Translations Of The Davenport Translations 5f162y

Noah Curtis Writing for Mathematics Groves March 16, 2011 Translations of the Davenport Translations Sabermetrics, a relatively new phenomenon within the baseball world, is the objective analysis of baseball. Sabermetrics is the attempt to take statistics of individual players, teams, and leagues and create a standard that is equivalent for all players everywhere. Baseball is a unique sport in the aspects of recorded statistics. For a century the same statistics have been kept for almost every section of organized baseball and have thus provided a wealth of information to be disseminated. As stated earlier, sabermetrics is the objective view of baseball. In this sense sabermetrics is used to identify which player on the Cubs contributed most to their offense or who was the most effective pitcher for the White Sox. It won’t answer the question of who someone’s favorite player is or if a game of baseball was exciting. With that in mind, sabermetrics is a quite interesting field for some of those who love the game of baseball as it serves to determine how truly great a player might be or how average an entire team might be. Clay Davenport, a somewhat prominent figure in the world of sabermetrics, once said, “Baseball statistics are just numbers, but to anyone who has followed baseball enough, they are capable of telling more stories than a Southern politician.”(Baseball Prospectus 2002) For the most part it is a very true statement. A player who hit .300 in Triple-A ball is not the same as a player who hit .300 in the majors. There is not only a difference in the quality of playing level, but also where the games are played. Many sabermetricians also tend to feel that statistics such as a player’s batting average have relatively low meaning to determining how many runs that player could/should/would contribute to their team, which is the ultimate goal of baseball. Sabermetrics is not a unified standard operating procedure, but more of a collection of thought-out calculations to tell different stories about the game of baseball. There are numerous sabermetric measures that fill many books and websites. Some people prefer some ways over others and others will disagree with those people. Either way, many formulas have been created in order to get what might be considered, “hidden data”, from the statistic lines of baseball games and seasons. The first question that is usually asked is, “What do I want to get from the information?” Maybe its finding out how many runs a player will create in a season or if a player

in the minors is ready for the majors. The idea is to turn the basic statistics of a baseball player or team into a precise argument for or against that team or player. One of the most interesting sabermetric measurements to me are the “Davenport Translations”. The Davenport Translations are an attempt to standardize common baseball statistics across all areas of baseball, from the short winter leagues in Arizona to the long, strenuous haul of a major league season. As far as sabermetricians are concerned, this isn’t anything new. What is interesting about the Davenport Translations though, is the discussion it has created amongst many sabermetricians. The Davenport Translations were first introduced in Baseball Prospectus, a leading publication of baseball analysis. The Davenport Translations are a collection of statistical numbers that correlate to events on the baseball field and equations that use those statistics to quantify a player’s ability, created by Clay Davenport. The two main components are EqR and EqA, equivalent runs and equivalent average, respectively. Over the years EqR and EqA have been used in newer algorithms to produce newer lines of thought, such as a player’s value over a replacement player or VORP, but one cannot understand such things without understanding EqR and EqA. The same way a child will not understand multiplication until they understand addition. EqR or Equivalent Runs is an offensive sabermetric measurement used to estimate runs created. This metric is grouped with other run estimators such as extrapolated runs, estimated runs produced, and runs created, which are themselves their own useful metrics and not to be discredited. To figure EqR you first figure what is considered the “Raw EqR” or RAW, which is defined as:

where H=Hits, TB=Total Bases, W=Walks, HB=Hit By Pitch, SB=Stolen Base, SH=Sacrifice Hit, SF=Sacrifice Fly, and CS=Caught Stealing. This is then converted into the estimated runs or EqR, stated as:

where Lg represents League, R represents Runs, and PA represents Plate Appearances. P, the author of “Walk Like a Sabermetrician”, states “EqR starts by taking the league average runs per

PA as a given, and then changes the estimate for the team based on how their RAW compares to the league RAW.” Thus, EqR creates an estimate of the absolute runs created. EqA or Equivalent Average is then the EqR per out or how many runs will be created per out. The formula to contrive EqA uses EqR and is stated as:

EqA is formulated to be put in of batting average, where .260 is average, .300 is a good performance, and .400 is a legendary performance. Clay Davenport said he wanted to put his metrics into that any baseball fan could understand, where the aforementioned numbers are the same for basic batting averages(Baseball Prospectus 2001). The sabermetrics-wiki at tangotiger.net, also mentions that in EqA’s full form it also adjusts for park and league environment. By no means are EqR and EqA easy computations to understand right off the bat. Tom Tango, co-author of “The Book”, suggests there are “lots of smoke and mirrors used in EqA.”(Why Is EqA so Complicated) He has a valid point in that statement. At baseballprospectus.com, EqA is written out as follows; “EqA is derived from Raw EqA, which is RawEqA =(H+TB+1.5*(BB+HBP+SB)+SH+SF-IBB/2)/(AB+BB+HBP+SH+SF+CS+SB) Any variables which are either missing or which you don't want to use can simply be ignored (be sure you ignore it for both the individual and league, though). You'll also need to calculate the RawEqa for the entire league (LgEqA). Convert RawEqA into EqR, taking into the league EqA LgEqA, league runs per plate appearance, the park factor PF, an adjustment pitadj for not having to face your own team's pitchers, and the difficulty rating. Again, you can ignore some of these as the situation requires. xmul can simply be called "2", while the PF, diffic, and pitadj can be set to "1". xmul=2*(.125/PF/Lg(R/PA)/pitadj) EQAADJ=xmul*(RawEqa/LgEqa)* ((1+1/diffic)/2) + (1-xmul) UEQR=EQAADJ*PA*Lg(R/PA) To get the final, fully adjusted EqA, we need to place this into a team environment. This is an average team: AVGTM=Lg(R/Out)*Lg(Outs/game)*PF*Games*(DH adjustment) The DH adjustment is for playing in a league with a DH. "Games" is the number of games played by this player. Replacing one player on the average team with our test subject: TMPLUS=AVGTM+UEQR-OUT*Lg(R/Out)*DH*PF Get pythagorean exponent pyexp=((TMPLUS+AVGTM)/Games)**.285 Calculate win percentage WINPCT=((TMPLUS/AVGTM)**pyexp)/(1+(TMPLUS/AVGTM)**pyexp)

Convert into adjusted space, where the Pythagorean exponent is set to 2. NEWTM=(WINPCT/(1-WINPCT))**(1/2) Fully adjusted EqR: EQR=.17235*((NEWTM-1)*27.*Games + Outs) Fully adjusted EqA EQA= (EQR/5/Outs)** 0.4” http://www.baseballprospectus.com/glossary/

Clearly, the original formulation of EqR and EqA provided by Baseball Prospectus is more complicated and involved than the simplified standard formula that was originally stated. The complexities of the originally intended formula have both their advantages and disadvantages, as well as the simplified standard formula. The more complex version presented by Baseball Prospectus is intricate to say the least, as it contains figures that aren’t readily accessible to the average sabermetrician who practices sabermetrics as a hobby; figures like park factors and pitching adjustment. That said though, it is that aspect that gives it it’s richness to painting a good picture of how good a player is or isn’t. The biggest downside to Baseball Prospectus’s version is the lack of explanation. While it does explain the process of the formula in all its unabashed, gory detail, it fails to give adequate reasoning to the process. It is as though Baseball Prospectus is expecting people to rely on faith and good nature that the formula works. And from a purely mathematical standpoint, that hardly ever works out. The process laid out by Baseball Prospectus, although intricate and seemingly detailed, can only be taken with a grain of salt due to the lack of argument in their explanation process. The simplified standard version, when compared to the complex version, is easily understandable, add up all the ways a hitter can contribute to scoring runs and divide by plate appearances and stolen bases and caught stealing. The last two mentioned, stolen bases and caught stealing, has been argued by some as useless in the denominator of equating the RAW. Some have brought up counter arguments to EqA with the problem concerning the stolen bases and caught stealing in the denominator. The fact that those stats are in the denominator makes the formula non-linear, but it has been argued that most players’ stolen bases and caught stealing are so relatively low that it hardly matters in the equation at the end of the day. This logic makes sense if one would compute Roger Maris’s historic 1961 season when he broke Babe Ruth’s single-season Home Run record, yet he never stole a base that season, nor was caught stealing. P, the author of “Walk Like a Sabermetrician”, elaborated on this point, using that season as a counter-point to EqR in his article, ‘An Analysis of Clay Davenport’s EqR and EqA’.

Within the article he argues that EqR is essentially a linear weights formula, or a formula where certain stats are worth more, i.e. a home run is worth more than a single. P uses some calculus and algebra to reconstruct Davenport’s EqR as a weighted linear equation, which he then uses to evaluate Maris’s memorable 1961 season with the Yankees. What he finds out is that as he adds stolen bases and caught stealing, the weights for the other statistical categories decrease and as he adds more and more stolen bases and caught stealing, the more out of control the weights and ultimately the EqR get. Tom Tango did a similar test for EqA in his article, ‘Why is EqA So Complicated’, in which he compared EqA to the much more common batting average statistic and his own creation, weighted-batting average(wBA). In Tango’s argument for his own creation he notices that when he tests EqA against his wBA and regular batting average at an unrealistic high number of at-bats in a season, holding hits constant. Batting average and his wBA act like one would expect and decrease at a constant expected rate, while “EqA breaks.” Unfortunately for Tom Tango, he fails to provide the reader with any hard numbers to illustrate his point of view and in a round about way discredits himself. While EqR and EqA are not necessarily the greatest ways of setting all baseball players across different eras, leagues, and divisions equal to each other, it appears to be the most generally accepted way of getting the image across. Davenport’s EqA comes across as a more natural stat line for baseball fans looking in on sabermetrics, as it equates the stats back to the more conventional way of viewing a batting average, where .260 is normal, .300 is pretty good, and .400 is outstanding. The other advantage that Davenport’s Translations have is that they are readily accessible, either through the internet or through any of the numerous volumes of Baseball Prospectus books. Even better is that all the work is done for you, including the tricky figures such as, park factors and pitching adjustment. When a wealth of information like that is available and as popular as it is, it is hard to dismiss it as un-noteworthy. The meat and potatoes of the Davenport Translations, EqR and EqA, are fairly indicative of sabermetrics as a whole, the same way they translate stat lines into metric units as a whole. Sabermetric measurements can be relatively easy to understand like the simplified standard version of EqR and EqA and sabermetric measurements can be as daunting as the complex version of EqA and EqR presented by Baseball Prospectus; both ways have their merits and demerits. The same can be said about most sabermetric measurements. While some sabermetric measurements have proved to be more reliable than others, there is still yet to be a universally

agreed upon way of objectively viewing and disseminating the copious amounts of baseball facts and figures that fill many volumes of books and internet servers. Understandably too, it is important to note that the use of sabermetrics within baseball is a relatively new concept. The book, “Moneyball: The Art of Winning an Unfair Game” by Michael Lewis published in 2003, was the first publication to mention the use of sabermetrics at the major league level and the book doesn’t mention the use of sabermetrics in the 1970s when SABR, Society for American Baseball Research, was created or even the 1980s, but 1996; less than 20 years ago. And many of the sabermetric measurements mentioned in the book are considered as factual stat lines that anyone hardly thinks of as sabermetric measurements anymore. The growth rate of sabermetric measurements is astounding and looks only to grow with time as it becomes more mainstream, even the Simpsons did a parody show devoted to sabermetrics. The Davenport Translations with all of their messed up glory should be a good learning tool for sabermetrics as a whole; and from the looks and sounds of it, it is. Many of the debates I came across about EqA and EqR on the internet were rather newly dated between 2007 and 2009, just a few years ago, even though EqR and EqA first appeared over a decade ago in the 1999 Baseball Prospectus book. And many of those debates were open and with good intentions to create a discussion on how sabermetric measurements should and should not be created. Personally, I’m rather new to sabermetrics and do not have have the adequate knowledge of sabermetrics to truly criticize or critique Clay Davenport’s EqR and EqA objectively. As a fan of the great game of baseball and a statistics and mathematics undergrad though, I find the discussion to be quite interesting and fascinating. A major publication of the yearly analysis of baseball has invested much of its resources into a sabermetric measurement that is still seemingly questioned by those in the sabermetrics community and seems to have a few holes in the argument for its use. I feel those reasons though are what define the Davenport Translations, which in themselves are translations of what sabermetric measurements should and should not be. For better or worse, whether EqR and EqA work or not, they tell an underlying story about the world of sabermetrics; many issues are unresolved and it has yet to grow into its full potential.

Works Cited

Baseball Prospectus http://www.baseballprospectus.com/glossary/index.php?mode=viewstat&stat=61 , March 16, 2011 Boston Red Sox Fan Forum http://sonsofsamhorn.net/topic/15585-rate-stat-comparison-eqa-vs-woba/ , March 1, 2007 Davenport, Clay ‘Davenport Translations’ Baseball Prospectus 2002 Edition , Brassey’s, Inc. 2002 Davenport, Clay ‘The Davenport Translations’ Baseball Prospectus 2001 Edition , Brassey’s, Inc. 2001 P http://walksaber.blogspot.com/2008/05/how-to-calculate-clay-davenports-eqr.html , May 12, 2008

http://walksaber.blogspot.com/2008/05/analysis-of-clay-davenports-eqr-and-eqa.html May 19, 2008 Tango, Tom M. http://www.insidethebook.com/ee/index.php/site/comments/why_is_eqa_so_complicated/ , December 19, 2006 http://www.tangotiger.net/wiki/index.php?title=Equivalent_Runs , February 22, 2008 Wikipedia http://en.wikipedia.org/wiki/Equivalent_average , February 28, 2010 [email protected] http://gosu02.tripod.com/id13.html , March 16, 2011 Wyers, Colin http://www.hardballtimes.com/main/blog_article/is-eqa-better-than-woba/ , September 9, 2009