WAR and the Hall of Fame Joshua Bayzick May 5,2015 Abstract Sabermetrics is a term coined by Bill James, and it is the search for objective knowledge about baseball. This mathematical approach to baseball produced a statistic called Wins Above Replacement (WAR), which takes into account batting, baserunning, and fielding to determine how many `wins' that position player was worth. This project looks at how player's WAR values change as they age. We will compare two groups of players, First-ballot Hall of Famers (HOF) and the average player. We know that the HOF group will have higher WAR values because they were well above average players, but the basic question is do they age differently than the average player. 1 Introduction A relatively new statistic called WAR (Wins Above Replacement) was developed by saber- metricians to answer questions such as \Who had the better career?" or \Who had the better year?" For example, in 2014 Alex Gordon had a batting average of .266 with 19 home runs and 74 RBI. In 2014 Yoenis Cespedes had a batting average of .260 with 22 home runs and 100 RBI. Based on these conventional statistics, they appear to have had fairly similar years. One might even argue that Cespedes was slightly better because of the RBI advantage. However, these conventional statistics do not measure everything a player does to help his team win a game. WAR, which takes into account batting, baserunning, and fielding, says that in 2014 Alex Gordon was worth 6.6 WAR for his team, while Ces- pedes was worth 3.3 WAR. Based on this WAR statistic, we easily conclude Alex Gordon had the better year overall. This paper will show you how parts of the WAR calculation are done and other uses of the statistic. 2 WAR Calculation The Sabermetrics website FanGraphs describes the statistic as follows: \WAR offers an estimate to answer the question, `If this player got injured, and their(sic) team had to replace them with a freely available minor leaguer or a AAAA player from their bench, how much value would the team be losing?'" The statistic summarizes a player's contribution to his team's win total in one statistic. One characteristic of WAR is that it is independent of ballpark, league and season. It is also important to note that WAR is an approximation. For example, a 6 WAR player may be worth between 5 and 7 WAR, but we can certainly say this player performed at a 1 high level. A WAR value of 7 is considered to be an MVP season, according to FanGraphs. Therefore, WAR values tend to be situated between 0 and 7. The table below details WAR values even further. Lastly, WAR values are calculated differently for position players than they are for pitchers. This paper will focus only on position players. WAR Level of Play 0{1 Scrub 1{2 Role Player 2{3 Solid Starter 3{4 Good Player 4{5 All Star 5{6 Superstar 6{7 MVP To determine how many wins a player is worth to his team, we must first find out how many runs that player is worth to his team. For position players, these runs come from three phases of the game: batting, baserunning, and fielding. We add these runs together and then adjust the values based on his position, league, and the value of a replacement player. This produces the total amount of runs this player is worth. Lastly, we divide the total runs by the runs per win to produce wins. 2.1 Batting Runs To determine how many runs a batter creates by batting, we must first calculate Weighted On Base Average (wOBA). Using wOBA, we can calculate weighted Runs Above Average (wRAA), and then finally we can calculate batting runs. The statistic wOBA is calculated by taking league data and using multiple regression to generate the optimum weight for each hitting event. In other words, wOBA is designed to generate the optimum relationship between the hitting events and the amount of runs scored. The formula for wOBA is : w · uBB + w · HBP + w · 1B + w · 2B + w · 3B + w · HR wOBA = 1 2 3 4 5 6 AB + BB − IBB + SF + HBP where w1; w2; : : : ; w6 are the weights of each hitting event, uBB represents unintentional walks, HBP represents the number of times a batter was hit by a pitch, and 1B, 2B, 3B, and HR represent singles, doubles, triples and home runs respectively. These weights will change every year, but in 2013 we have 0:690 · uBB + 0:722 · HBP + 0:888 · 1B + 1:271 · 2B + 1:616 · 3B + 2:101 · HR wOBA = AB + BB − IBB + SF + HBP After using a player's statistics to calculate his wOBA, we can calculate wRAA. The formula for wRAA is wOBA − lg wOBA wRAA = · PA wOBA scale This formula finds the difference between a player's wOBA and the league's, and then scales this value so that plate appearances are an appropriate multiple. 2 Finally, we can calculate batting runs by using the formula leagueR PF · leagueR leagueR AL/NL nonpitcher wRC BR = wRAA+ − PA+ − PA leaguePA leaguePA leaguePA AL/NL PA Essentially this formula takes batting runs and then adjusts that value for the park effect of a player's home field, and also for the league. The park adjustment is necessary because baseball fields have different dimensions and characteristics. Some parks suppress runs and others encourage runs. This adjustment makes sure that no player has an advantage based on the park they played in. The last term simply balances the effect of the league. For example, the American League (AL) usually produces more runs since there is a Designated Hitter to bat for the pitcher. Thus, more runs are scored in the AL and it takes more runs to account for a win. 2.2 Baserunning Runs How many runs a player adds based on his baserunning is determined by two statistics: Ultimate Baserunning and Weighted Stolen Base Runs. These statistics are mostly pro- prietary, but they measure how effective a baserunner is. They account for the amount of steals, the success rate of steals, and even how often a player advances extra bases on a hit. They utilize video review to find values for these statistics. 2.3 Fielding Runs Fielding Runs are also largely based on proprietary data. There are a few metrics available, such as Ultimate Zone Rating, Total Zone, and Defensive Runs Saved. There are different kinds of WAR based on the fielding metric used. These WAR values are similar, but the kinds of WAR must be distinguished from one another if the formula is different. We are using FanGraph's version of WAR (referred to as fWAR). Video is employed here as well to better estimate the range of a fielder. 2.4 Adjustments After summing the Batting Runs, Baserunning Runs, and Fielding Runs, we must adjust this value. There are three adjustments. The first is a positional adjustment. These are adjustments based on the position the player played. Certain positions are more difficult to play than others, and the positional adjustment tries to account for this. The second adjustment is a league adjustment. This just makes certain that the runs above average balances out to zero. This is often a minor adjustment. The last adjustment is the replace- ment player adjustment. So far, all of our calculations have been based around the average player. A replacement player is below the league average, so we must add some runs to the player to compare them to a replacement player. These adjustments are typically very small. 2.5 Final Calculation To calculate WAR we take the sum of the six components: batting runs, baserunning runs, fielding runs, and the three adjustments. This total is the amount of runs a player 3 contributes. To find the amount of wins the player was worth, we must divide the total number of runs by a Runs per Win value. This value changes year to year, but typically is somewhere around 10. Thus, the full calculation for WAR is Batting + Baserunning + Fielding + Positional Adj. + League Adj. + Replacement WAR = Runs per Win 3 Uses of WAR Now that we know how WAR is calculated, we must understand what it offers to the baseball community. The main goal of the statistic is to generate one number to account for player performance. It is very easy for anyone to understand the phrase: \He was a 6 win player." As the Sabermetrics approach takes hold, WAR is being used increasingly in the administering of individual awards, such as the MVP and Cy Young awards. Another application is even its use in calculating the dollar value of a player for contract negotiations. 4 The Basic Question This brings us to our research question: \Do Inner Circle Hall of Fame Players age differently than the average player?" It is important to note that the Hall of Fame player will have higher WAR values, but we are concerned with the change in the values as the player ages. Further, we will define Inner Circle Hall of Famers, as players elected to the Hall of Fame their first year on the ballot. They must have been retired for seven years to be considered, and to be elected they must appear on 75% of the ballots of the sportswriters who vote. There are 32 First Ballot Hall of Fame position players, including Babe Ruth, Ted Williams, Mickey Mantle, and Willie Mays (See Appendix A). 4.1 Definition of Data Sets Due to the nature of WAR and the development of the game we will only use players from the live-ball era, which began in 1920.