Over the last 10 years, MLB payrolls, and player salaries, have grown significantly as league revenue continues to rise. According to Forbes, MLB pulled in $9 billion in revenue last season. Teams are pulling in billions of dollars through massive television contracts — the Yankees pulled in $1.5 billion in a 2012 deal, the Angels secured a $3 billion deal in 2011, and the Dodgers reached a deal for over $8 billion (although the TV situation in LA is still a mess for fans). Fifteen MLB teams (exactly half) are valued at $1 billion or more, with the Yankees ($3.2 billion) and Dodgers ($2.4 billion) on top.

The chart below shows each team’s 2006 payroll and 2015 payroll and the rate of growth over those 10 years. While all teams fluctuated on a year-by-year basis (looking at you, Atlanta and Miami), 27 teams saw payroll increase, and 25 teams saw an increase of over 10 percent.

The average 2006 MLB team had a payroll of $77.6 million, while the average 2015 MLB team had a payroll of $121.9 million (an increase of $44.4 million, or 57.2%). The Toronto Blue Jays, more or less, represent the average MLB team payroll growth over the 2006-2015 period. The Marlins, who had slashed their payroll to a ridiculous $15 million after a trademark Marlins fire sale in the 2005-2006 offseason, saw the biggest payroll increase by percentage, followed by Washington and Kansas City who have clawed their way out of baseball’s cellar over the last 10 seasons. The Astros, coming off a World Series appearance in 2005, had the franchise’s biggest payroll ever in 2006. Several years of losing and rebuilding saw that number drop by 25.4 percent, although the Astros are reportedly looking to spend this offseason. The Braves are undergoing a massive rebuild and shedding all salary, while the Mets have been slowly climbing out of their financial troubles.

Perhaps the most surprising rank on this chart is that of the Yankees, who have increased payroll a mere 9.7 percent over the last 10 years. In fact, the team had a higher payroll in 2005 ($208.3 million), then they did last season ($203.8 million). In 2006, the Yankees were the only team spending more than $130 million on payroll and had a $70+ million financial advantage over MLB’s second-biggest spenders (the Red Sox). Now, the Dodgers have passed New York in spending, and nine teams have crossed the $130-million mark (and more will follow this offseason). Yankee ownership has pointed to the goal of getting under the $189 million luxury tax threshold.

Nine of the 10 World Series champions over this period increased payroll after winning it all (2007 Boston being the exception).

The Giants’ 2012-2013 offseason acquisitions of Angel Pagan, Marco Scutaro, and Jeremy Affeldt, along with arbitration increases for Buster Posey, Sergio Romo, Hunter Pence, and others added up to around $60 million worth of additional payroll for 2013. Of course, winning the World Series is a huge financial boon to an MLB team with increased ticket sales, increased merchandise sales, bigger TV contracts, etc…

The next chart contrasts overall (2006-2015) regular season winning percentage with the increase in payroll over the same time period.

(Note: I removed the Miami Marlins from this chart since a) they are an extreme outlier because of the 2005-2006 fire sale, and b) I’m not sure team ownership is concerned with winning percentage.)

Many people assume that spending automatically leads to winning, but this is not always the case. The Nationals (two 100-loss seasons coupled with a massive increase in spending) pretty much single-handedly pull this trendline down. The Angels, Giants, and Dodgers have seen increased payrolls result in regular season (and for the Giants, postseason) wins, while the Mariners, Rockies, and Royals (2014-2015 notwithstanding) have not. The Yankees again stand out as the winningest team, while keeping payroll relative stable.

(Note: For the same reason as above, the Marlins have been removed from this chart.)

As we would expect, investment in payroll leads to fan interest and increased attendance numbers. Also, the teams with more recent success (Toronto, Pittsburgh, Washington) received a huge boost in attendance numbers over the last few seasons. They have all significantly increased payroll since 2006.

Only one team in MLB raised its payroll less than average and still enjoyed a winning percentage above .500 AND an increase in attendance. Unsurprisingly, this team was the St. Louis Cardinals who raised payroll a mere 35.3 percent, played .549 baseball from 2006-2015, enjoyed a small uptick (around 2 percent) in attendance in 2015 compared with 2006, and won two World Series titles (2006, 2011) for good measure.

In “Hardball Retrospective: Evaluating Scouting and Development Outcomes for the Modern-Era Franchises”, I placed every ballplayer in the modern era (from 1901-present) on their original team. Therefore, Joe Torre is listed on the Braves roster for the duration of his career while the Brewers declare Darrell Porter and the Cardinals claim Keith Hernandez. I calculated revised standings for every season based entirely on the performance of each team’s “original” players. I discuss every team’s “original” players and seasons at length along with organizational performance with respect to the Amateur Draft (or First-Year Player Draft), amateur free agent signings and other methods of player acquisition.  Season standings, WAR and Win Shares totals for the “original” teams are compared against the “actual” team results to assess each franchise’s scouting, development and general management skills.

Expanding on my research for the book, the following series of articles will reveal the finest single-season rosters for every Major League organization based on overall rankings in OWAR and OWS along with the general managers and scouting directors that constructed the teams. “Hardball Retrospective” is available in digital format on Amazon, Barnes and Noble, GooglePlay, iTunes and KoboBooks. The paperback edition is available on Amazon, Barnes and Noble and CreateSpace. Supplemental Statistics, Charts and Graphs along with a discussion forum are offered at TuataraSoftware.com.

Don Daglow (Intellivision World Series Major League Baseball, Earl Weaver Baseball, Tony LaRussa Baseball) contributed the foreword for Hardball Retrospective. The foreword and preview of my book are accessible here.

Terminology

OWAR – Wins Above Replacement for players on “original” teams

OWS – Win Shares for players on “original” teams

OPW% – Pythagorean Won-Loss record for the “original” teams

Assessment

The 2001 Seattle Mariners          OWAR: 59.1     OWS: 326     OPW%: .567

Based on the revised standings the “Original” 2001 Mariners outpaced the Athletics, taking the American League pennant by four games. Seattle topped the circuit in OWS and OWAR. GM Woody Woodward acquired 32 of the 38 ballplayers (84%) on the M’s 2001 roster.

Ichiro Suzuki (.350/8/69) earned the 2001 American League MVP and Rookie of the Year Awards following a spectacular season. Suzuki topped the leader boards with 242 base knocks, 56 stolen bases and seized the batting crown. Bret Boone (.331/37/141) supplied career-highs in virtually every offensive category and placed third in the MVP race. Alex Rodriguez (.318/52/135) surpassed the 50-home run mark for the first time in his career and paced the League with 133 tallies. Edgar Martinez rapped 40 doubles and supplied a .306 BA with 23 jacks and 116 RBI. First-sacker Tino Martinez (.280/34/113) and Ken Griffey, Jr. (.286/22/65) provided additional thump while outfielder Jose Cruz Jr. posted a 30-30 campaign.

Ken Griffey, Jr. places seventh among center fielders according to Bill James in “The New Bill James Historical Baseball Abstract.” Teammates listed in the “NBJHBA” top 100 rankings include Rodriguez (17^th-SS), Edgar Martinez (31^st-3B) and Omar Vizquel (61^st-SS). “A-Rod” only had five full seasons under his belt at the time which accounts for his low rating.

Joe Mays deserved his lone All-Star nod, notching 17 victories with a 3.16 ERA. Mike Hampton accrued 14 wins while Joel Piñiero fashioned a 2.03 ERA in 11 starts. Kazuhiro Sasaki locked down 45 contests and Derek Lowe added 24 saves, forming a stout relief corps.

The “Original” 2001 Seattle Mariners roster

Honorable Mention

The “Original” 2007 Mariners OWAR: 55.1     OWS: 317     OPW%: .591

Seattle obliterated the competition in the American League Western division by a 16-game margin, securing the pennant while tallying the highest OWS and OWAR scores in the Majors. Alex Rodriguez (.314/54/156) claimed his third A.L. MVP Award and paced the circuit in home runs, RBI, runs scored (143) and SLG (.645). Ichiro Suzuki delivered a .351 BA and topped the American League with 238 base hits. David Ortiz blasted 35 round-trippers and knocked in 117 baserunners. “Big Papi” registered 116 tallies and topped the charts with 111 bases on balls along with a .445 OBP.  Kenji Johjima whacked 29 doubles and batted .287 in his sophomore season. Raul Ibanez contributed a .291 BA with 35 two-base hits, 21 dingers and 105 ribbies. Ken Griffey Jr. dialed long distance 30 times and merited his thirteenth and final visit to the Midsummer Classic. J.J. Putz fashioned a 1.38 ERA, saved 40 contests and earned his lone All-Star appearance.

On Deck

The “Original” 1997 Red Sox

References and Resources

Baseball America – Executive Database

Baseball-Reference

James, Bill. The New Bill James Historical Baseball Abstract. New York, NY.: The Free Press, 2001. Print.

James, Bill, with Jim Henzler. Win Shares. Morton Grove, Ill.: STATS, 2002. Print.

Retrosheet – Transactions Database

Seamheads – Baseball Gauge

Sean Lahman Baseball Archive

Since you are here at FanGraphs, you likely already read August Fagerstrom’s recent piece on Getting Mike Trout to 168.4 WAR. It’s a pretty fun thought experiment, but I’d like to take it one step further and create the best possible player by using the best season in history by age. I’m not sure the exact methodology August used to get his seasons, but mine is going to use the same baseline:

• Position players with at least 100 PAs only
• No Bonds or Ruth (we’ll take a look at them later)
• No duplicates, always take a players best year
• No pre-1900 guys

I’m also not going to adjust anyone’s numbers for the time period like August, mostly because I don’t feel like it, but also so we can get some silly years that would not play today at all. Anyway, let’s create a magical mystery player!

Age 18: Phil Cavarretta – 1935

WAR: 1.2

FanGraphs’ player search is kind enough to go back to age 14, but there is no one who fits my above criteria with positive value before 18, so we’ll just ignore them. The only pre-18 player who was worthwhile at all was Bob Feller at 17, but he’s a pitcher.

As for Cavaretta, he had a decent career, although his best seasons came during World War II when the rest of the league was in the service. Cavarretta had hit for a cycle the year prior to this one, which is cool I guess, but he wasn’t all that impressive, aside from the fact that he was, from what I can tell, the only 18-year-old who started a full season. Whitey Lockman in his age 18 season was almost as valuable in one-fourth the PAs.

Age 19: Bryce Harper – 2012

WAR: 4.6

It’s amazing that, prior to this season, there were people disappointed with Bryce Harper. He had the best seasons of any teenager ever (runners up, Mel Ott and Edgar Renteria, who you never put together in your head before right now).  What else did people expect? Harper to moonlight as the Nats’ set-up guy?

Age 20: Alex Rodriguez – 1996

WAR: 9.2

You knew this guy was lurking somewhere around here. He was Bryce Harper when Harper was a toddler. It’s actually rather amazing the number of spectacular young players we’ve seen in recent years. Between Harper, A-Rod and Mike Trout, we’ve seen the four best seasons from a player younger than 22 since 1943.

Age 21: Mike Trout – 2013

WAR: 10.5

You already know about this guy. He’s pretty good I hear.

Age 22: Eddie Collins – 1909

WAR: 10.0

You think Harper and Trout are a brilliant pair of young players? Try Eddie Collins and Ty Cobb. Both were 22 in 1909 and they put up WARs of 10.0 and 9.7 respectively. Luckily (or unluckily) for American League fans, both would go on to have brilliant careers, with both in the top 15 for career position player WAR. If just one of our two youngsters puts up a career of this quality, we’ll be lucky to see it.

Collins is a bit of a forgotten man compared to Cobb, but his career ought not be. He had a career .333/.424/.429 batting line, despite playing in deadball, and he was also an elite defender at second base and an excellent base runner. He’s probably best known today for being one of the clean players on the Black Sox, which is sort of like Frank Sinatra being known for his roll in High Society.

Age 23: Cal Ripken – 1984

WAR: 9.8

Cal Ripken actually was the fifth best 23-year-old player, but the other four were good enough to appear further down the list. Not that I’m complaining, because Ripken was pretty good this year. For being a guy known for his durability, Ripken was a great young player as well; probably the best between Mays/Mantle and A-Rod.

Age 24: Lou Gehrig -1927

WAR: 12.5

I love that these two guys slot in back-to-back. I also love that Gehrig wasn’t even the most valuable player on his team in 1927, with Ruth slotting in a slightly better mark of 13.0 WAR. What an absurd team that was. Seriously, imagine that Harper and Trout were on the same team this past season. Now imagine they were 35% better than they actually were. Now imagine that this team also had Manny Machado and Jason Heyward, who are standing in for Earle Combs and Tony Lazzeri on the ’27 Yankees. Now imagine yourself, rolled up on the floor in the fetal position, weeping silently as these guys make your favorite team look like little leaguers. You think to yourself, “eventually they’ll get old and bad and my team will have a chance at a championship.” Then you wake up from your coma thirty years later and the Yankees are still the best team in baseball. Because of the next guy.

Age 25: Mickey Mantle – 1957

WAR: 11.4

Okay, the 1957 Yankees weren’t quite as good as their predecessors, losing the World Series to Hank Aaron and the Milwaukee Braves. Mantle and Berra weren’t quite Ruth and Gehrig. But they were still pretty good. Mantle put up a .512 OBP in 1957, which is silly, and would be even sillier had Barry Bonds not desensitized us from silly OBPs.

Age 26: Norm Cash – 1961

WAR: 10.6

Norm Cash is not a name you see come up very often, but for one year, he was just as good as all these all-timers. The rest of his career he was basically a 3-4 WAR player, but in 1961, Cash caught the BABIP bug. His .370 mark this year was nearly one hundred points higher than his career mark. It also helped that he hit a career high of 41 home runs.

Age 27: Ted Williams – 1946

WAR: 11.8

This was the Splender Splinter’s first year back from three years of service in WWII. Depriving us of three years of Ted Williams hitting is probably at the bottom of the list of Nazi war crimes, right next to stealing the Ark of the Covenant, but it’s there.

Age 28: Rogers Hornsby – 1924

WAR: 12.5

Okay, we’ve mentioned Collins and Cobb, Mantle and Mays, and Trout and Harper as great pairs of contemporaries, but how about Babe Ruth and Rogers Hornsby? Ruth also managed a 12.5 WAR in 1924, which is pretty funny. This was the year that Hornsby hit .424. This is also the best year for our magical mystery player. His career 104.1 WAR is basically Frank Robinson. We still have 18 more seasons to go.

Age 29: Al Rosen – 1953

WAR: 9.1

Al Rosen is sort of like Norm Cash in that he only had one season of this caliber, but, unlike Cash who played for seventeen years, he only played seven full seasons. Who knows what might have been if not for injuries and other such circumstances that cut Rosen’s career short. He was probably the best executive of the guys on this list, guiding the 1989 Giants to a pennant as General Manager.

Age 30: Ty Cobb – 1917

WAR: 11.5

I think that Ty Cobb came up the most of any player I ran into while researching this list. He was a great young player, a great old player, and a great normal-aged player. I rank Ty Cobb’s second to only Barry Bonds’ as my favorite player page to marvel at.

Age 31: Joe Morgan – 1975

WAR: 11.0

At this point, some of these legendary seasons are starting to look ordinary at this point. Only a .466 OBP? Gotta pick of the slack Joe! In all seriousness, Morgan was a great player and this was his best year. I haven’t been keeping track of stolen bases so far, but 67 at age 31 is really impressive.

Age 32: Sammy Sosa – 2001

WAR: 9.9

Sosa hit 64 dingers this season, which makes for our magical mystery player’s career high mark. Of course Barry Bonds hit 9 more than Sosa in 2001. Sosa doesn’t have a reputation as a single-season hero like Norm Cash, mostly because he was a a legitimate star for a good while, but its amazing how much this season stands above the rest in his career. The only other time he broke 6 WAR was 1998 and his 186 wRC+ is 25 points higher than any other season in his career.

Age 33: Willie Mays – 1964

WAR: 10.5

You knew this guy was going to show up sooner or later. I probably could have picked one of about a dozen Mays seasons for this thought experiment and it wouldn’t have changed the results much.

Age 34: Honus Wagner – 1908

WAR: 11.8

You probably knew this guy was going to be here as well. While his 11.8 WAR isn’t quite as high as some of the more ridiculous years from Ruth, Bonds, and Hornsby, this might have been the most dominant season ever. Joe Tinker placed second in WAR this year with 7.5. Wagner had over 50% more value.

Age 35: Nap Lajoie – 1910

WAR: 9.3

Lajoie was so good that they named the team after him. I imagine our magical mystery player would also have a team named after him at this point, as he has now passed Babe Ruth in career WAR. He still has another decade left to play. Then again, I imagine there are some obnoxious fans who think he’s done. I mean, he only hit 4 home runs this year when he hit 47 two years ago and 64 the year before that.

Age 36: Luke Appling – 1943

WAR: 7.8

Interesting run of middle infielders we’ve had here. Appling is well behind Bonds and Ruth in this age bracket, but that doesn’t diminish how great of an old player Appling was. He missed 1944 and most of 1945 to war, but then proceeded to put up four more All-Star level seasons. He would also hit a home run off Warren Spahn in 1982 at age 75.

Age 37: Hank Aaron – 1971

WAR: 7.1

This season was probably Aaron’s ninth or tenth best year, but he hasn’t been particularly close to make this list prior to this point. I guess that shows how consistent of a hitter Aaron was.

Age 38: Bob Johnson – 1944

WAR: 6.4

No, I did not make that name up. But I don’t blame you for thinking that, as Wikipedia has him listed behind thirteen other Bobs Johnson including a weatherman, a butcher, a psychiatrist, an Arkansas State Representative, three other major leaguers, and a squirrel boy.

Johnson actually was a pretty good player in his day, although this season was likely exaggerated due to the paucity of good players left in the game in 1944. That being said, he’s a pretty solid Hall of Very Good type player who had a fine season when he was 38.

Age 39: Dummy Hoy – 1901

WAR: 4.8

I swear I’m not making these up! Hoy’s nickname actually comes from the fact that he was deaf, not because he was unintelligent. In fact, it seems he was quite smart for a ballplayer at the turn of the century. Hoy was also pretty good at playing baseball, as he managed a .400 OBP despite his old age and stole 27 bases.

Wait, did I just gloss over the fact that he was DEAF! In 1901 there was a 38-year-old, deaf, All-Star level player. He produced more WAR than Ted Williams did at age 38. He also got hit by 14 pitches in this season, which my brain wanted to blame on his deafness for about a third of a second before I realized how little sense that made.

Age 40: Sam Rice – 1930

WAR: 4.6

WAR rates this as Rice’s best season in his twenty year career. It seems he never peaked and just spent his entire career as a 4 WAR type guy. It managed to get him into the Hall of Fame. Our magical mystery player at this point has a career WAR four times Rice’s career mark.

Age 41: Stan Musial – 1962

WAR: 4.0

Stan Musial hit .330/.416/.508 in 1962. That is a better batting average and on base percent than Mike Trout had this season. I think that requires no further comment

Age 42: Carlton Fisk – 1990

WAR: 5.0

Our poor magical mystery player has taken up catching for the first time in his career, here at age 42. A least he hasn’t caught 2000 games already like Fisk had. It’s actually incredible that Fisk was able to pull his broken body out of bed, let alone put up a 133 wRC+. Just to put in perspective how slim the pickins are getting, only nine players put up at least 1 WAR in their age 42 seasons. Four of them have already appeared on this list, and Barry Bonds is a fifth that I am not allowed to take. Luckily, Fisk was better than all of them with the exception of Luke Appling.

Age 43: Tony Perez – 1985

WAR: 1.5

Perez and Fisk are the only two batters to manage a 1 WAR season at age 43. Interestingly enough, Perez was not a very good old player, with his last 1 WAR season prior to this one coming at age 38.

Of note is that of the twelve players to manage 100 PAs in their age 43 seasons, eight are in the Hall of Fame. The only one who is neither in the Hall nor otherwise mentioned here is Graig Nettles.

Age 44: Pete Rose – 1985

WAR: 0.8

Pete Rose stuck around this long because he was aiming for the all time hits record. This doesn’t concern our magical mystery player, who achieved that four years ago.

Age 45: Julio Franco – 2004

WAR: 1.2

I could give this season to Omar Vizquel to allow magical mystery player to hang on with one more season from Julio Franco but I’d rather he go out with a bang. Or at least as much of a bang as a 45-year-old can provide. Franco was actually an above average hitter with a 113 wRC+ in 2004. He would hang on for three more seasons, but the rules prevent me from tacking those on here at the end. Not that it matters much, since Franco was basically replacement level from here on out.

Finally, the greatest player of all time is riding off into the sunset at age 45. How good was he? He managed 4892 hits in his career with 620 of them being home runs. His career batting line was .333/.421/.549. He played all around the field, spending at least one full season at each position. Seventeen Hall of Famers contributed to his career. Somehow, he only won 5 MVP awards (1927, 1946, 1953, 1957, and 1975).

Career Wins Above Replacement: 220.4

That’s Babe Ruth plus Will Clark or Larry Doby. Here’s his full ‘career’ if you want to call it that:

Speaking of Babe Ruth, I almost forgot our other, very important exercise. In creating the magical mystery player, I purposely left out any seasons from Babe Ruth or Barry Bonds, who were both a completely different level of silly good. In the comments of the aforementioned article from August Fagerstrom, I took the best season between just Bonds and Ruth, much in the same way as I did with everyone else here. Now, there is a bit of smudging. Ruth’s pitching stats are included, but it’s not a whole lot. Furthermore, neither player managed 100 PAs in their age 19 or 40 seasons, but I included the best of them anyway. But here’s the player I got.

3208 hits

833 home runs

.336 batting average

.483 on-base percent

.692 slugging percent

210.0 WAR

Oh… oh my. That WAR is awfully close to our magical mystery player. And magical mystery player has 5000 more career plate appearances. If you prorate the home runs to even just 15,000 plate appearances (still over 2000 behind magical mystery player) you end up with exactly 1000 home runs. With that, I leave you with this. It is tangentially related.

Projecting starting pitcher performance has proved more difficult than projecting hitter performance, mostly because pitcher skill level and performance tends to be more volatile. Another issue is that pitcher performance indicators are heavily reliant on batted-ball outcomes. This means a team’s defense and luck (e.g., softly hit balls that drop for hits) become a large part of run prevention, all of which are mostly out of the pitcher’s control. This realization has led to the development of a variety of pitching statistics that attempt to reduce pitcher performance into metrics that rely on outcomes only under pitcher control, such as walks, strikeouts, and home runs (e.g., Fielding Independent Pitching, FIP). Given that these metrics are the state of the art in terms of summarizing and describing a player’s past performance (not necessarily predictive measures; see Dave Cameron’s 2011 article here), it is useful to develop ways to attempt to predict these metrics from prior predictive statistics. As such, the goal of the current analysis was to develop prediction models using various regression tree methods that best predict starting pitcher performance metrics.

Data
Data for these analyses were compiled from several different sources, including Fangraphs.com and by using the ‘Lahman’ and ‘Retrosheet’ packages in R. Data were aggregated from the prior three seasons (2012-2014), as well as the 2015 regular season. The final data set included average performance statistics of starting pitchers from 2012-2014 who also pitched at least 50 innings during the 2015 season (N=127). The primary outcome was 2015 pitcher Wins Above Replacement (WAR). Predictors included aggregated values of over 30 performance metrics from the prior three seasons, including standard and advanced statistics (e.g., K-BB%), batted-ball measures (e.g., GB%), quality of contact statistics (e.g., hard contact %), and PITCHf/x measures (e.g., average fastball velocity).

Analytic Approach
The goal of this analysis was to use several different data modeling techniques to develop models that best predicted pitcher performance during the 2015 season from pitching data from the 2012-2014 seasons. Three separate techniques were utilized that fall within the general family of Classification and Regression Tree (CART) methods. CART methods use search procedure algorithms to find variables that are most important for prediction, then, determine the best possible cut point on the selected predictor in order to subset the data into multiple predictor spaces (Breiman, Friedman, Olshen, & Stone, 1984; Steinberg & Cola, 2009). These procedures allow for non-linear associations and higher order interactive effects. Regression trees were grown using several different packages in R, including the rpart and party packages. These packages are capable of growing large regression trees, but also include cost complexity and control parameters that allow for the assessment of over fit and tree size reduction. Next, a technique known as boosting using the gbm package in R was used to identify the predictors of highest importance for predicting pitcher performance. Although similar to ensemble CART methods that re-sample data to grow multiple large regression trees (e.g., bootstrap aggregation), boosting is a slow learning algorithm that grows regression trees sequentially, not independently. Each tree is fit to the residuals from the previous tree in order to isolate the misfit and re-shape the regression tree.

Results
First, the complete dataset was split in half in order to create training and test data sets. Next, the training data was used to fit a regression tree predicting 2015 WAR from all variables in the dataset. In the first model, liberal control parameters were set for the size of the tree, meaning a large tree was grown that selected all the best possible predictors. Each chosen predictor was then optimally split until each pitcher could be placed into a terminal node. The results from the initial model demonstrated that average strikeout rate per plate appearance (K%) was the best predictor of WAR with an optimal split of 22.39%. The initial model R2 demonstrated that 97% of the variance in WAR could be explained by this regression tree. Despite the high amount of variance explained, this model has likely over fit the data. In other words, the model is overly fit to the empirical data set, which means the model is too complex and unlikely to replicate across other samples. Reducing the size of the tree, or pruning the tree, will result in higher bias, but will reduce variance in the predicted values.

Initial Regression Tree Overfit to the Sample Data

In order to determine the optimal tree size (i.e., prune the tree) cost complexity pruning using 10-fold cross validation was done on the training data set. Based on the model deviance, the optimal tree size was determined to be between 4 and 6 terminal nodes. After pruning the tree, the R2 was reduced to .68, but the mean square error (MSE) was also reduced from 6.8 to 3.6 in the training data set. Next, the optimized tree was fit to the test data set, which produced an R2 of .57 and a MSE of 1.4. Surprisingly, after the initial split on K% the next-best predictors were related to quality of contact statistics (go here for more detailed information). Although there is a large amount of measurement error in these variables, it is still interesting these measures are predictive of WAR.

An inherent problem with regression trees is that continuous predictors with more unique values are more likely to be chosen because they contain a higher number of possible split points. The party package in R attempts to control for this issue by taking into account the distributional properties of the predictors (Hothorn, Hornik, & Zeileis, 2006). As such, similar models were fit predicting 2015 WAR using the party package in R. Results were similar to the model using the rpart package, which found that average strikeout rate was the best predictor with a split of 22.3%. However, it was determined that the data only required one optimal split, partitioning pitchers into those who were above and below a strikeout rate of 22.3% (see Figure below). Although this model explained significantly less variance in WAR (R2 =.29) than the larger tree, this model is likely to have higher stability and predictive utility in new samples.

Optimized Regression Tree using the Party Package

Finally, boosted regression trees were fit to the data to examine the optimal predictors of 2015 WAR. The number of trees (B=1,700) was chosen by examining the decline in the squared error loss for the out of the bag sample. The shrinkage parameter was set to λ =.001 with an interaction depth of d=1. For the training data the MSE was 1.79 and the R2 was .59. The model was then tested against the left-out half of the dataset (test dataset), which produced a MSE of 1.98 and an R2 of .55. Given the small differences in the R2 value and MSE for the test and training data sets, this model appears to show relative consistency. The most important predictors were determined by the importance function in the gbm package. Average strikeout rate, average fastball velocity, and average strikeouts per plate appearance minus walks per plate appearance were the most important predictors of 2015 WAR. To see a list of the relative influence of all variables refer to the table below.

Order of Variable Importance Predicting 2015 WAR

Based on these results it is clear that K% is a strong predictor of future WAR, which is not surprising because pitcher WAR is based on FIP (derived from K, BB, HR outcomes). Average fastball velocity and K% minus BB% also came out as a relatively strong predictors of WAR in the boosted regression tree models. Quality of contact was found to be an important predictor, but more analysis should be done in other samples to see if these measures have consistent predictive ability.

The Angels are an odd team. They are perennially competing for a spot in the playoffs and in 2014 they had the best record in the AL, but each year it seems that they are out-performing their talent.

The simplest explanation is that the team is buoyed by Mike Trout, which is true. A team with the best player in baseball, and always one of the highest payrolls in baseball, should not be lagging this much. The Angels should be more than a perennial playoff contender. They should be World Series contenders. So, if there ever was a time for Arte Moreno to hand out his money, it’s this off-season which provides the Halos with everything they need to resolve the biggest issues the team faces.

They currently have $130,278,770 in payroll obligations, excluding pre-arbitration and arbitration-eligible players. The Angels carried payrolls of $168,299,326 and $151,298,162 in 2014 and 2015, respectively. MLB Trade Rumors projects $20,100,000 in arbitration salaries for six players, which brings the Angels 2016 payroll for 14 players to $150,278,770. If you leave three spots open on the 40-man roster, giving the Angels three players to add through free agency, and estimate that the remaining 23 players will cost the Angels $500,000 each, or $11,500,000 total, it would bring the payroll to a best-case scenario of $161,728,770.

Arte Moreno has said he would cross the luxury tax threshold, but that seems more like PR than an actual possibility, so I’ll cap the potential payroll at $189,000,000. That leaves the Angels with $27,271,230 of money to spend before surpassing the luxury tax threshold.

The Angels could use an upgrade to their DH/1B depth and a player like Mike Napoli would fit well with them, but that’s not a pressing need. The bullpen is also an area that could improve, however it’s not really a dire situation.

The most glaring holes on the Angels roster are the third base position and a corner outfield spot. Technically, it’s left field, but Kole Calhoun can play in any corner, so someone who plays either right or left field would work. For that matter, they would be fine with a center fielder because Trout could probably flex out of center field if needed.

A trade, at least a meaningful one, is out of the question because the Angels gave up their only valuable assets in the Andrelton Simmons deal. That may have been a pretty big mistake depending on how much money they plan to spend this offseason.

There does not seem to be a better fit for the Angels than Daniel Murphy. He could be the solution they have been seeking in their search for a left handed bat to slide in the middle of the order. Murphy’s defensive ability, or lack thereof, is somewhat overblown. Metrics tend to be fairly neutral on him, and some of his misadventures at second base overshadow the fact that he’s a competent third baseman. That is where he would best serve the Angels. FanGraphs’ contract crowdsource pegs Murphy for a contract with a $12,000,000 average annual value. I think Murphy could end up getting more than that, but let’s roll with that. The Angels are now down to $15.3 million.

That brings us to the outfield. Jason Heyward, Yoenis Cespedes, and Justin Upton would all fit in Anaheim. However, the Angels could only afford one of them if they backload the contract, which is possible, but set that possibility aside for the moment.

The other options would be Denard Span, Gerardo Parra, Nori Aoki, and Rajai Davis.

Span would seem to be an unnecessary injury risk for a team that would need him on the field to compete for a World Series and does not have a great backup option for the position. However, a healthy Span is a good fit with the Angels. He would add some much needed speed to that lineup and would probably fit in their budget, costing around $12,000,000 on a three-year contract.

Alternatively, a platoon of Nori Aoki or Gerardo Parra with Rajai Davis would probably cost the team around $10,000,000 combined and would provide competent left field options.

The issue with Span or an Aoki or Parra/Davis platoon is that it just puts the Angels back where they were: in the mix. It doesn’t distinguish them, and it doesn’t make them World Series contenders. It’s not improbable that a team with Murphy and one of the lesser outfield options could make a World Series run, it’s just also not improbable they would be sitting at home in October.

And that’s my potential issue with the Andrelton Simmons trade.

There’s been some discussion on the best way to use minor league resources in light of the Red Sox’s trade for Craig Kimbrel. However, I think it’s much more interesting to examine the issue by looking at the Angels and what they gave up in their trade for Andrelton Simmons.

Sean Newcomb was one, and maybe the only, valuable asset that the Angels possessed that they could move in an attempt to improve the team. They undoubtedly did that by getting Andrelton Simmons, but Simmons didn’t solve any immediate issues. He’s an improvement over Erick Aybar, but Erick Aybar really wasn’t an issue. And the trade begs the question, are the Angels looking past this year? The main benefit of Simmons is what he brings the team in 2017 and 2018, being a very good shortstop under a reasonable contract.

I don’t know if Billy Eppler shopped Newcomb around for a player like Carlos Gonzalez or any other available outfielders. Maybe Newcomb wasn’t enough. And Jay Bruce seems like a good fit, but Jay Bruce is a bet; he’s one of those players whose reputation of past performance seems to outpace his recent performance (Bruce had -.9 WAR in 2014 and .1 in 2015. Steamer projects him to have a .6 WAR in 2016).

Maybe Billy Eppler has all the money he needs to add Heyward, Cespedes, or Upton, or maybe he’s convinced he has the ability to add one of them on a back-loaded contract. Jeff Weaver and C.J. Wilson are off the payroll next year and all payroll obligations owed to Josh Hamilton will be off the books after 2017, so the financial situation looks better in the future.

And there are a lot of alternatives here. The Angels could band-aid third base by bringing back David Freese, or adding Juan Uribe. That may leave them with enough money to bring in one of the marquee free agents, but it still leaves them short of being a baseball powerhouse. It just makes them another good team with a shot at making the playoffs.

All of this is to say that the Angels are an interesting team. Mike Trout keeps them on the brink of being very good each year, but if Arte Moreno is willing to spend like the Dodgers and Yankees the Angels could be great. If they added Daniel Murphy and Jason Heyward they would have to be considered one of the best teams in the league. However, if they added Simmons at the cost of only being able to address either their third base or corner outfield issue instead of addressing both, then it seems like a misuse of their only minor league asset, and of Mike Trout’s greatness.

It was a defining moment in the 2015 World Series. Proven closer Jeurys Familia watches as a slow chopper is hit to third baseman David Wright. Wright glances back to Eric Hosmer on third and throws to first. Without hesitation, Hosmer sprints home and beats out a wild throw from first baseman Lucas Duda to stun the crowd at Citi Field and tie the game in the 9th. Hosmer made a big play on a big stage. But that wasn’t the only time in his career, the 2015 season, or even that World Series that Hosmer has shown a flair for the dramatic in big moments.

So I did a little digging.

The statistic “Clutch” quantifies how much better or worse a batter performs in high-leverage situations compared to a neutral situation. This does not necessarily make or break a good player. However, the statistic can show the track record of a player’s ability (or inability) to elevate his own game in big moments. The scale is centered at an average player clutch rating of 0 and typically ranges from -2 to 2 in any given season, with 2 being considered both a rare and excellent rating.  This statistic is better used to look at what has happened in the past rather than predict the future. To my surprise, Hosmer has dominated the clutch leader boards the last five years. Not Miggy, not Longo, not Big Papi. Hosmer.

Since his debut season in 2011, Hosmer has a cumulative clutch rating of 5.49 while the league average has been -0.38 according to fangraphs.com. The second-highest in that time span? Jacoby Ellsbury at 4.41, over a full point away. To this point in his career, Hosmer has a cumulative clutch rating that ranks 22nd in baseball history. He is ahead of legends such as Ken Griffey (5.35), Rickey Henderson (4.91), and fellow Royal George Brett (4.79). His 2015 campaign that yielded a clutch rating of 2.17 was one of the top 100 greatest clutch seasons ever recorded (tied for 63rd). Although there is no way to prove Hosmer will remain a clutch hitter, he is currently on pace to smash the all-time highest career clutch rating set by Hall-of-Famer Tony Gwynn (9.49).

So what makes Eric Hosmer clutch at the young age of 26? His high baseball IQ. He is constantly aware of the situation and knows what he has to do to produce runs for his team. Let’s use this past World Series as an example. In Game 1, Hosmer came to the plate in what was easily the one of the biggest at-bats of the season. Bottom of the 14th. Tie game. Bases loaded. Nobody out. Infield in. Seasoned veteran Bartolo Colon on the mound.

(Video copyright of MLB Advanced Media)

See what he did there? He knew the infield was in and he knew he could not do two things: strike out or hit the ball on the ground. He had to get the ball deep in the air, despite having a GB% of 52.2% in 2015. He gets a fastball in the heart of the zone and lifts the ball into right, deep enough to get the winning run home and record the seventh walk-off of his career.

The next day, he comes up in another big situation against young pitching phenom Jacob deGrom. Bottom of the 5th. Tie game. Runners on second and third.

(Video copyright of MLB Advanced Media)

With Escobar’s speed on second, Hosmer knew all he needed was a base hit to give the Royals a two-run lead. He sticks with a slider that caught a little too much of the bottom half of the plate and ropes a grounder up the middle. The 26-year-old didn’t let the moment get to him and over-swing, but instead took what the pitch gave to him. Clutch.

Although Royals fans have seen rather inconsistent numbers from Eric Hosmer through the first five years of his career, it is not overlooked how important he has been to bringing a winning atmosphere back to Kansas City as they had hoped he would. After all, he was the third overall pick in 2008 MLB amateur draft. But big expectations and big moments don’t scare Hosmer. He’s been the most clutch hitter in the league.

Moving on from an analysis of starting pitchers, we move to relievers.

Relief pitchers happen to be the easiest group of players to project as their final salary is nearly entirely driven by saves although for non-closers, holds become very important to differentiate between setup men (who make slightly more) and middle relievers.

For a RP who is arbitration-eligible for the first time, here are the statistics that correlate most with eventual salary:

Career SV: 83.28%

Platform SV: 79.07%

Career WPA: 38.15%

Career SV%: 35.60%

Career fWAR: 35.18%

Platform SV%: 27.06%

Platform SO: 25.75%

When initially looking for player comps, these are statistics we are going to focus on. Keep in mind that although ERA is not listed, it is nonetheless important as ERA is still one of the default statistics used during a hearing and one of the first bases for comparison.

Note: WPA and Shutdowns (SD) have strong correlations, however those two stats are not widespread enough to be used during a hearing. My model includes WPA, but does not include SD as the inclusion of SD de-emphasized the importance of saves while it inflated the salaries of situational relievers. While ideally that should be the way salaries are determined, that does not happen in practice so it made sense to omit SD from the model.

Let’s use Indians closer, Cody Allen, as an example of a first-year-eligible reliever. Cody Allen is arbitration-eligible for the first time going into 2016 with 3 years and 76 days of service time (3.076). In his platform season (2015), Allen recorded 34 saves with a 89.47 SV%, 99 SO and a 2.99 ERA. Over his career, Allen has compiled 60 saves with a 84.51 SV%, 4.19 WPA, 5.0 fWAR and a 2.64 ERA. The objective here is to find the players who avoided arbitration by signing a 1-year contract with statistics that are most similar to Allen’s. The more recent, the better. The best way to do that is to set a floor and a ceiling and then work your way towards the middle.

First, let’s look at David Aardsma’s 2009 platform season (old, but still useful). Like Allen, Aardsma was an effective closer with high save totals and a strong ERA. Aardsma recorded 38 saves, 80 SO with a 2.52 ERA. Over his career, Aardsma had compiled 38 saves with a 80.85 SV%, 2.25 WPA, 1.5 fWAR and a 4.38 ERA. Although the platform stats are very similar, Allen’s career numbers are far superior. Therefore, we can definitively state that Allen should receive more than Aardsma did. As such, Aardsma’s 2010 salary of $2.75 million should be the floor.

Next, let’s look at Greg Holland’s 2013 platform season. Like Allen, Holland was an effective closer with high save totals and a very strong ERA. Holland recorded 47 saves with a 94.0 SV%, 111 SO and a 1.21 ERA. Over his career, Holland had compiled 67 saves with a 88.16 SV%, 7.87 WPA, 6.9 fWAR and a 2.41 ERA. Although their career numbers are relatively close, Holland had a dominant platform season that surpassed Allen in every way. Therefore, we can definitively state Allen should receive less than Holland did. As such, Holland’s 2014 salary of $4.675 million should be the ceiling.

Given the above, Cody Allen is likely to receive somewhere between $2.75 million and $4.675 million. Now that we have a range, let’s find someone towards the middle.

In 2013, Ernesto Frieri recorded 37 SV with a 90.2 SV%, 98 SO and a 3.80 ERA. Over his career he recorded 60 saves with an 89.55 SV%, 5.62 WPA, 2.3 fWAR and 2.76 ERA Those numbers are quite similar across the board with both players having an identical career save total and only 3 more platform saves. Frieri’s 2014 salary was $3.80 million so we can determine Allen will receive a similar amount. Andrew Bailey ($3.9 million in 2012) is a decent comp as well.

As for my model, Allen projects to receive $3,595,732 +/- $130,998 which is perfectly in line with the comps above. MLBTradeRumors projects him at $3.5 million so both of our models are very close here (and will be most of the time).

For a player who has already been through the arbitration process before, the valuation is completely different as career statistics are no longer used the 2nd, 3rd, 4th, etc. time around (except in a few rare cases).

For a RP who has previously been through the arbitration process, the stats that correlate most with eventual salary are:

(1) Platform SV: 70.40%

(2) Platform fWAR: 41.36%

(3) Platform RA9-WAR: 36.58%

(4) Platform SV%: 34.79%

(5) Platform WPA: 34.34%

(6) Platform SO: 30.04%

For example, let’s look at Reds closer Aroldis Chapman who is arbitration-eligible for the third time going into 2016. As an Arb-2 going into 2015, Chapman received a $8.05 million salary. That figure includes everything he had done in his career up to that point. Thus, when determining his 2016 salary, we don’t need to focus on previous seasons. We need only determine what his 2015 season was worth and give him a raise. In his platform season (2015), Chapman recorded 33 saves with a 91.67 SV%, 116 SO, 1.99 WPA, 2.4 fWAR, 2.7 RA9-WAR and a 1.63 ERA. We want to find the players whose stats are most similar to Chapman.

First, let’s discuss Juan Carlos Oviedo’s (formally known as Leo Nunez) 2011 platform season where he recorded 36 saves with an 85.70%, 55 SO, 1.07 WPA, 0.1 fWAR, 0.2 RA9-WAR and a 4.06 ERA. Although Oviedo was fortunate enough to record more saves, Chapman was the far better player overall; so much so that, despite having fewer saves, we can determine that Chapman will definitely receive a larger raise than the $2.35 million raise Oviedo received going into 2012. Therefore, we can consider a raise of $2.35 million to be his floor. Oviedo is the perfect example of how important saves are (for arbitration purposes) when it comes to relievers.

Next, let’s look at Heath Bell’s 2010 platform season (again old, but useful still) where he recorded 47 saves with a 94.0 SV%, 86 SO, 4.49 WPA, 2.3 fWAR, 2.6 RA9-WAR and a 1.93 ERA. Like Chapman, Bell was an All-Star closer with virtually identical numbers except for WPA and SV, where Bell clearly outproduced him. Moreover, Bell was named the NL reliever of the year. As such, Bell’s raise of $3.5 million going into 2011 should be the ceiling.

Given the above, Aroldis Chapman is likely to receive a raise somewhere between $2.35 million and $3.5 million for a final salary between $10.4 million and $11.55 million.

Chapman is a perfect example of why first determining a range is important as Chapman represents a type of player who just has not been through the arbitration process in this service group before. Since 2006, there has not been a closer who recorded less than 40 saves with dominant numbers. Looking at saves we have Chris Perez (39 saves – $2.8 million in 2013), Brandon League (37 saves – $2.75 million in 2012), Jonathan Papelbon (37 saves – $2.65 million in 2011) and Joel Hanrahan (36 saves -$2.94 million in 2013). Somewhere around those numbers and perhaps a bit higher is what we should expect.

My model projects that Chapman should receive a raise of $2,743,587+/- $152,366 for a total 2016 salary of $10,793,587+/- $152,366, although I think my projection underestimates the impact his dominant numbers will have despite the lowish save totals (due the lack of comps). I would expect a raise of around $3 million. MlbTradeRumors is projecting a raise of $4,850,000 for a total salary of $12,900,000, which not only surpasses Heath Bell’s raise, but shatters Jim Johnson’s record-setting raise for a non-first-year reliever of $3,875,000 when he recorded 51 of 54 saves in 2012. Given the importance of saves and the relative unimportance of the other stats, I don’t see how such a high number is possible. Nonetheless, Chapman is a very interesting case study as he has the potential to change the way relievers are viewed during the arbitration process.

Next up: position players.

We’re halfway through November and the winter meetings are right around the corner. Teams are gearing up for next year and taking a look at their rosters, deciding what direction they want their team to head. Today I want to look at the Toronto Blue Jays and hypothesize a direction they could go.

The Blue Jays had a great 2015 and continuing that momentum is crucial for the newly recharged fan base. They have a number of quality young players who contributed this past year. Kevin Pillar, Chris Colabello, Ryan Goins, Marcus Stroman, Roberto Osuna and Devon Travis (when healthy) all had nice seasons and remain under team control in some shape or form for the next 3-5 years. The Jays also have some large expiring contracts after the 2016 season in the form of R.A. Dickey, Edwin Encarnacion and Jose Bautista who have been important pieces to Toronto’s success. Add in Russell Martin, Josh Donaldson and Troy Tulowitzki and the Blue Jays should once again compete in the AL East in 2016. One of the glaring issues however is their starting rotation and bullpen.

With Marco Estrada signed the Blue Jays have a starting rotation of Dickey, Stroman, Estrada and Hutchison. Reports have come out and the Jays will reportedly have a similar budget to last year, around $140 million. After the guaranteed contracts, arbitration estimates and league-minimum salaries are accounted for the Blue Jays will have about $18-$19 million to spend on starting pitching and bullpen help. There are a number of directions the Blue Jays could go; it’s a solid class of starting pitching this year and with the $18 million left in the salary they could for sure pick up a quality starting pitcher to fill out the rotation. They could also spent the money on a lockdown relief pitcher and try to transition either Aaron Sanchez or Roberto Osuna to the rotation. Or they could split up the money and get an older starting pitcher and get whatever reliever is available for the remainder of the money. Another option, and the one that I’m going to explore, is the trade route.

With all the moves the Blue Jays made at the deadline, their farm system isn’t as strong as it was at midseason last year but the recent developments with the Atlanta Braves got me thinking about trade ideas — mainly Julio Teheran. With the Braves set to open a new stadium in 2017 the mentality has been to shed money and stock prospects for the opening season in the new stadium. This works out great for the Blue Jays who have some talent left in the farm system that could be useful to the Braves. The fourth-ranked prospect in the Blue Jays system and coincidentally the fourth-ranked catching prospect in baseball is Max Pentecost. Atlanta has been stocking arms in recent trades but with Christian Bethancourt struggling in his time in the majors, the Braves clearly don’t have a long-term solution behind the dish. The former 1st round pick, 11th overall is currently in advanced-A ball and his estimated time of arrival in the majors is 2017, perfect for their rebuilding plans. If the Jays were to include one maybe two young pitchers on a similar timeline like Conner Greene and/or Marcus Smoral, perhaps that would be enough to pluck Teheran away from Atlanta.

Teheran is only 24 years old and will turn 25 for the 2016 season. He’s owed a bargain-basement price of $3,466,666 for next season, is under contract through 2019, and has a club option for 2020. With starting pitcher salaries estimated anywhere from $10-$25 million and up this offseason, Teheran and his $3.5 million in 2016 season seem like a steal. Plus the Blue Jays would be getting Teheran for the prime years of his career and although last year was an off year, he’s shown signs of being an ace. Teheran would complete the starting rotation for the Jays in 2016 and after Dickey’s contract expires, Toronto would be left with a rotation of Stroman, Teheran, Hutchison and Estrada for the 2017 season. The other nice thing about Teheran is that his $3.5 million contract leaves Toronto with roughly $15.5 million left over to fill out the bullpen or upgrade other areas. Teheran would be an affordable and valuable piece to a rotation that desperately needs it and would be far better then spending 3 to 4 times his annual 2016 salary on a pitcher that may already be or not far away from the decline of his career.

As I mentioned above, with the money saved on the Teheran trade, the Blue Jays could add a piece to the bullpen or upgrade other areas but in compiling data for this article, I got to thinking about what the Jays could do for the future. 2017 has roughly $36 million coming off the books for Toronto and with a young core of controllable players, the Jays have some room to make a move. One of the contracts expiring is RF Jose Bautista. I personally think the Jays should re-sign Bautista after 2017 but I don’t think putting him in right would make sense. With Encarnacion’s contract set to expire as well, the DH spot would be available for Bautista, should he choose to stick around. That would leave RF empty and looking at the outfield class of 2017 (Beltran, Suzuki, Gregor Blanco, Josh Reddick, Brandon Moss, Mark Trumbo and of course Bautista) the group leaves something to be desired.

That brought me to the 2016 class, led by arguable the best right fielder in the game, Jason Heyward. The Jays have been rumored to be after SP free agents David Price and Zack Greinke but for the amount of money they’ll command and the stages they’re at in their career, I think the money might be better spent on a player whose best days are ahead of him. That in my opinion is Jason Heyward. We know Heyward is a solid player, who’s shown flashes of brilliance and is young enough to still put it all together consistently. In a lineup like the Blue Jays’, Heyward would thrive much the way Josh Donaldson officially broke out as a superstar last year. Heyward would have the protection and opportunities to truly develop into the player he’s about to get paid to be. The problem with signing Heyward would be the Blue Jays would have to free up a sizable amount of money and the only real place to look is at shortstop in the form of Troy Tulowitzki.

Tulowitzki was a surprise addition for the Blue Jays last year and definitely added strength to an already dangerous lineup but with the depth that Toronto has with Ryan Goins able to play SS and the return of Devon Travis, the 31-year-old Tulowitzki becomes an expensive option for the remainder of his career. Perhaps the Jays should trade Tulowitzki to free up money to sign Heyward to a long-term deal? Instead of watching the expensive decline of Tulo for the remainder of his contract, Toronto could still sell high to a team willing to take on the contract, receiving bullpen help and possibly an extra outfielder to help address current needs.

I then started going through MLB teams to see which ones would possibly be in a situation to make the trade happen. The Diamondbacks, White Sox and Mets all stood out as possible suitors while the Rangers, Yankees, Padres and Mariners also seemed like possible options. For the purposes of this article I’m only going to focus on the first three.

With a 2015 budget of about $76,622,575 million the Arizona Diamondbacks definitely have room to financially take on Tulo’s contract; the question is, is that where LaRussa and Dave Stewart want to take the team? None of us truly know but if the asking price is right, perhaps Randall Delgado and Ender Inciarte, maybe the thought of Tulo and Goldschmidt would fit their plans. They did spend $68.5 million for 6 years of Yasmany Tomas and with the emergence of David Peralta and A.J. Pollock, the Diamondbacks have outfielders to spare. If the trade were to go through the Blue Jays would gain about $18,487,000 giving them a total available amount of about $33,980,334. That would definitely be enough to sign Heyward to a 7-10 year deal (depending on what the market drives his year amount to) at anywhere from $20-$29 million per season. With the $36 million coming off the books in 2017, Toronto would have about $37 million to spend on the DH spot (Possibly Bautista) and SP or RP spot open (depending on how they handle Sanchez and Osuna). Compared to the $50 million amount they could have in 2017 minus whatever they pay for a starting pitcher this off season. In reality that $50 million would probably be more like $30-$35 million with two rotation spots available as well as the DH. If the Teheran trade and Heyward signing were to happen, here is what the 2016 and 2017 Blue Jays lineup would look like.

2016 Lineup                2017 Lineup

C = R. Martin                C = R. Martin
1B = E. Encarnacion    1B = C. Colabello
2B = D. Travis              2B = D. Travis
3B = J. Donaldson       3B = J. Donaldson
SS = R. Goins                SS = R. Goins
LF = B. Revere              LF = B. Revere
CF = K. Pillar                CF = K. Pillar
RF = J. Heyward         RF = J. Heyward
DH = J. Bautista          DH = ?

SP = R.A. Dickey                 SP = M. Stroman
SP = M. Stroman                 SP = J. Teheran
SP = J. Teheran                   SP = D. Hutchison
SP = D. Hutchison            SP = M. Estrada
SP = M. Estrada                   SP = ?

RP = R. Osuna                     RP = R. Osuna
RP = A. Sanchez                  RP = A. Sanchez
RP = L. Hendricks              RP = L. Hendricks
RP = B. Cecil                        RP = B. Cecil
RP = R. Delgado                  RP = R. Delgado
RP = S. Delabar                   RP = S. Delabar
RP = A. Loup                        RP = A. Loup

BN = E. Inciarte                   BN = E. Inciarte
BN = J. Thole                        BN = D. Pompey
BN = C. Colabello                 BN = ?
BN = D. Barney                     BN = ?

If Heyward’s contract was structured so that his first year was set at $20 million, the Jays would enter 2016 with about $13-$14 million left in the budget for any additional moves. It would also shore up right field a year before it’s an issue while upgrading the bullpen and perhaps leading the way for Sanchez or Ozuna to enter the rotation for 2017. The point is Toronto has money coming available next year but in order to get the player that best fits their future needs, they might have to make a move now instead of waiting till next year.

The next team I thought might make sense as a trade partner was the Chicago White Sox, who recently released long time SS, Alexi Ramirez. The White Sox had a budget of $118,860,487 in 2015 and were supposed to be contenders with the additions of Melky Cabrera, Jeff Samardzija, David Robertson and Adam LaRoche but instead fell way short and put together an all-around forgettable season. With the release of Ramirez, shortstop seems to be an area of need for Chicago, and Tulowitzki with Abreu, Cabrera and LaRoche would be a great fit on the south side.

Unlike the Diamondbacks however the White Sox don’t have as much potential new money available, so off-setting the cost of Tulo’s contract would have to be taken into account when thinking about a trade. Someone like Zach Duke, who is owed $5,000,000 over the next two years might be a good addition to the Toronto bullpen. If the Sox would somehow include often-injured Avisail Garcia, this trade might really swing in Toronto’s favor but really saving money for a Heyward run would be more important then any name on the back of a jersey.

For argument’s sake I’m going to use the Duke/Garcia for Tulowitzki trade as an example. The difference in salaries would be about $12.7 million and that added to the $15,493,334 left over after the Teheran trade, Toronto would have about $28,193,334 left over to make Heyward an offer. And again, if the contract was structured so that the first year paid Heyward $20 million, the Blue Jays would have about $8 million left over for additional offseason/mid-season upgrades.

The last team that I thought would make sense for a potential Tulo trade was a team that was linked to him while he was still in Colorado, the New York Mets. Coming off a spectacular run to the World Series, the Mets are set to lose Yoenis Cespedes and Daniel Murphy to free agency. In 2015 they had a payroll of $120,415,688 and Cespedes and Murphy combined for $11,729,508 of that total budget, over half of what Tulowitzki is owed going into 2016. For the Mets, their quality rotation is under team control or earlier arbititration for the next few years, so continuing the winning environment at a fraction of the cost is of utmost importance. The health of David Wright is suspect and with a nice young group in Conforto, d’Arnaud, Duda, and Lagares, trading for someone of Tulo’s caliber might help their development and continue the winning environment.

The Mets would be in the same situation that the White Sox are — they can’t add too much salary, so off-setting costs would play into the equation. If the Mets traded Jonathan Niese, who’s owed about $9 million in 2016, and Kirk Nieuwenhuis, they’d clear about $10,688,729. Add that with the money saved from letting Murphy and Cespedes walk and they could easily bring in Tulowitzki’s contract. The Blue Jays would have about $26 million to work with and again, if Heyward’s first year was set at $20 million, they’d have about $6,182,063 to work with for offseason/mid-season upgrades.

All of this is unauthorized speculation but I do think that the Blue Jays are in a unique situation where they can really make some moves that could set them up for years of success. Chasing the big-name starting pitchers may seem like the obvious move but taking advantage of other team’s situations could allow them to acquire elite talent for minimal cost and the money saved on starting pitching could be used to solve future needs that aren’t quite here yet. As always, thanks for reading and let me know what you think.

Brandon Crawford is coming off an All-Star season in which he not only won his first Gold Glove, but his first Silver Slugger as well. The last to win both awards in San Francisco? Barry Bonds in 1997. Although Crawford may not have all the tools that Bonds did, he has come a long way since he made his debut at shortstop for the Giants in May of 2011. Crawford entered the league projected as a shortstop with plus defense, but also as an offensive project. So what sparked him to have the second-most home runs (21) among all shortstops, more than his totals from 2013 and 2014 combined, and a SLG% of .462 that led the all other qualified shortstops in the league by more than 20 points? An aggressive approach at the plate paired with slight mechanical adjustments. Consider Crawford’s Z-Swing%:

Now consider his hard-hit%:

These graphs, courtesy of data from FanGraphs, tell an interesting story. For the first four years of his career, Crawford’s Z-Swing% and hard-hit% had a direct correlation. In the first two years of his career, Crawford had a Z-Swing% that was barely above average in the league and a hard-hit% that was below average. Last year, however, his Z-Swing% skyrocketed to more than 8% above league average and he had a hard-hit% that was, for the first time in his career, above average. Yet, there is something odd about his recent success at the plate.

Crawford was not making more contact than in the past; he had just improved on the quality of contact with his new swing and more aggressive approach. Last year, he posted the 16th-worst SwStr% (percentage of swings and misses) in the league at 13.6% and a below-average 73.6% Contact%. Crawford also showed more aggression on pitches outside the zone, posting an O-Swing% (percentage of swings on pitches outside the zone) of 35.2% which is also worse than the league average of 31.8%. All of these were the worst numbers in their respective categories for his young career.

Despite all of this, his aggression at the plate and his change in mechanics led him to become a top power hitter at his position last year and a legitimate threat in the second half of the Giants batting order. Although the trend in these numbers may be hard to fully validate due to the small sample size, the new-found pop in the bat could make Crawford a much more valuable player (as finding power among shortstops in today’s league is a rarity). If his Z-Swing% and hard-hit% continue to be linearly related, Crawford may very well continue his progress in 2016 and bring power to a Giants lineup that was fourth to last in total home runs last season. One thing is for certain: his flow will remain among the game’s elite.

(pearlswithplaid, pearlswithplaid.blogspot.com)

In my first article for FanGraphs Community, I noted, in the summer of 2014, that batters were being hit by pitches at a near-record pace. Here is a graph showing the number of plate appearances per hit batter, from 1901 to present. I’ve reversed the scale—fewer plate appearances between HBP mean that batters are getting hit more frequently—in order to illustrate the steady climb from the World War II years to today. While the hit batter rate has flattened out since 2001 (the high point on the chart), the rate in 2015, a hit batter in every 115 plate appearances, is the 14^th highest in major league history.

After I cast about for an explanation for the rise, a commenter came up with what I believe is the best explanation: strikeouts (or, as the Cistulli-designated viscount of the internet, Rob Neyer, has dubbed it, the strikeout scourge). Or, more specifically, the increase in pitchers’ counts vs. hitters’ counts during at bats. When the pitcher is ahead in the count, he is more likely to target the margins of the strike zone, either to try to get the batter to chase or to set up the batter for the next pitch. When the batter’s ahead, the pitcher doesn’t have that luxury, and must focus more on pitching in the zone for fear of losing the batter to a walk. When a pitcher’s aiming for the inside edge of the zone and misses inside, the batter can get hit.

For example, here are career zone breakdowns for Chris Sale (who was a co-leader in hit batters in 2015) against right-handed hitters. At left is his location on 0-1, 0-2, and 1-2 counts. The chart at right shows 1-0, 2-0, 3-0, 2-1, 3-1, and 3-2 counts. The charts are from the catcher’s point of view, so the left side represents inside pitches. When Sale’s ahead in the count, 38% of his pitches are in the five leftmost zones. When he’s behind, that proportion drops to 31%. That’s typical. (What’s not typical is that Sale is ahead in the count a lot more than he’s behind, but you probably already knew that. Images from Baseball Savant.)

              Ahead in the count                          Behind in the count

This dynamic was clearly evident in the past season. When looking at plate appearances that ended when the pitcher was ahead in the count, batters were hit once in every 90 plate appearances. In plate appearances that ended with the batter ahead in the count, batters were hit once in every 254 plate appearances. Batters were nearly three times as likely to be hit by the pitch when they were behind in the count.

This raises a question: what other outcomes are affected by the count? We know that batters don’t do as well in general when the pitcher’s ahead. Are there outcomes other than batting average and slugging percentage that are affected by pitcher’s count?

Before answering that, I wanted to verify that pitchers are, in fact, increasingly ahead in the count. With rising strikeout rates and falling walk rates, this would seem to be tautological, but I checked anyway. I looked at the counts on which plate appearances ended for every year from 2001 to 2015. For example, in 2015, there were 183,628 plate appearances in the majors. 60,513 ended with the batter ahead (1-0, 2-0, 3-0, 2-1, 3-1, 3-2), 62,0553 ended with the count even (0-0, 1-1, 2-2), and 61,062 ended with the pitcher ahead (0-1, 0-2, 1-2). Here’s how they’ve tracked:

I didn’t go back further than 2001, but that’s not because I was being selective; it’s because the data from 2001 forward tells the story. Prior to 2001 the trends simply continued. In 2000, batters were ahead in 38% of plate appearances and pitchers in 28%, compared to 35% and 30% in 2001. The advantage to pitchers has fairly steadily expanded. I think we can say with some confidence that the past two seasons are the first two in modern baseball history in which more plate appearances ended with the batter behind than with the batter ahead.

So, having established that there are indeed more pitchers’ counts, what events are most affected by this change? To find out, I calculated the frequency of outcomes in 2015 on plate appearances with the batter ahead compared to plate appearances with the pitcher ahead. For example, in the 60,513 plate appearances that ended with the batter ahead, there were 13,501 hits. That works out to 4.5 plate appearances per hit. In the 61,062 plate appearances that ended with the pitcher ahead, there were 12,311 hits, or 5.0 plate appearances per hit. The p value for those two proportions, given the sample sizes, is 0. In other words, the difference is statistically significant, and we can safely say there is a difference in hit frequency when ahead in the count compared to behind in the count.

Here’s the full list:

According to this analysis, when the pitcher’s ahead in the count, it results in a decrease in hits, doubles, triples, home runs, and sacrifice flies. When the pitcher’s ahead, it results in an increase in stolen-base success rate, hit batters, sacrifices, and wild pitches. Those mostly make intuitive sense: when the pitcher’s ahead, the batter’s more cautious with his swings, resulting in fewer hits and less power. Similarly, when the pitcher’s ahead, he’ll work away from the heart of the plate, and misses become wild pitches and hit batters. By contrast, when the pitcher’s behind, he works closer in to the strike zone, resulting in pitches that are easier for the catcher to handle, lowering his pop time and increasing the chance of catching the runner on a steal attempt. (Max Weinstein illustrated last year that caught stealings are more likely on pitches in the strike zone.) The increase in sacrifices seems non-intuitive, since 0-2 and 1-2 counts usually shoo away the bunt due to the risk of a strikeout on a foul ball, but 0-1 counts make up for it. Batters were more likely to successfully sacrifice on 0-1 counts (1.4% of 0-1 plate appearances) than any count other than 0-0 (2.7%) in 2015.

Given that pitchers’ counts have increased and hitters’ counts have decreased, this model would predict changes in outcomes for which the differences are statistically significant. I looked at the frequency of hit batters, sacrifice flies, and wild pitches, along with the stolen base success rate, for 1979-1981 (the recent low-water mark for strikeout rate) and 2013-15. I excluded sacrifices because they’re both down sharply due to strategic reasons (managers are calling for fewer bunts) more than anything else. They results are consistent with the model.

• Strikeouts per plate appearance: up 61%
• Hit batters per plate appearance: up 98%
• Sacrifice flies per plate appearance: Down 16%
• Wild pitches per plate appearance: up 39%
• Stolen-base success rate: up 7% (though that increase, from 66% to 73%, is probably largely strategic, since there are were 54% fewer stolen base attempts per plate appearance in 2013-15 than 1979-81, even though that may not make sense)

The graphs below, while admittedly busy, track the offensive events for which the analysis of 2015 count-related data indicated statistical significance (again, excluding sacrifices). I’ve selected the past 30 seasons. First, the affected base hits (total hits, doubles, triples and homers):

Offense rose through the 1990s despite rising strikeouts but has fallen since.

Now, the less intuitive outcomes of hit batters, wild pitches, sacrifice flies, and stolen-base success:

As the 2015 count data suggest, increased strikeouts, and therefore increased pitchers’ counts, has yielded more wild pitches, fewer sacrifice flies, a higher stolen-base success rate (though, again, that’s probably a reflection more of strategy), and, most significantly, way more hit batters (73% higher than in 1986; I truncated the scale in order to make the rest of the graph more readable).

This isn’t to suggest that these changes are solely a result of pitchers getting ahead in the count more frequently, but it does seem to be a contributing factor. Admittedly, much of the fallout from the rise in strikeouts is pretty unremarkable. There are more strikeouts and fewer walks now than in the past, so the pitcher’s ahead in the count more and the batter’s ahead in the count less; that’s unremarkable. That’s resulted in less offense — specifically, fewer hits overall and fewer extra-base hits; that’s also unremarkable. What I find more interesting are the other trends trends unrelated to strategy: the increase in hit batters and wild pitches and the decrease in sacrifice flies. It’s easy to get upset about batters getting hit by pitches, pitches rolling to the backstop, and difficulties in driving in runners from third with fewer than two outs. What’s less apparent is the degree to which those events can be linked, like lower scoring, to the rise in strikeouts.