the first baseman a putout).

In most cases, a fielding percentage of greater than 50% should be expected.

Double Plays (DP)-The total number of Double Plays in which the fielder was involved in a single game.

In addition, keep in mind that a double play cannot be completed in an inning in which there are already two outs, because the first out of this play finishes the inning.

Any number of fielders (typically no more than four) can be part in a game (but a solo triple play is possible, albeit very very rare).

As a result, it is believed to be a measure of how frequently a player fields the ball (or, maybe, how frequently the ball is hit in his way!) Passed Balls (PB) – The number of “passed balls” that a catcher is permitted to throw (a pitch he should have caught, but fumbled and allowed base runners to advance).

- Games Started (GS)-The total number of games in which the pitcher has participated.
- Games Finished (GF)-The number of games in which the pitcher completed the game in which he or she pitched (i.e.
- inning pitched (IP) – The total number of innings pitched in a game.
- For example, a pitcher who comes in and lets up three hits before being benched may be considered to have played “zero” innings in the game.
- Runs (R)-The total amount of runs scored off the pitcher’s bat, including those scored as a result of fielding mistakes by the opposing side.
- EARNED RUNS (ER) – The amount of “earned” runs scored off a pitcher, excluding runs scored as a consequence of a fielding mistake by the pitcher’s club.

It is considered “unearned” if the run is scored as a result of an error, or if the inning is only still in progress as a result of an error (for example, if there should have been three outs and the inning over, but an error meant one of the “outs” was not made), or if the runner advances as a result of an error (i.e.

You’ll discover that around 90 percent of runs scored are earned runs, which is a good rule of thumb.

Based on the amount of “bases on balls” (walks) issued by the pitcher, this statistic is known as Bases on Balls (BB).

The amount of “intended bases on balls” (walks) issued by the pitcher is referred to as the Intentional Bases on Balls (IBB) statistic.

In baseball, the number of “wild pitches” thrown by the pitcher (pitch that gets past the catcher, allowing base runners to advance, and which is considered by the Official Scorer to be the pitcher’s fault, not the catcher’s fault) is called the Wild Pitches (WP).

Won-Lost Decisions (W-L) – In baseball, a “win” and a “loss” are always credited/charged to one pitcher on each club, regardless of the outcome of the game.

Example 1: A starter goes six innings and exits with a 3-1 lead after pitching six innings.

The starter receives the victory since his team was always in the lead after he exited the game.

His side pulls up 5-3 in the eighth inning, and the game ends 5-3 as a result of the opposition’s final out of the seventh inning.

In order to be awarded a victory, a starter must complete at least five innings of work.

Whenever a pitcher completes an inning, he is considered the “pitcher of record” until he is actually replaced at the start of the next inning.

Notes: The distinction between wins and losses is arbitrary.

Alternatively, he could allow nine runs in five innings, leave the game with a 14-9 lead, and walk away with the victory.

Over the course of a season, these factors tend to balance out, but Earned Run Average (see below) is often considered a more accurate measure of a pitcher’s worth.

Saves (Sv) – In baseball, a premium is put on the pitcher who comes in at the end of the game and manages to hold on to a slim lead in order to preserve a victory.

the hitter who comes up after the hitter at the plate), and finishes the game without giving up the lead, he is credited with a “save.” Additionally, a save may be awarded to a closing pitcher who “pitches successfully” for at least three innings (in the opinion of the official scorer).

Instead, a save is only awarded when a pitcher inherits a tight lead and retains it.

“Blown saves” are rare, and a strong closer is required to “convert” at least 90 percent of the Save Opportunities that present themselves.

If you come in with a three-run lead, no runners on base, and only one out, it’s much easier than coming in with a one-run lead, bases loaded, and no outs.

In reality, it’s a statistical analysis of “middle relievers.” A pitcher’s Earned Run Average (ERA) is reported as the number of Earned Runs allowed by the pitcher in nine innings, which is the normal duration of a game.

The Walks and Hits Per Innings Pitched (WHIP) statistic is produced by multiplying the number of “bases on balls” issued and the number of hits allowed by the number of innings pitched and dividing the result by the number of innings pitched.

When it comes to keeping runners off the bases, it’s a solid indicator of how efficient a pitcher is. Note: WHIP is a relatively “new statistic”, growing increasingly prominent. Anything with a value less than one is considered to be excellent.