Complete baseball stats, with player and team rankings.  

Mathematics in Baseball: The Science of the Art

Featuring:  XERA - Baseball's statistical scouting report . . . and standard stats, too. XERA measures the productivity of any player or team, plus his/its strengths and weaknesses, by calculating a normal distribution of traditional baseball numbers. It's backed up by more than 100 league-seasons of data, optimized through linear programming analysis.

There is a well-known close correlation between the proportion of runs scored and allowed to a team’s expected winning percentage. Is there an equally close relationship of singles, doubles, triples, homeruns, walks, strikeouts, stolen bases etc. to runs? In the long run, the answer is yes – here’s why:

Baseball’s numbers are beautifully balanced. Whenever a batter gets a hit, a pitcher gives up a hit. If one team scores a run, the other team gives up a run. When one team wins, its opponent loses. When a pitcher allows an earned run, the hitters on the other team must have produced an earned run. Therefore, an earned run average, theoretically, exists for hitters as well as pitchers. XERA (eXpected Earned Run Average) turns that theory into reality. How close does the XERA of hitters correlate to the actual ERA of the pitchers of the corresponding season? Check it out:

XERA for the 55-year period = 4.00, actual ERA = 4.01. Maximum difference = 0.10 (1987 & 1993)

We haven’t found any other sabermetric figure that so consistently evaluates relative baseball talent over so many seasons of data. Check out the Xbase tab (at the far right of) Various XERA Stat Sheets for details and underlying data.

ERA is commonly accepted as baseball’s most revealing indication of pitchers capabilities, but how does one best judge a hitter? Batting average? Home Runs? Stolen Bases? Wouldn’t it be equally valuable to know the ERA of a hitter? XERA is a precisely weighted average (developed with Linear Programming) of standard hitter’s statistics, combined into one number to represent overall productivity – and that number is further analyzed to illustrate specific strengths and weaknesses of hitters and pitchers.

There were five objectives in the development of XERA:

1)      Find the relative importance of the various elements (walks, hits, etc.) of standard baseball statistics.

2)      Evaluate hitters and pitchers by the same (relative) criteria. 

3)      Rate the players by a single, easily recognized, traditional baseball number.

4)      Make it possible to reduce the XERA figure into distinct elements to determine specific strengths and weaknesses.

5)      Keep it simple. Calculating XERA should require no more than readily available statistics, like those published weekly in USA Today. It isn’t necessary to have box scores or a play-by-play account of every game to calculate XERA.


Major league scout and author of How to Make Pro Baseball Scouts Notice You, and other fine baseball books, Al Goldis, called XERA “Baseball’s statistical scouting report.”


Quick Click Links===>       Various XERA Stat Sheets        Standings and Ranks        Baseball trivia page        Easy Money                     

Contact us at and, yes, we're happy to answer your baseball or mathematics questions!

Updated daily: Standings and Ranks This page will show detailed 2015 MLB standings, runs scored, opponents runs scored, and Runs2 standings. We also show runs scored/allowed on a per-game basis. We have magic numbers for each division leader, and mathematically projected full-season wins for each team, from the beginning of the season (of course, the projections get more precise as the season progresses). This and the individual stats will start when all MLB teams have played a game.

Updated daily: We have detailed 2015 XERA and standard stats on most active hitters (not pitchers) and pitching stats on most active pitchers. These stats are published before noon, and include last night's games. Click this (the Various XERA Stat Sheets Quick Click Link), and then just click the Hitters15 tab or the Pitchers15 tab. The complete stats involve extracting information from 3 databases. That information is then correlated to formulas that were pre-positioned into Excel spreadsheets, and sorted. The reports include the Scouting Report "Grades" for each player listed.

Updated weekly: Be sure to check out the 2015MLB tab in the Various XERA Stat Sheets section, as well, for XERA Rankings of each team, based on the collective XERAs of each team's players.  This feature now includes XERA grade ratings. Generally speaking, the grade ratings will be fairly consistent with the grade ratings in the Standings and Ranks section. Because XERA ratings are based on a normal distribution of accumulated player stats, not just actual runs and runs-allowed per game, it takes on additional meaning. When there is a significant difference between the two grades, look for the rankings to mutate toward the XERA grade over time. 

     If you're not yet familiar with XERA, we suggest clicking this link ►►► XERA Objectives to learn more.

We use, and highly recommend, Lee Sinins' Complete Baseball Encyclopedia (an unsolicited endorsement of my favorite source of baseball stats) as our reference for traditional baseball stats.

The Computer Annex of Sarasota has honored us (GillXL, LLC) with its “Excellence in Excel” award, again in 2014 - our seventh consecutive year of that honor! New applications used in this XERA website, along with binomial and hypergeometric distribution worksheets, were cited as some the reasons for those awards. THANK YOU! 

The same (Linear Programming) techniques that developed XERA and its related formulas, can be used very effectively in business, for cost analysis, quality control, estimating, etc. If you'd like to optimize formulas or data for your application, Dwight Gill can do it for you, as well as translate and reformat virtually any database file (even text-based) into a sortable Excel application. Please contact us at This website and all its associated formulas and stats, are by Dwight Gill.

Scroll down to the list with the light-blue background (like this) to find more details about the various baseball stats reports on this website. 

THIS symbol (throughout the text) will link to a variety of unique sabermetric material. These pages should provide a good overview of XERA and other useful baseball stats. 

Yes, this is a unique baseball site. We also recommend,, and the aforementioned Lee Sinins' Complete Baseball Encyclopedia (CBE) as outstanding baseball references. The CBE web address is  

We offer updated information that was originally published in Mathematics in Baseball : The Science of the Art, by statistician Dwight Gill (a member of American Mensa) and sports writer Tad Reeve, just before the spring of 1989 and updated years later (XERA formulas are occasionally given small revisions to accommodate new information) by Dwight Gill. XERA (eXpected Earned Run Average) is baseball's statistical scouting report. We have one-hundred eight league-seasons of data (1960-2014 AL and NL data) to verify XERA's accuracy and comprehensive nature. All the formulas were developed by Dwight Gill. The original XERA book is no longer in print (because of its season-specific nature), but many of its concepts have been assimilated by major league teams - especially to statistically evaluate players. The New York Mets used then-updated XERA formulas during the 2004 season and after. The newest formulas (post-2009) are the most precise, yet, and are easier to calculate than the originals. The stats throughout this website have been updated to relate to the current formulas. No "normalizing factor" is used in the current XERA formulas, the same equations are used every year. XERA invites comparisons to any other systems, or actual data. Click THIS  to see whyClick THIS to see a more detailed introduction to XERA - Baseball's Statistical Scouting Report:

We'll also be showing a number of other baseball-related statistics, in addition to XERA. Our baseball statistics are based on the science that deals with the analysis and interpretation of numerical data, that uses proven mathematical calculations of probability, not merely the data itself.

The Various XERA Stat Sheets Quick Link, and then the appropriate tab will lead to various XERA baseball reports . . .        

1) 2015 MLB tab to see XERA, and plenty of conventional stats, for every 2015 major league team.  

     The XERA History page has the same information for 2007, 2008, 2009, 2010, 2011, 2012, 2013, and 2014.

2) Hitters15 tab to see XERA, and plenty of conventional stats, for the hitters of 2015.

     The XERA History page has the same information for 2008, 2009, 2010, 2011, 2012, 2013, and 2014.

3) Pitchers15 tab to see XERA, and plenty of conventional stats, for the pitchers of 2015.

     The XERA History page has the same information for 2008, 2009, 2010, 2011, 2012, 2013, and 2014.

4) Grt Hitters tab to see XERA demonstrate the skills of 275 of baseball's greatest hitters (career, all time) . . . 

5) Grt Pitchers tab to see XERA demonstrate the skills of 248 of baseball's greatest pitchers (all pitchers with 150 wins or saves, career, all time) . . . 

6) 20W Seasons tab to see detailed XERA data, and standard stats, for all 819 20-game winners since the 1900 season.

7) H Seasons tab to see how detailed XERA data, and standard stats, for 720 of the best hitting seasons in baseball history.

8) LeftRight tab to see how XERA makes it possible to determine the true (run-scoring) effects of the lefty/righty theory with final 2007, and 2006 stats. 

9) BarryB tab to see a detailed year-by-year XERA breakdown of Barry Bonds' incredible career - before 2000 and after . . . This guy got dramatically BETTER after he turned 35 . . . or was it the steroids? In response to a number of requests, we've added tabs for the the careers of Hank Aaron, Lou Gehrig, Babe Ruth, Ted Williams and the late Harmon Killebrew, as well. Pitchers Sandy Koufax and Tom Seaver are also included. We've also added Mariano Rivera, perhaps the finest relief pitcher in baseball history. Who else would you like to see? 

10) Changes tab to see, by the numbers, how the game has changed over the years. Easily find the eras when pitching dominated the game, when power entered the game, when high batting averages were the norm. We've recently added graphs to help visualize those changes.

Got questions about online betting sites? Check it out on one of the pages of this website, or contact us at We want to provide baseball fans, and professionals, with useful, interesting and unique information.

Click THIS to check out the answers to your early questions.

2014, in review: Check out the 2014MLB Tab in the Various XERA Stat Sheets Quick Click Link. Note that the top 4 ranked teams all finished first in their respective divisions, and the top 6 teams (and 7 of the top 8) were in the playoffs!

2013, in review: Check out the 2013MLB Tab in the Various XERA Stat Sheets Quick Click Link. Note that the top 10 ranked teams all made it to the postseason! 5 of the top 6 teams won their division! None of the top 11 finished lower than second. XERA only ranks teams based on a normal distribution of cumulative stats. It does not consider runs or wins by any team!

2012, in review: Nine of the 10 playoff teams were in the XERA top 12. The Rays and Braves were the two teams, in that group, that did not make the playoffs. Baltimore was the only playoff team not in the top 12 in XERA.

The final 2012 regular-season XERA team ratings had the Nationals (including Stephen Strasburg) at number one, and the Astros at the bottom. Check out the 2012MLB tab at Various XERA Stat Sheets, for everyone else. When the actual win-loss record, runs2, and XERA are averaged, the Nationals were #1, and Astros #30, maintaining their ranks across-the-board, for both teams. Check out the 2012MLB tab at the Various XERA Stat Sheets Quick Click Link for final 2012 ratings of every major league team. It's more evidence that XERA is the best statistical evaluator of baseball talent. The more tab, in the Standings and Ranks Quick Click Link, has additional team ranking categories.

There were 7 post-season series in 2012. EVERY one of them was decided in the MINIMUM or MAXIMUM number of games, nothing in between (~77 to 1 odds).

Down three games to one to the Cardinals in the NLCS, the San Francisco Giants won their last seven post-season games, to win the 2012 NLCS and the World Series! A great ending to another fabulous baseball season!

In the 2012 regular season, in inter-league play, the AL downed the NL by 32 games (142 - 110), and 108 runs!

2011, in review: Seven of the eight postseason teams finished in the top nine positions in our XERA rankings (the Red Sox and Giants were the other two - the Diamondbacks were #13). Check out the 2011MLB tab at the Various XERA Stat Sheets Quick Click Link for final 2011 ratings of every major league team. 

We correctly picked all six division winners in early September. We, also, incorrectly, picked the two Wild Cards. Our picks, the Braves (9-18) and the Red Sox (7-20) had incredibly bad September performances. That, combined with fine records by the Cardinals (18-8) and Rays (17-10) contributed to an exciting September race.

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