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Baseball Statistics Joseph Mark October 6, 2009

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History of Baseball Germans – Schlagball English – Rounders –1745 referenced as base ball –Formalized rules in 1884 Pitched like a softball 9 players field, unlimited bat

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Baseball in America Abner Doubleday (1839) –Mills report in 1908 Alexander Cartwright (1845) –Formalized rules

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Stats to know At Bats (AB) – Batting appearances, not including bases on balls, hit by pitch, sacrifice hits (bunts), sacrifice flies, & catchers' interference, or obstruction Plate Appearance (PA) - number of completed batting appearances no matter the result (at-bats + walks + hit-batsmen + sacrifice hits (bunts) + sacrifice flies + catcher's interference/obstruction Hits (H) – times reached base because of a batted fair ball without an error by the defense Runs (R) – times reached home plate legally and safely Total Bases (TB) – 1 * singles + 2 * doubles + 3 * triples + 4 *home runs Sacrifice Fly (SF) – number of fly ball out which allows a runner to score Sacrifice Hit (SH) – a deliberate hit allowing a runner to advance Strike out (K) – number of times put out by recording three strikes Walk (BB) – number of times reached base by receiving four balls

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Stats to know Innings Pitched (IP) – number of outs recorded pitching / 3Innings Pitched (IP) – number of outs recorded pitching / 3 Earned Run Average (ERA) – earned runs * 9 / innings pitchedEarned Run Average (ERA) – earned runs * 9 / innings pitched Complete Game (CG) – # of times a pitcher was the only pitcher for his teamComplete Game (CG) – # of times a pitcher was the only pitcher for his team Shutout (SHO) - # of complete games allowing zero runsShutout (SHO) - # of complete games allowing zero runs Save (Sv)Save (Sv) Win (W) - number of games where pitcher was pitching while his team took the lead and went on to winWin (W) - number of games where pitcher was pitching while his team took the lead and went on to win Walks + Hits per Inning Pitched (WHIP)Walks + Hits per Inning Pitched (WHIP)

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Basic Baseball Stats Batting Average (AVG) – hits / at batsBatting Average (AVG) – hits / at bats Home Runs (HRs)Home Runs (HRs) Runs Batted In (RBIs)Runs Batted In (RBIs) Earned Run Average (ERA) – ER * 9 / IPEarned Run Average (ERA) – ER * 9 / IP Strikeout (K)Strikeout (K) Wins (W)Wins (W)

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Importance of Statistics in Baseball Game of individual matchups –Pitcher vs. Hitter Nolan Ryan vs. Gates BrownLonnie Smith ABHABH

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“Stats don’t lie, but they don’t tell the whole truth”WIPERAWHIPKCGSHOWP League high

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“Stats don’t lie, but they don’t tell the whole truth” Player A batting average 199 strikeouts Player B batting average 57 strikeouts

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But what we didn’t tell you Player A – 48 home runs 81 walks Player B – 9 home runs 23 walks

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So we have more stats On-base percentage (OBP) –(H + BB + HBP) / (AB + BB + HBP + SF) Slugging Percentage (SLG%) –Total bases / at bats On Base Plus Slugging (OPS) –OBP + SLG

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Picking a stat is hard to do How do we pick just one?!

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Sabermetrics Bill James – Society for American Baseball Research –Bill James defined sabermetrics as "the search for objective knowledge about baseball." Thus, sabermetrics attempts to answer objective questions about baseball, such as "which player on the Red Sox contributed the most to the team's offense?" or "How many home runs will Ken Griffey Jr. hit next year?" It cannot deal with the subjective judgments which are also important to the game, such as "Who is your favorite player?" or "That was a great game."

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Usefulness of Sabermetrics Shortcomings of batting average/home runs/rbis Better predictor of future performance Runs Created Markov Runs per Game Win Shares

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Runs Created “With regard to an offensive player, the first key question is how many runs have resulted from what he has done with the bat and on the basepaths. Willie McCovey hit.270 in his career, with 353 doubles, 46 triples, 521 home runs and 1,345 walks -- but his job was not to hit doubles, nor to hit singles, nor to hit triples, nor to draw walks or even hit home runs, but rather to put runs on the scoreboard. How many runs resulted from all of these things?”

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Runs Created –RC/27: (RC x 3 x LgIP) / (2 x LgG) / (AB – H + SH + SF + CS + GDP) Compare each player’s contribution over 1 game Win Share –Measure of total performance, cumulative Markov RPG –takes into account runs scored, on base (hits + walks + hit by pitch), total bases, runs batted in, and stolen bases using (stolen bases * stolen bases) / stolen base attempts SABR stats A = On-base factor B = Advancement factor C = Opportunity factor

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Comparison of Runs Created vs. Actual Runs Scored by All 30 Major League teams in 2008

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Wins Shares, please share Win Shares Explained First, you divide responsibility for a team's wins between the offense (batting and baserunning) and defense (pitching and fielding). You do this by calculating the team run differential through a method James calls Marginal Runs. You first calculate the average number of runs scored per team in the league. You next adjust your team's runs scored and runs allowed for the ballpark in which they played half their games (i.e. home games). Then you add together two figures: all runs scored over 52% of the league average (credited to the offense), and all runs allowed less than 152% of the league average (credited to the defense). This is total marginal runs. Next, you take the percent of marginal runs contributed by the offense, multiply it by the number of wins times three. This is the total number of offensive Win Shares. You do the same thing for defensive Win Shares. Next, you attribute offensive Win Shares to individual players. This is done through two key metrics: Runs Created and Outs Made. Runs Created is a formula built by James and refined over the years. It starts with the basic equation of OBP times total bases and then adds player credit for other factors, including stolen bases, caught stealing, grounding into double plays, batting average and home runs with runners in scoring position and the kitchen sink. Runs Created is calculated for every single batter, including pitchers (if they're in the National League). Next, you subtract the league "background" Runs Created (52% of the league average) from each player's Runs Created based on the number of Outs Made by that batter, adjust it for ballpark, and credit each player with the result; essentially individual marginal runs created. Add these up for all players and use each player's percentage of the whole to allocate offensive Win Shares to each. Note that any player whose Runs Created are less than 52% of the league average runs created per out is credited with no Win Shares. This doesn't happen very often (except for pitchers). That was the easy part. Now you've got to deal with the defense. The first step is to divide defensive Win Shares between pitching and fielding. This done through a complicated formula that accounts for FIP elements that can be attributed only to pitchers (home runs, walks and strikeouts) as well as a team's DER (Defensive Efficiency Ratio, adjusted for the ballpark) and other fielding statistics such as passed balls, errors and double plays. Typically, about 70% of defensive Win Shares are credited to pitching, and 30% to fielding. The Win Shares system is bound so that pitching never is credited with less than 60%, or more than 75%, of defensive Win Shares. Next, you allocate pitching Win Shares to individual pitchers. This is accomplished through an even more complicated formula that starts with each pitcher's marginal runs not allowed (same approach as team marginal runs not allowed), wins, losses and saves. Special consideration is given to relievers by estimating the number of high-leverage innings they pitched (ninth innings with one-run leads are more important than first innings with no score) and something called "Component ERA" which is essentially ERA re-calculated according to the actual underlying run elements.

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Continued… Finally, pitchers are deducted Win Shares if they are absolutely lousy hitters. Call this the "Dean Chance" factor. All these elements are then mixed together in a complicated formula to allocate pitching Win Shares to individual pitchers. As in offensive Win Shares, any pitcher who gives up more than 152% of league-average Runs Scored (adjusted for ballpark) does not receive any credit for pitching Win Shares. One note: responsibility for unearned runs is split 50/50 between pitching and fielding. Which leads us to the next, most complicated step: allocating fielding Win Shares to fielding positions, and then to individual fielders. The calculations differ for each position. Essentially, James has selected four defensive statistics to evaluate positions. Here they are by position, listed in order of importance: –Catchers: Caught Stealing, Errors, Passed Balls and Sacrifice Hits Allowed –First Basemen: Plays Made, Errors, Arm Rating and Errors by third basemen and shortstops –Second Basemen: Double Plays, Assists, Errors and Putouts –Shortstops: Assists, Double Plays, Errors and Putouts –Third Basemen: Assists, Errors, Sacrifice Hits Allowed and Double Plays –Outfielders: Putouts, Team DER, Arm Elements and Assists and Errors Lots of things to note about the fielding calculations. –First, the statistics are adjusted based on the number of innings a lefthander pitches for the team, which has an impact on which side of the field batters hit the ball to. –Second, these stats are calculated as a proportion of the team's total, divided by the league-average proportions of the total. In other words, if a shortstop has 50 assists and his team has 100 assists in total, he receives just as much credit as the shortstop who has 100 assists and plays on a team with 200 assists in total. This is important, because it adjusts the fielding stats for the fact that fielders may be playing behind pitchers with certain tendencies such as giving up more ground balls vs. fly balls. –Third, double plays are only factored in as a proportion of potential double plays. If teams don't have a lot of runners on first, they have less of a chance to turn double plays, and Win Shares takes this into account. –Fourth, team DER is used to credit outfielders with fielding Win Shares because it is James' observation that outfielders have a much larger impact on DER than infielders. James acknowledges that there is some "circular logic" here. –Fifth, there is a final element included in the formula to allocate fielding Win Shares to individual fielders. This element is called "Range Bonus Play." It particularly impacts outfielders in the following manner: if one outfielder handles more opportunities per inning played than the other outfielders on the team, he will be credited with more fielding Win Shares. This especially impacts centerfielders, who typically handle more chances per inning played than the corner outfielders.

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Markov RPG

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Correlation between various individual hitter statistics OPSRCRC /27Win SharesMarkov RPG OPS1 RC.9121 RC / Win Shares Markov RPG

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Mythbusters: The Contract Year It is a commonly held belief that players perform better during the final year of their contract in the hopes that a good year will enable them to sign a lucrative new deal

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Difference in Means Testing ContrastsBatting Average P-Value HR/PA P-Value OPS P-ValueRuns Created/27 P-Value Markov RPG P-Value All Players A - Players B - Players

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RC/27 returns significant results for A players when tested alone and B players when tested alone. These results show that the mean for A players increases, on average, from to RC/27, whereas B players tend to decrease, on average, from to The fact that these two groups of players have a tendency to move in opposite directions in this respect explains why the results are not statistically significant when compared en masse. OPS and Markov RPG actually increase AFTER signing a new contract!

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Mythbusters 2: Waiting for your Pitch Another commonly held perception is that batters that “wait for their pitch” are more likely to get a hit and when they do hit the ball, it will go farther (perhaps resulting in more home runs)

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The regression equation is OPS = P/PA Predictor Coef SE Coef T P Constant P/PA S = R-Sq = 4.5% R-Sq(adj) = 4.2% The regression equation is Markov RPG = P/PA Predictor Coef SE Coef T P Constant P/PA S = R-Sq = 5.2% R-Sq(adj) = 5.0% Regression using Pitches per Plate Appearance to predict OPS Regression using Pitches per Plate Appearance to predict RPG

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Correlations of A&B Groups of Players w/ OPS and RPG for 2008 seasonCorrelationP-value A Players PPA vs. A Players OPS A Players PPA vs. A Players RPG B Players PPA vs. B Players OPS B Players PPA vs. B Players RPG

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Can We Predict Walks? Test (1) vs (2) Mean PPA PPA1/PPA2MeanWalks (1) / (2) Est. Diff in Means Total Walks TP-Value Top 1/3 vs Mid 1/ / / Mid 1/3 vs Bot 1/ / / Top 1/3 vs Bot 1/ / /

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How About Home Runs? Divided players into thirds according to number of pitches seen per at bat. –Those who saw the most pitches in the first third, those who saw the least number of pitches per at bat in the bottom third, and a middle third. Players in this top group hit on average home runs per plate appearance slightly higher than the of the middle group, and both are significantly higher than the of the bottom group

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So should you wait for your pitch? ∆PPA∆Walks∆HRs∆OPS∆RPGTotal.0326* *-.2241* Increase PPA.1725*3.01*-1.064*-.019*-.198 Decrease PPA -.15* * * Summary of Changes * Indicates significance at 5%

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Conclusions Changing the number of pitches seen per plate appearance does not necessarily increase a player’s raw performance measures. Rather, a player who sees an increase in the number of pitches per plate appearance from year to year will have a better change in performance relative to a player who sees a decrease in number of pitches per plate appearance from one year to the next.

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Conclusions Players performance is not significantly better during a contract year, in fact, it may actually be worse. Increasing the number of pitches you see does not increase performance –However, you will walk more –If you see fewer pitches, you are more likely to do worse

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Baseball keeps stats for EVERYTHING Hitting Stats –Singles, doubles, triples, G/F, GIDP, HBP, LOB, R, SF, SB, TB Pitching Stats –ERA, WHIP, GF, GS, K/9, BB/9, HLD, IBB, IP, CG, SHO, SV, SVO, WP Fielding Stats –PO, A, TC, E

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References and Works Cited Cover, Thomas, and Carroll Keilors, “An Offensive Earned-Run Average for Baseball,” Operations Research, Vol. 25 No. 5, September-October 1977, pp ESPN MLB Team Stats, ESPN Internet Ventures 2009, ype=2&group=9&type=reg&sort=&split=0&season=2008 Free Agent Tracker, ESPN Internet Ventures 2009, James, Bill, The Bill James Handbook, ACTA Sports, Skokie, Illinois, 2009 Krautman, Anthony C., and Margaret Oppenheimer, “Contract Length and the Return to Performance in Major League Baseball,” Journal of Sports Economics, Vol. 3, No. 1, 2002, pp Lewis, Michael, Moneyball, Norton, W. W. & Company, Inc., New York, New York, Sagarin, Jeff, Jeff Sagarin MLB Ratings, October 7, 2008, Studeman, Dave, Major League Baseball Graphs, May 16, 2004, The Hardball Times, THT Win Shares, October 1, 2008,

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