Major League Baseball Offensive Production in the Designated Hitter Era (1973 Present) Jonathan Tung University of California, Riverside tung.jonathanee@gmail.com Abstract In Major League Baseball, there are two sub-leagues, the National League and the American League. While the game of professional baseball is generally played under the same rules, there is one major exception. That is, games played in American League ballparks have a designated hitter inserted into their batting lineup, replacing the often weak-hitting pitcher, while games played in National League ballparks include lineups in which the pitcher must bat for themselves. Theoretically, American League teams should exhibit higher offensive capabilities and output over their counterparts in the National League. The focus of this study is to examine whether or not American League teams exhibit a significant difference over National League teams in several offensive categories.
Table of Contents 1 Introduction 2 Explaining Offensive Production 2.1 Defining Offensive Production Statistics 2.1.1 Batting Average (BA) 2.1.2 On-Base Percentage (OBP) 2.1.3 Slugging Percentage (SLG) 2.1.4 On-Base Plus Slugging (OPS) 2.1.5 Weighted On-Base Average (woba) 3 Examining Differences in Runs Between Leagues 3.1 Examining Batting Average 3.2 Examining On-Base Percentage 3.3 Examining Slugging Percentage 3.4 Examining On-Base Plus Slugging 3.5 Examining Weighted On-Base Average 4 Conclusions Acknowledgements References Appendix Data Tables
1 Introduction There are two sub-leagues that make up Major League Baseball (MLB). These two leagues are the National League (NL) and the American League (AL). In both leagues, nine players take the field and play defense, and nine players take turns batting in an order called a batting lineup dictated by each team s manager. There is one major difference in the rules for games played in National League ballparks and American League ballparks. Beginning with the 1973 season, in American League ballparks under Rule 6.10, a hitter may be designated to bat for the starting pitcher and all subsequent pitchers in [the] game without otherwise affecting the status of the pitcher(s) in the game. [1] In other words, a typical American League lineup will consist of eight position players and one designated hitter, while a typical National League lineup will consist of eight position players and the pitcher. Subsequently, an American League lineup will consist of nine players whose job description includes being a competent batter, while a National League lineup will only consist of eight players who fit that description. We can consider pitchers in general to be non-hitters. While there certainly are some pitchers with the ability to hit, they are very few and far between. It should be noted that it is typical in games played under National League rules for the pitcher to be replaced by a pinch-hitter (a position player on the bench) as the game progresses in an attempt to muster more offense. Thus, the difference of one extra batter in one particular American League game may not have a visibly significant effect, in that each batter averages between 3 and 4 plate appearances per game, but a National League pitcher may only get 2 or 3 plate appearances per game. In other words, the difference between American League and National League games is really only about 1 or 2 plate appearances from a non-hitter. However, over the course of a season where each team is scheduled to play 162 games, and especially over the course of multiple seasons, these seemingly subtle differences can have a significant effect on offensive production between American League teams and National League teams. The focus of this study is to determine whether these differences in lineup construction in American and National League games have a significant effect on offensive output and production since the advent of the designated hitter (DH). We will examine data from the 1973-2013 seasons. We will look at several offensive categories, starting from basic rate statistics and working our way to more advanced rate statistics that were created as a result of the sabermetrics movement in professional baseball. 2 Explaining Offensive Production The game of baseball is all about runs. At the end of every game, the team with more runs is declared the winner. As a result, runs and the events that lead to runs are important to study to gain a deeper understanding of baseball.
In order to gain a better understanding of the offensive environment we are studying, we can get a general outlook by considering the number of runs per game, a rate stat, scored by American and National League teams during the era of the designated hitter (1973-present). For the sake of using complete seasons, we will use data through the 2013 season, as the 2014 season is in progress. We can see this data visualized in Figure 1. Figure 1. Runs Per Game for MLB Over Time We should try to avoid counting stats because players who play in more games will naturally accumulate more of a counting stat. Generally, rate stats are better than counting stats in comparing production. While the runs per game statistic is a rate statistic, that does not necessarily suggest that it is a comprehensive statistic that is flawless in explaining offensive production. It does control for the amount of games played, but it does not control for the number of innings played, as it is rare for every team to have the identical number of innings played at the end of a season, due to the possibility of extra-inning games. However, we can use this to contextualize other statistics that we will see in this study, such as OBP (on-base percentage), SLG (slugging percentage), OPS (on-base plus slugging), and woba (weighted onbase average). All of these statistics will be defined. We will also explain the benefits and drawbacks, should they exist, of each of them.
2.1 Defining Offensive Production Statistics Perhaps the most commonly referenced offensive baseball statistics are batting average, home runs, and runs batted in (RBIs). While these stats are still displayed around every major league ballpark and on each and every game s broadcast, these stats do not paint an accurate and complete picture. More specifically, home runs and RBIs are counting stats, so players who play in more games will naturally have a greater amount of home runs and RBIs. In addition, while home runs are undoubtedly good things, they are not the only event or sequence of events that produce runs. Additionally, RBIs are context dependent stats. The only way to rack up RBIs without having runners on base is to hit a home run. While batting average is a rate stat, computed by dividing the number of hits by the number of at-bats, the issue with batting average is that it equally weights all hits, when it is quite obvious that not all hits are created equally. For example, a home run is obviously better than a single. The important thing to take away from these stats is that they each have their uses, but they should not be used alone to summarize or explain offensive performance. In the baseball community, there exists a thing called the triple slash line of statistics. The triple slash line is usually written as BA/OBP/SLG where BA is batting average, OBP is on-base percentage, and SLG is slugging percentage. An example would be.300/.400/.500. We can use this triple slash line as a starting point to define and discuss a number of useful statistics. 2.1.1 Batting Average Batting average (BA or AVG) is probably the single most referenced offensive baseball statistic. Its value can be computed using the following formula: where H is the number of hits and AB is the number of at-bats. It is a simple rate statistic that assigns equal weights to all types of hits. We discussed the drawbacks of using batting average as a sole explanatory statistic for offensive production earlier, but it must be reiterated that it is obvious that it is not ideal to equally weight all hits, when there is an obvious hierarchy among the types of hits a batter can produce. 2.1.2 On-Base Percentage On-base percentage (OBP) is exactly what it sounds like, essentially any plate appearance that ends without a batter making an out. It is incredibly important for the offensive success of a team because players with high on-base percentages avoid making outs and reach base at a high rate, prolonging games and giving their team more opportunities to score. [2] Its value can be computed using the following formula:
where BB is the number of walks (base on balls), HBP is the number of times hit by a pitch, and SF is the number of sacrifice fly balls. 2.1.3 Slugging Percentage Slugging percentage (SLG) is an oft-used measure of the power of a hitter. It assigns more weight to extra-base hits and can be calculated by taking the total bases divided by the at bats. More specifically, its value can be computed using the following formula: where 1B is the number of singles, 2B is the number of doubles, 3B is the number of triples, and HR is the number of home runs. 2.1.4 On-Base Plus Slugging On-base plus slugging (OPS) is exactly what it sounds like. It is the sum of the player s on-base percentage and their slugging percentage. It can be computed using the following formula: In a sense, this is a catch-all stat in that it accounts for all the different aspects of offense: contact, patience, and power. [3] However, the major issue with this statistic is that it assigns equal weight to OBP and SLG, when OBP has been proven to be roughly twice as important as SLG% in scoring runs (x1.8 to be exact). [4] Thus, while OPS is not perfect, it is a good gateway statistic to less traditional statistics such as batting average and RBIs. 2.1.5 Weighted On-Base Average Weighted on-base average (woba) is one of the most important and popular catch-all offensive statistics. It was created by Tom Tango to measure a hitter s overall offensive value, based on the relative values of each distinct offensive event. [5] What distinguishes woba from OPS is that woba combines all the different aspects of hitting into one metric, weighting each of them in proportion to their actual run value. [6] The weights change from year to year, but the formula for the 2012 season follows: ( ) ( )
where ubb is the number of unintentional walks (base on balls) and IBB is the number of intentional walks (base on balls). woba is set to the same scale as OBP, so a league-average woba in a certain year should be in a neighborhood of the league-average OBP. woba is also context neutral, in that it does not factor in whether or not there were runners on base for a player s hit, or the score of the game at that time. In summary, woba is probably the best statistic that exists and is relatively widely known to encapsulate offensive production. 3 Examining Differences in Runs Between Leagues From Figure 1 earlier, we can see that for the vast majority of the time period of interest, 1973 2013, American League teams scored more runs per game than National League teams. However, we would like to know whether this difference is statistically significant. We can find this out by setting up null and alternative hypotheses. H 0 : AL and NL runs per game are the same. (AL runs per game = NL runs per game) H a : AL runs per game exceeded that of the NL. (AL runs per game > NL runs per game) The test we choose to use to determine whether there exists a difference depends on our assumptions of the underlying distribution of the AL and NL runs per game. In order to assess the normality of the distributions of the runs per game for each league, we can look at Q-Q plots. These Q-Q plots can be seen in Figures 2 and 3.In addition to using Q-Q plots to assess the normality of the data, we can use the on each league. The results of this can be seen in Table 1. Table 1. Results (Runs Per Game) Variable AL Runs Per Game Variable NL Runs Per Game Test Statistic W = 0.974 Test Statistic W = 0.9409 p-value 0.4599 p-value 0.03369 Because the p-value for the NL runs per game is less than 0.05, we cannot assume normality. Thus, to test the aforementioned hypotheses, we should use the non-parametric Mann- Whitney U Test. The results of this test can be seen in Table 2. Table 2. Mann-Whitney U Test Results (Runs) Mann-Whitney U Test Variables AL and NL Runs Per Game Test Statistic W = 1237.5 p-value 0.0001176
Figure 2. Q-Q Plot for NL Runs Per Game Figure 3. Q-Q Plot for AL Runs Per Game
The results of the Mann-Whitney U Test on the aforementioned hypotheses indicate that there is sufficient evidence to reject H 0 in favor of H a at a significance level of α = 0.05. Thus, we can conclude that AL runs per game exceeded NL runs per game during this time period. 3.1 Examining Batting Average Along the same lines of the procedure for examining differences in runs per game between the two leagues, we can examine the difference between batting average between the two leagues, if such a difference exists. But first, we should look at a plot of the batting averages over time for each league. This can be seen in Figure 4. Figure 4. Batting Average for MLB Over Time It is immediately apparent that during the era of the designated hitter, the AL batting average has always been higher than the NL batting average. To determine whether this difference is statistically significant, we will want to test these hypotheses. H 0 : AL Batting Average = NL Batting Average H a : AL Batting Average > NL Batting Average
In order to test these hypotheses, we can first check the normality of the underlying distributions. To do so, we will enlist the use of the s once again. The results of the normality tests can be seen in Table 3. Table 3. Results (Batting Average) Variable AL Batting Avg Variable NL Batting Avg Test Statistic W = 0.9569 Test Statistic W = 0.9744 p-value 0.1227 p-value 0.4743 From the results in Table 3, we can assume that the underlying distributions are approximately normally distributed. Our next step is to determine whether the variances are equal. We can use an F-test to check for homogeneity of variances between the two leagues batting averages. The results of the F-test can be seen in Table 4. Table 4. F-Test Results (Batting Average) F Test Variables AL and NL Batting Average Test Statistic F = 1.2862 (with df = 40, 40) p-value 0.4296 The F-test indicates that we can safely assume that the variances of each league s batting averages are equal. The next step is to perform a two sample t-test using a pooled estimator for the variance. The results of the T-Test can be seen in Table 5. Table 5. T-Test Results (Batting Average) T Test Variables AL and NL Batting Average Test Statistic t = 5.2289, df = 80 p-value 6.66E-07 The results of the two sample t-test indicate that we can reject H 0 at the significance level α = 0.05. Thus, we have sufficient evidence to conclude that AL batting average is significantly greater than NL batting average. 3.2 Examining On-Base Percentage We should begin by plotting the on-base percentages for the two leagues. This plot can be seen in Figure 5.
Figure 5. On-Base Percentage for MLB Over Time For the vast majority of the seasons between 1973 and 2013, the AL OBP is greater than that of the NL. We should take a closer look at the data and determine whether there is a significant difference by testing these hypotheses. H 0 : AL On-Base Percentage = NL On-Base Percentage H a : AL On-Base Percentage > NL On-Base Percentage We will first check for normality of the data by using. Table 6. Results (On-Base Percentage) Variable AL On-Base Percentage Variable NL On-Base Percentage Test Statistic W = 0.9486 Test Statistic W = 0.9648 p-value 0.06228 p-value 0.231 As a result of the results in Table 6, we can assume normality for the data. Our next step is to test for homogeneity of variances using an F-test and then proceed with a two sample t-test to test for a difference in mean on-base percentage. These results can be seen in Tables 7 and 8.
Table 7. F-Test Results (On-Base Percentage) F Test Variables AL and NL OBP Test Statistic F = 1.1175, df = 40, 40 p-value 0.7271 The F-test results in Table 7 indicate that we can assume equal variances. Table 8. T-Test Results (On-Base Percentage) T Test Variables AL and NL OBP Test Statistic t = 3.7024, df = 80 p-value 0.0001955 The two sample t-test results in Table 8 indicate that we can reject H 0 at the significance level α = 0.05. Thus, we have sufficient evidence to conclude that AL on-base percentage is significantly greater than NL on-base percentage. 3.3 Examining Slugging Percentage To begin, we should plot the slugging percentages for the two leagues over time. The results of this plot can be seen in Figure 6.
Figure 6. Slugging Percentage for MLB Over Time It is evident that for a large proportion of the designated hitter era, the average American League slugging percentage was visibly larger than the average National League slugging percentage. We can formally verify or disprove this notion by testing the following hypotheses. H 0 : AL Slugging Percentage = NL Slugging Percentage H a : AL Slugging Percentage > NL Slugging Percentage We will first check for normality of the data by using the. Table 9. Results (Slugging Percentage) Variable AL Slugging Percentage Variable NL Slugging Percentage Test Statistic W = 0.9654 Test Statistic W = 0.9261 p-value 0.2418 p-value 0.01078 The results of the indicate that we cannot assume normality. In particular, the NL slugging percentage fails the normality test. Thus, in order to test for differences, we will opt for the non-parametric Mann-Whitney U Test. The results of this test can be seen in Table 10.
Table 10. Mann-Whitney U Test Results (Slugging Percentage) Mann-Whitney U Test Variables AL and NL Slugging Percentage Test Statistic W = 1148.5 p-value 0.002166 The results of the Mann-Whitney U Test in Table 10 indicate that we can reject H 0 at the significance level α = 0.05. We have sufficient evidence to conclude that during the designated hitter era, AL slugging percentage is significantly larger than NL slugging percentage. 3.4 Examining On-Base Plus Slugging It is a good idea to visually inspect the data as a first step and notice any observable trends. We can see the plot of the on-base plus slugging values over time in Figure 7. Figure 7. On-Base Plus Slugging for MLB Over Time Because on-base plus slugging is simply the sum of on-base percentage and slugging percentage, it is quite obvious that since the American League exhibited significantly larger
values of both on-base percentage and slugging percentage over time, that we can expect to see larger on-base plus slugging values for the American League. However, we want to be sure of this and formally test the following hypotheses. H 0 : AL On-Base Plus Slugging = NL On-Base Plus Slugging H a : AL On-Base Plus Slugging > NL On-Base Plus Slugging We will first check for normality of the data by using the. Table 11. Results (On-Base Plus Slugging) Variable AL OPS Variable NL OPS Test Statistic W = 0.9774 Test Statistic W = 0.9384 p-value 0.5791 p-value 0.0276 The results of the indicate that we cannot assume normality. In particular, the NL OPS fails the normality test. We will use the Mann-Whitney U Test to test for the aforementioned hypotheses. The results of this test can be seen in Table 12. Table 12. Mann-Whitney U Test Results (OPS) Mann-Whitney U Test Variables AL and NL OPS Test Statistic W = 1169.5 p-value 0.001155 The results of the Mann-Whitney U Test in Table 12 indicate that we can reject H 0 at the significance level α = 0.05. We have sufficient evidence to conclude that AL on-base plus slugging is significantly greater than NL on-base plus slugging. This aligns with our previous results with on-base percentage and slugging percentage considered separately. 3.5 Examining Weighted On-Base Average To begin our analysis of weighted on-base average, it is wise to first do some visual inspection of the data and see if anything sticks out. We can see this plot in Figure 8.
Figure 8. Weighted On-Base Average for MLB Over Time Here, we notice that virtually every single year since the advent of the designated hitter, the American League weighted on-base average is greater than that of the National League. We can verify this by testing these hypotheses. H 0 : AL Weighted On-Base Average = NL Weighted On-Base Average H a : AL Weighted On-Base Average > NL Weighted On-Base Average We will first check the normality of the data by using the. Table 13. Results (Weighted On-Base Average) Variable AL woba Variable NL woba Test Statistic W = 0.9627 Test Statistic W = 0.9615 p-value 0.1961 p-value 0.1779 The results of the indicate that we can assume normality for both AL and NL woba. Thus, we can proceed by testing the hypotheses using a two sample t- test. However, we will first check for equal variances using an F test. The results of these two tests can be seen in Tables 14 and 15.
Table 14. F-Test Results (Weighted On-Base Average) F Test Variables AL and NL woba Test Statistic F = 0.8422, df = 40, 40 p-value 0.5895 Table 15. T-Test Results (Weighted On-Base Average) T Test Variables AL and NL woba Test Statistic t = 5.4614, df = 80 p-value 2.59E-07 The F-test results in Table 14 indicate that we can assume equal variances for AL and NL woba. In Table 15, the two sample t-test results indicate that we can reject H 0 at the significance level α = 0.05. We have sufficient evidence to conclude that AL weighted on-base average is significantly greater than NL weighted on-base average. 4 Conclusions During the designated hitter era, from 1973 up until 2013, American League teams have exhibited more offensive output in six different offensive categories compared to National League teams. More specifically, American League teams scored a significantly larger number of runs per game, had a demonstrably higher batting average, on-base percentage, slugging percentage, on-base plus slugging, and weighted on-base average than their National League counterparts. We came to these results using a combination of two sample t-tests and Mann- Whitney U tests. These results should not be surprising, since the addition of one competent batter in place of a weak-hitting pitcher over a long period of time, such as the designated hitter era, which has spanned 41 years and counting, can have a significant effect on offensive production. It is often true that the designated hitter is one of the better offensive players that a team has, typically a player that has trouble playing defense, but has above average abilities with the bat in his hands. This makes it even less surprising that American League teams had higher offensive output during the 41 year time period we studied.
Acknowledgements Special thanks to www.fangraphs.com and their custom report generator for their publicly available historic data. Special thanks to www.baseball-reference.com for their publicly available historic data. American League: http://www.baseball-reference.com/leagues/al/bat.shtml National League: http://www.baseball-reference.com/leagues/nl/bat.shtml All statistical computing and graphs were done using R 3.1.0. R code is available upon request. References [1] Divisions Of The Code. http://mlb.mlb.com/mlb/downloads/y2008/official_rules//06_the_batter.pdf. June 7, 2014. [2] OBP. http://www.fangraphs.com/library/offense/obp/. June 7, 2014 [3][4] OPS and OPS+. http://www.fangraphs.com/library/offense/ops/. June 7, 2014 [5][6] woba. http://www.fangraphs.com/library/offense/woba/. June 7, 2014
Appendix Data Tables Runs Per Game Seasonal Data: Year AL R/G NL R/G Overall 1973 4.28 4.15 4.21 1974 4.1 4.15 4.12 1975 4.3 4.13 4.21 1976 4.01 3.98 3.99 1977 4.53 4.4 4.47 1978 4.2 3.99 4.1 1979 4.67 4.22 4.46 1980 4.51 4.03 4.29 1981 4.07 3.91 4 1982 4.48 4.09 4.3 1983 4.48 4.1 4.31 1984 4.42 4.06 4.26 1985 4.56 4.07 4.33 1986 4.61 4.18 4.41 1987 4.9 4.52 4.72 1988 4.36 3.88 4.14 1989 4.29 3.94 4.13 1990 4.3 4.2 4.26 1991 4.49 4.1 4.31 1992 4.32 3.88 4.12 1993 4.71 4.49 4.6 Year AL R/G NL R/G Overall 1994 5.23 4.62 4.92 1995 5.06 4.63 4.85 1996 5.39 4.68 5.04 1997 4.93 4.6 4.77 1998 5.01 4.6 4.79 1999 5.18 5 5.08 2000 5.3 5 5.14 2001 4.86 4.7 4.78 2002 4.81 4.45 4.62 2003 4.86 4.61 4.73 2004 5.01 4.64 4.81 2005 4.76 4.45 4.59 2006 4.97 4.76 4.86 2007 4.9 4.71 4.8 2008 4.78 4.54 4.65 2009 4.82 4.43 4.61 2010 4.45 4.33 4.38 2011 4.46 4.13 4.28 2012 4.45 4.22 4.32 2013 4.33 4 4.17 National League Offensive Seasonal Data American League Offensive Seasonal Data Season AVG OBP SLG OPS woba Season AVG OBP SLG OPS woba 1973 0.254 0.322 0.376 0.698 0.315 1973 0.259 0.328 0.381 0.71 0.323 1974 0.255 0.326 0.367 0.693 0.317 1974 0.258 0.323 0.371 0.694 0.319 1975 0.257 0.327 0.369 0.696 0.318 1975 0.258 0.328 0.379 0.707 0.324 1976 0.255 0.32 0.361 0.681 0.314 1976 0.256 0.32 0.361 0.681 0.315 1977 0.262 0.328 0.397 0.725 0.321 1977 0.266 0.33 0.405 0.735 0.326 1978 0.254 0.32 0.372 0.692 0.312 1978 0.261 0.326 0.385 0.711 0.322 1979 0.261 0.325 0.385 0.71 0.316 1979 0.27 0.334 0.408 0.743 0.331 1980 0.259 0.32 0.375 0.695 0.311 1980 0.269 0.331 0.399 0.731 0.328 1981 0.255 0.319 0.364 0.683 0.311 1981 0.256 0.321 0.373 0.693 0.317 1982 0.258 0.319 0.373 0.692 0.309 1982 0.264 0.328 0.402 0.73 0.326 1983 0.255 0.322 0.376 0.698 0.312 1983 0.266 0.327 0.401 0.728 0.325
Season AVG OBP SLG OPS woba Season AVG OBP SLG OPS woba 1984 0.256 0.319 0.369 0.688 0.309 1984 0.264 0.326 0.398 0.724 0.325 1985 0.252 0.319 0.374 0.693 0.308 1985 0.261 0.327 0.406 0.733 0.325 1986 0.253 0.322 0.38 0.702 0.312 1986 0.262 0.33 0.408 0.737 0.328 1987 0.261 0.328 0.404 0.732 0.319 1987 0.265 0.333 0.426 0.759 0.331 1988 0.248 0.31 0.363 0.673 0.301 1988 0.259 0.324 0.391 0.715 0.321 1989 0.246 0.312 0.365 0.678 0.305 1989 0.261 0.326 0.384 0.709 0.32 1990 0.256 0.321 0.383 0.704 0.315 1990 0.259 0.327 0.388 0.715 0.322 1991 0.25 0.317 0.373 0.69 0.31 1991 0.26 0.329 0.395 0.724 0.325 1992 0.252 0.315 0.368 0.684 0.309 1992 0.259 0.328 0.385 0.713 0.323 1993 0.264 0.327 0.399 0.726 0.322 1993 0.267 0.337 0.408 0.745 0.331 1994 0.267 0.333 0.415 0.747 0.326 1994 0.273 0.345 0.434 0.779 0.34 1995 0.263 0.331 0.408 0.739 0.326 1995 0.27 0.344 0.427 0.771 0.34 1996 0.263 0.33 0.408 0.738 0.323 1996 0.277 0.35 0.445 0.795 0.347 1997 0.263 0.333 0.41 0.744 0.327 1997 0.271 0.34 0.428 0.768 0.337 1998 0.262 0.331 0.41 0.741 0.326 1998 0.271 0.34 0.432 0.771 0.338 1999 0.268 0.342 0.429 0.771 0.338 1999 0.275 0.347 0.439 0.786 0.344 2000 0.266 0.342 0.432 0.773 0.337 2000 0.276 0.349 0.443 0.792 0.345 2001 0.261 0.331 0.425 0.756 0.326 2001 0.267 0.334 0.428 0.762 0.329 2002 0.259 0.331 0.41 0.741 0.323 2002 0.264 0.331 0.424 0.755 0.329 2003 0.262 0.332 0.417 0.749 0.326 2003 0.267 0.333 0.428 0.761 0.33 2004 0.263 0.333 0.423 0.756 0.327 2004 0.27 0.338 0.433 0.771 0.334 2005 0.262 0.33 0.414 0.744 0.324 2005 0.268 0.33 0.424 0.755 0.328 2006 0.265 0.334 0.427 0.761 0.328 2006 0.275 0.339 0.437 0.776 0.335 2007 0.266 0.334 0.423 0.757 0.33 2007 0.271 0.338 0.423 0.761 0.333 2008 0.26 0.331 0.413 0.744 0.326 2008 0.268 0.336 0.42 0.756 0.331 2009 0.259 0.331 0.409 0.739 0.324 2009 0.267 0.336 0.428 0.764 0.334 2010 0.255 0.324 0.399 0.723 0.318 2010 0.26 0.327 0.407 0.734 0.324 2011 0.253 0.319 0.391 0.71 0.312 2011 0.258 0.323 0.408 0.73 0.321 2012 0.254 0.318 0.4 0.718 0.312 2012 0.255 0.32 0.411 0.731 0.318 2013 0.251 0.315 0.389 0.703 0.309 2013 0.256 0.32 0.404 0.725 0.318