Mark Trumbo is Not the Ideal Orioles Leadoff Hitter - Chris Davis Is

This post runs as a follow-up to Jon Shepherd's lineup optimization proof of concept.

Buck Showalter tinkers with lineups, but he'll never be able to try out every combination. Lineups can be considered permutations of the roster - combinations in which order is relevant, such that the same nine players can be ordered differently for a new lineup. The total number of distinct permutations of nine players on a 25-man roster is given by the following equation:

9! / (25-9)! = 741,354,768,000

Given the possibility of trades and acquisitions, not to mention the Orioles' penchant for shuttling players between the Majors and the Minors, the true number of possible lineups over the course of a season is even higher. Given only 9 batters, as Jon Shepherd worked with in his proof of concept research, the number of lineup permutations drops to a much more manageable 362,880 distinct possibilities. No amount of lineup tinkering will allow Showalter to test each of these lineups; he would need 2,240 seasons of 162 games to see them all take the field, and I doubt Manny Machado will even be an Oriole after all that time.

As a fan enabled with myriad tools for lineup optimization (and Jon's algorithm that explains the variance run production quite nicely), I sought to find the best Orioles lineup given those same nine batters that we can reasonably expect to feature as starters at least very frequently in 2017. I sifted through all 362,880 possibilities thanks to the built-in permutation generator in Python, ran each through Jon's algorithm, and recorded the results.

Because I considered all possible lineups, I had no need to establish a set of assumptions that would guide me. I don't need to start with Chris Davis batting fourth because of his skillset. I expected to see a sort of cycle in the most productive lineups, resembling something like 3-batter groups that end with a power hitter. This follows Jon's suggestion that a batter's ability to produce runs is predicated largely on whether the batters before him can reach base. I did not expect to see a prototypical leadoff hitter batting first, because innings rarely end so tidily as to allow the following inning to start over at the top of the lineup. More often the man leading off an inning will not be the leadoff hitter, and in my eyes, this indicates that the importance of a "true leadoff hitter" is vastly overstated (the importance of a player with true on base skills is not).

The most productive lineup suggested by this exercise is the following:
1B Chris Davis
LF Hyun-soo Kim
2B Jonathan Schoop
DH Mark Trumbo
3B Manny Machado
RF Seth Smith
CF Adam Jones
C Welington Castillo
SS J.J. Hardy

This lineup is worth an estimated 885 runs over the course of 162 games, not accounting for handedness splits. That would be 141 runs more than the Orioles scored in 2016, and 50 runs more than the Mark Trumbo-led lineup that Jon suggested last week. In fact, Davis was the leadoff hitter in four of the 10 most productive lineup permutations. Perhaps Trumbo is not the ideal leadoff hitter after all, but Davis, his left-handed counterpart with a similar batter profile, is!

This lineup is worth 287 runs more than the worst lineup combination possible from these nine players, a Machado-led abomination that slotted Trumbo, Adam Jones, and Davis as the 6, 8, and 9 hitters, respectively. Such a batting order would fly in the face of traditional lineup construction as well as this new machine-led practice.

More importantly, if we assume that last year's run prevention is indicative of this year's run prevention, we can estimate how well the best and worst lineups would perform according to pythagorean win-loss. Again, assuming that the 715 runs scored against the Orioles in 2016 carries over and would be identical in 2017 (unlikely, and a tenuous assumption at best), the pythagorean win-loss record would estimate the following results for the best and worst lineup permutations:

Projected Runs Scored, 2017	Runs Against, 2016	Pythagorean Win %	Pythagorean W-L
885	715	59.6%	96-66
598	715	41.2%	68-94

By this estimate, the best possible lineup is worth 28 wins. This matches up with the rule of thumb that 10 runs is equivalent to one win. The best possible lineup, with a projected 885 runs, is expected to score 100 runs more, or 10 wins better, than the traditional lineup put forth in Jon's article.

If this exercise is to be considered accurate, then lineup optimization is critical to a team's success. It boggles the mind that the more analytical front office and managerial combinations haven't considered context-dependent lineup optimization if they are believed to be the difference between a team fighting for a playoff spot and one of the best teams in the league with minimal tinkering.

I end with the same question Jon posited: have teams neglected the importance of lineup optimization because of some normalized tools and broad rules of thumb?

I choose to believe that there are human factors pushing teams away from this sort of radical overhaul, specifically that players wouldn't like it. As antiquated as they are, RBIs and lineup position seem to be points of pride for many players, and it's not a stretch to think that a prototypical leadoff hitter can market himself as such and earn a higher payday than he would if the skillset asked of the first lineup spot was fungible. Making players uncomfortable likely has real effects, even if there's no technical reason why batting seventh should be any different than batting second. It may also drive free agents to consider other teams that won't torpedo their ability to market themselves, or toss their routine into a blender every time someone new joined the team.

Further, many fans and owners would likely be too quick to call an experimental lineup a failure. One bad game out of batters would be enough to lampoon the manager who organized it, and persistence in the face of a handful of failures would probably lead to the manger's and/or GM's ousting. In terms of self-preservation for a manager or GM, it makes far more sense to leave those wins on the table and use the standard, sub-optimal batting order formula that every other team uses. It's similar logic to why NFL coaches kick field goals and PATs more often than they should, when going for a first down or two-point conversion improves win expectancy: it's safer to lose doing what's accepted than to lose doing something radical, even if the radical idea made the loss less likely.

There may also be a technical limitations to this process that has prevented teams from truly optimizing lineups. It took nearly three days to run all 362,880 batting order permutations through Jon's algorithm, and that was only with 9 batters. All possible lineup permutations given the full 25-man roster caused a memory error on my computer. I can't imagine trying to expand this algorithm to consider the 40-man roster, which would hold over 99 trillion permutations. Doing this on a regular basis for each team would take more than just modeling and coding knowledge; it would require a deep understanding of how to efficiently manage physical storage, and likely a huge amount of it at that.

However, the benefits that can come from analyzing the order of just the nine batters the team expects to play most often seems to have some benefit that doesn't require a supercomputer or a superanalyst. I then return to the thought that maybe shaking up the lineup may be akin to shaking a hornet's nest, both in terms of upsetting players and risking careers.

Forecasting Single-Game Attendance

I've explained before how season-long attendance can be forecast with a handful of different variables, all of which relate to the quality of the team. Since the team is the on-field product that fans buy when they attend games, it makes sense that team quality drives attendance. Sure, games are a form of entertainment, but as many Orioles fans can attest, it's a lot more fun to watch a winner.

To continue this practice of forecasting attendance, I decided to take a look at what factors influence single-game attendance at Camden Yards. Perhaps this work would qualify Camden Depot to help the Orioles plan promotional night or concession inventory (always buy 1 extra bobblehead for me, Orioles)!

The features I decided to build my regression on were pretty straightforward:

• Day of week
• Month of year
• Year
• Opening Day
• Day/night game
• Game-time temperature
• Weather condition (rain, sun, overcast, drizzle, or dome)
• Winning percentage (or pythagorean winning percentage)
• Runs per game, for and against
• Current streak type (has the team won or lost the last few games they've played?)
• Games back in the division
• Opponent
• Promotional night
• Kids' promotional night
• Size of promotion/number of items given away
• Family night/field trip days (kids run the bases, etc.)
• Fireworks night
• Gender-specific promotional night (Mother's and Father's Day, specifically)

These are all pretty top-line features. They're generally pretty available (old promo night details are hard to find), nothing is super-SABR, and it makes sense that any of them might affect attendance.

I ended up dropping day/night game, runs for/against, family nights, fireworks nights, and gender-specific promotional giveaways because they all tended to be on Fridays, Saturdays, and Sundays, which introduces some complications because day of week was already included. I also dropped the year from the analysis because I was concerned that it was too similar to winning percentage.

I chose to use a lasso regression model, because it (in summary) zeroes out coefficients that aren't actually significant to attendance. And interestingly, a lot of coefficients were zeroed out: most teams, some months, some weather conditions - and winning percentage. The final list of included and meaningful coefficients is shown here:

As you can see, this is a much shorter list than we started out with! I want to call out the teams that affect attendance at Camden Yards when they come to town:

Within the AL East, the Yankees and the Red Sox cause attendance to spike, while the Rays drive attendance down. That makes sense with our understanding of fan tendencies: Rays fans don't go to games anywhere, much less hundreds of miles from home, and Yankees and Rays fans are both everywhere and willing to travel to see their teams at Camden Yards. Being the Orioles' primary rivals, I'm sure their presence makes O's fans want to show up as well.

Other nearby teams, the Phillies and the Nationals, also drive attendance up. The Nationals' annual visit to Baltimore is the largest single-game attendance boost from a team.

The White Sox probably don't really drive people away from the ballpark. They simply have the misfortune of being the team that was in town following the unrest in Baltimore City and, as a result, the team that played the Orioles in front of an empty stadium.

The most surprising thing for me was the effect. or lack thereof, of playing winning baseball on attendance. While a good team draws more fans throughout the year, it seems that fans are drawn to the ballpark day to day for how well it works with their social schedule. Weekends are popular draws, as are the summer months, and people show up for promotions and family nights. Interestingly, attendance also decreases as temperature rises (I suspect that that function is parabolic, with a nice warm day drawing more fans than either a cold one or a very hot one). But how good the Orioles are seems less important than how convenient it is to attend a game.

To be fair, this regression uses data from 2012 to 2015, years in which the Orioles were generally pretty good. Winning percentage, or pythagorean winning percentage, might be a stronger predictor of attendance if some of the more turbulent years were included as well. So how well does it work?

It does a decent job, but we're within, usually, 10,000 attendees one way or the other. Not terrible, but considering that some games have as few as 15,000 attendees, this might not be the model to base inventory plans on. This regression has an R^2 of 0.635, indicating that this model describes 63.5% of the variation in single-game attendance. Another limitation, as far as long-term inventory planning goes, is that this model uses weather as a predictor of attendance - which it most certainly is! Walk-up ticket sales spike when it's nice out, but the weather probably isn't something concessions stands would know far enough in advance to use to their advantage.

BORT: Brian Matusz And A Lost Pick

In March of 2009, the local Orioles blogosphere was in its primordial golden epoch where sites were plentiful and largely operated by only a person or two.  Back then, I developed the Baltimore Orioles Round Table to make the community more cohesive and increase audience awareness for other sites.  Now, the lone person writing for an Orioles site is not so common anymore.  We all have large stables.  In this current incarnation,  the objective is not to increase awareness between sites, but to provide multiple slants at a single issue.  Enjoy!

The Brian Matusz trade and Dan Duquette's willingness to deal draft picks.
Participants: Elie Waitzer, Patrick Dougherty, Avi Miller

Elie Waitzer: The Orioles got two Minor League arms - Brandon Barker and Trevor Belicek - from the Braves in exchange for Brian Matusz, but the real swap had nothing to do with any of those players. Atlanta immediately DFA'd Matusz, and the neither of the arms were thought of as prospects. If you want to read about how Barker and Belicek might pan out, Chris Mitchell did a good write up on Fangraphs.

Broken down into simple terms, this was a creative win-now/win-later trade between Dan Duquette and Braves GM John Coppolella. Baltimore got present-day financial flexibility by offloading the remaining $3M of Matusz contract. Atlanta got future financial flexibility in the form of an additional $830K in bonus pool allocation that comes with the 76th draft pick that will allow the Braves to be more aggressive in the draft.

This is clearly not a stand-alone trade, and it's how Duquette springboards off of this move that will determine whether it was worth it for the Orioles to reduce their ability to potentially grab better talent in mid-late rounds of the drafts (with the 27th, 54th, and 69th picks.) 

The best case scenario is that the $3M in savings will give Duquette some extra wiggle room at the trade deadline to make the O's a more attractive trading partner for teams looking to deal starting pitching. The ability to take on more of a player's contract gives Baltimore an edge over other teams, and makes up in part for the fact that they won't be able to offer the kind of prospects other teams will (Keith Law ranked the O's farm system 27th at the start of 2016). 

Before the start of the season, Matt Kremnitzer looked at the best and worst cases for the rotation and set a pessimistic tone by referencing Fangraphs' dismal projections for the O's starters. Despite their collective 3.80 ERA, the ragtag starting staff has vastly outperformed expectations, ranking ninth in the league by total WAR (3.9) thus far. But the pleasant start has been fueled largely by strong starts from Chris Tillman and Kevin Gausman, not by solid depth 1 through 5.  If this move leads (or partially leads) to the O's landing rotation help in the form of James Shields, Rich Hill, Jimmy Nelson, or any solid arm that can take innings away from Mike Wright and Tyler Wilson, I'll consider it a win. Until then, the jury is out. 

Patrick Dougherty: They say to trust your gut, and with a few days to think on this deal, I feel the same way I did when my phone buzzed with the notification. Brian Matusz has been a non-factor for the Orioles for years, and taking his $3.9 million salary (or the $3M of it that the Braves will assume) off the books is, in a vacuum, a win. I thought the Orioles were overpaying for Matusz when they made the one-year deal to avoid arbitration because I didn't think of him as anything more than a mediocre LOOGY (lefties have hit him for a .276 average in his career, although Matusz has successfully stayed away from giving lefties walks or home runs). Apparently, the team thought Matusz could work his way into a less specialized bullpen role, or at least into a decent return in a trade. Clearly, he could not.

The minor good of ridding the team of a player who directly affects about 3% of the Orioles' innings in a year (50 IP/1,458 innings in 162 9-inning games) is vastly outweighed by the bad of giving up the 76th pick in next year's draft. The stars-and-scrubs method of roster construction is highly variant and, in my opinion, a mistake to pursue. Particularly for a team that is in one of the smallest markets in the league and likes to paint itself as being cash-strapped, the best way to build a competitive roster is through drafting and developing well. The Orioles do neither.

In some cases, I may be tempted to argue that because the Orioles have proven themselves to be largely incapable of drafting and developing players, particularly pitchers, it makes sense for the team to ditch picks in favor of cash with which to bring in arms that have learned the game elsewhere. That specialization of labor model might be attractive if the Orioles sat atop a pile of cash the way the Yankees or the Dodgers do, but I'm tired of making the argument in favor of giving up on what is the Orioles' most obvious path for continued, cheap success.

Instead, I'll go in the opposite direction. Because the Orioles are ineffective drafters, they should be taking a shotgun approach: take the best players available as often as possible and pray that one of them becomes the exception to the organization's deflating rule.

If I sound fed up, I am. During the offseason, the Warehouse talks about the importance of draft picks and why the team just can't give them up to sign premiere free agents who were extended qualifying offers. This Matusz trade marks the second time in two years that the organization has given away a pick to dump the relatively meager salary of an average reliever (not to mention the pick given up for Bud Norris and the many international signing slots the team has traded away in recent years).

The Matusz trade is, in my opinion, a failure both in terms of the potential that the team jettisoned by trading away a competitive balance pick, and in terms of continuing the Orioles' precedent of undervaluing draft picks. I don't believe $3 million in wiggle room is going to allow the team to bring in a stud pitcher at the deadline; they cost a lot more than that, and the budget is already stretched, as far as anyone outside the Warehouse knows. I do believe that the team consistently undervalues draft picks - or realizes that they're so bad with them that they're using them as currency because they've given up.

Avi Miller: So why exactly did the Orioles even tender Matusz heading into 2016? Complaints abound among the Baltimore fan base, Dan Duquette knew very well that Matusz would command a fourth-year arbitration salary above $3.2 million, his 2015 earnings.

Matusz, despite popular belief, could have been a very serviceable middle relief arm in 2015. Though his career average against when facing left-handed hitters is .276, as Patrick noted, I redirect your attention to his 2015 showing against that same group: .185/.231/.333 across 109 batters faced.

Thus, as a LOOGY, Matusz slotted in quite nicely. Even when he took the mound against almost the equivalent number of batters in the right-handed batter's box, the results were not dreadful: .238/.375/.346 across 97 batters faced (16 walks killed him against this group).

So a salary expectation in the mid-$3 million range for a left-hander after a 49-inning season to the tune of a 2.94 ERA wasn't absurd, to say the least. And here's why.

Name	Games	Innings Pitched	ERA	FIP	xFIP	fWAR	K/9	BB/9	HR/9	BABIP	GB%
Brian Matusz	186	151.2	3.32	3.50	3.87	1.8	9.44	3.15	0.89	.289	36.4%
Tony Sipp	172	142.2	3.22	3.45	3.63	1.7	10.54	3.41	1.01	.253	32.6%
Zach Duke	171	150.2	3.58	3.57	3.16	1.1	9.44	3.52	0.90	.301	55.9%

The table above compares Matusz to two other notable lefty relievers, Tony Sipp and Zach Duke. The numbers shown are from the 2013-2015 seasons.

Tony Sipp, a veteran who had a choppy history with both Cleveland and Arizona before settling in Houston a couple years ago, signed a three-year, $18 million contract to return to the Astros prior to the 2016 campaign.

Zach Duke, taking an even bumpier road starting in Pittsburgh back in 2005, earned a three-year, $15 million contract with the White Sox two offseasons ago.

As such, Brian Matusz was on his way to a nice little payday following the 2016 season. How he gets there now is a bit more in question.

Do Childhood Memories Affect Attendance?

Not long ago, I found myself late to a discussion about whether a person's favorite team being good when they were a kid makes them more likely to be a fan as an adult. The natural corollary would be that kids growing up around a bad team would be less engaged with the team later in life. This clearly isn't the case, as the Cleveland Browns continue to play in front of dozens of people (shots fired). 

But whether people have childhood memories of joyful success or soul-crushing sadness of their favorite team may affect how big of a fan they are - their magnitude of fandom, so to speak. By treating attendance as a proxy for magnitude of fandom in a region, I was able to measure whether childhood memories, good or bad, have an affect on adults.

I expanded a (pretty good!) season-long attendance regression I built while writing for BSL to include combinations of new parameters that measure extreme seasons 20 years in the past. To make sure I captured a chunk of a fan's formative years, I used a range of 5 years around the season 20 years ago. Parameters for predicting attendance in the 2014 season would be 1992-1996, for example. The parameters listed below were selected as examples of extreme seasons, both successful and not:

• >= 100 wins
• playoff berth
• World Series berth
• <= 65 wins
• division cellar

I built multiple regressions with varying combinations of these parameters, which all seemed to predict attendance pretty well. The chart below shows the ability of each regression, categorized by parameters used, to forecast attendance:

...but there's a real issue with the inclusion of these parameters. While the scores look great and the extreme memories may make sense to some, the coefficients were generally opposite of what would be expected. For instance, if you were to believe that a childhood World Series berth makes people more likely to be fans, you would expect it to carry a positive coefficient. That would indicate that it is a positive event that drives attendance among adults. The regression that included parameters for childhood World Series and cellar-dwelling memories that has an R^2 value of nearly 0.98 assigns the following coefficients (shown in green against the blue "no memory" control regression) to its parameters:

These coefficients are entirely out of sync with our expectations; they suggest that teams winning the pennant or even making the playoffs as a wildcard that year are pushing fans away, and memories of a World Series berth make people incredibly unlikely to go to games as an adult. It doesn't matter what its alleged predicted value is. This model is not grounded in any reasonable hypothesis and it's overfit to the data added to it.

The only regression that appeared to have any semblance of modeling reality is one that only includes memories of the team in the cellar:

See the smaller coefficients in this zoomed-in version

No coefficients radically changed direction, although it appears additional emphasis is placed on rostering a All Star starter and winning a wild card at the expense of winning a pennant. And it seems to predict that high beer and hot dog prices attract more fans. At least memories of being in the cellar pushes people away from attending.

I tend to favor the original model that doesn't include extreme memories, in particular because I don't believe very young fans know the difference between their team being in 4th or 5th in their division. In fact, I don't think very young fans care very much about the on-field product, and are more likely to harbor positive memories of spending time with their family at the ballpark. Those memories are far more likely to make adults want to return the favor with their own kids.

And anyway, as always, the most important coefficient is how well the team is doing in that season. It makes sense. It's not hard to tell over 162 games whether a team is good, and fans want to see an exciting team that gives them a good chance to go home happy.

In other words, you're all bandwagoners.

Blueprint For The 2016 Orioles (Option 4): Well-Rounded And Not Tied Down

If the 2015 season proved anything to me, it's that the Orioles' biggest issues are and always have been on the mound and not at the plate. The 2015 squad, despite losing eventual 44-home-run-hitter Nelson Cruz to the Mariners in free agency, hit 217 home runs and pushed 713 runs across the plate. That's the second-highest home run total in franchise history, behind only the 1996 squad, and more runs than in 2012 or 2014, both playoff seasons.

I'm not equating postseason berth or success with pitching success specifically. A baseball team can win games many different ways. However, the Orioles' pitchers are, at this point, too mediocre to be relied on if the team expects to contend. I would love to focus an offseason plan on adding arms, but this season's free agent market for pitchers is incredibly top-heavy, and I don't expect the Orioles to be players for the available aces. As a result, my offseason plan focuses on mild improvements to multiple positions instead of making a splash at one. Meanwhile, the Orioles can use the opportunity to make a low-risk/high-reward play on free agents looking to prove their worth and give extended innings to young pitchers and let them learn on the job.

Qualifying Offers

But first, the qualifying offers. Extending a QO to Chris Davis and Wei-Yin Chen are no-brainers. They will be denied, and the Orioles will in return receive draft pick compensation for their loss. Matt Wieters is a much tougher nut to crack. 2016 will be Wieters' age-30 season, and a good year could set him up for a longer-term paycheck to close out his productive years as a catcher. He may treat a QO as a high-paying one-year deal to establish value for a good contract in his age 31 to 34 seasons. At the same time, injury concerns and declining catcher productivity with age may be enough of an incentive for Wieters to agree to a longer-term deal for more moderate, but guaranteed, income.

To be worth (in terms of free market price of a win) the $15.8 million deal a QO represents, Wieters would need to be worth 2.25 wins. That's a good goal for Wieters, and attainable given a full season of health, but is also close to what Caleb Joseph offers for a lot less money (he's first arbitration eligible in 2018). I wouldn't offer Wieters the QO despite the boss' insistence because I'd rather use $16 million on an area of weakness than to place a bet on getting a compensatory pick.

Not offering a QO on Wieters is foolish. Just like not offering one on Markakis last year. At most, you spend 4 MM on B level prospect.

— Camden Depot (@CamdenDepot) October 6, 2015

Non-Tenders

Based on MLB Trade Rumor projected arbitration salaries, I suggest non-tendering Brian Matusz. He has not proven himself to be worth $3.4 million in a bullpen role that nearly any minimum-salary left-hander could do. I would also non-tender Paul Janish and Nolan Reimold. The former isn't anything you can't find for league minimum or in the minors, and the latter is too old and too often injured to be considered a possible option off the bench.

I suggest keeping Miguel Gonzalez through arbitration. His projected $4.9M in arbitration is a little steep to stash in the bullpen, but he could be a serviceable spot starter in case of injury, a decent back-end rotation option if he comes back from injury, or

Free Agents

Doug Fister is looking for a change of scenery and hopefully a return to the rotation, and Baltimore is just the place to make that happen. The Nationals reportedly don't think that Fister is worth a QO. After a pretty terrible 2015 in which he played for just $11.4M, perhaps the Orioles can offer a 1-year, $10M "prove it" deal to the now-31-year-old right hander. A dominant pitcher when healthy, Fister lost a lot of time to the DL during his stint with the Nationals. Even if Fister can't hack it in the rotation, the Orioles are adding a great (but expensive) arm to the back of their bullpen and potentially setting themselves up with trade bait at the deadline. This would just force Bundy (who I will touch on later) into the rotation earlier, or force the Orioles to lean on a rotation of internal options.

Mike Napoli will be brought in on a one-year, $5.25M deal. Like Nate said, he can be easily replaced with Christian Walker should he struggle in Baltimore. Even if he's not fit to play first, Napoli can moved to a DH platoon to swat lefties so that his paychecks don't go to complete waste.

Adding Denard Span on the 3-year, $36M proposed by Ryan R. sounds like a great idea. Span brings defense to left field, can play center when Jones is in the lineup as the DH, and can actually hit for a decent average. The hip injury only brings down Span's price, helping the Orioles off the field as much on it.

As Nate noted, Bundy has to be on the Major League roster or be placed on waivers, so he's in the bullpen at the very least.

To fill the hole in right field, bring Gerardo Parra back on a 3-year, $22M deal and look to give him frequent breaks against lefties. When he hits the bench, Steve Pearce will take over on a 1-year, $3M offer. Pearce can also fill in at DH or first if needed as the batters in those roles don't make the cut.

Filling out the bullpen with league-minimum arms shouldn't be too hard. Playing the options ams here allows Buck Showalter and Dan Duquette to see who sticks and maybe squeeze a little extra juice out of a cheap contract via performance or midseason trade.

Summary of Major Moves

• Doug Fister (SP), 1/$10 million
• Mike Napoli (1B/DH), 1/$5.25M
• Denard Span (LF), 3/$36M
• Gerardo Parra (RF), 3/$22M
• Steve Pearce (RF/1B/DH), 1/$3M

Total 2016 payroll: $110M

That's enough wiggle room in the $120M max to play with in trades, taking riskier names on the bullpen market, or even getting a long-term deal with Manny Machado.
I like to think that this approach, while not particularly splashy, is a well-rounded and reasonable approach to patching many of the team's holes heading into 2016 while maintaining flexibility for the following years. Some of my contract estimates may be aggressively low, and the $10M wiggle in the budget allows them to go a little higher on someone like Span if necessary. I'd like to see them build in some reserve funds during the offseason to make a run at a player who falls into their lap, like Nelson Cruz did. And if nobody is there, bank it and look to improve at the deadline.

-----

Option 1: Seeking A Cornerstone
Option 2: Building A Rotation
Option 3: Building Major League Depth And A Minor League System
Option 4: Well Rounded And Not Tied Down 
Option 5: Purchasing Innings in Bulk
Option 6: Trying To Make Chicken Salad
Options 7a/b/c: Shepherd Seeks A Few Outside Consultants

How Horizontal Trajectory Affects BABIP

Batting average on balls in play has long been used as a yardstick for batters. Players whose BABIP is higher than the league average and their historic stats are said to be fortunate and likely to see a major drop in production when their luck runs out.

It occurred me that BABIP could be used as a defensive metric when Ben Lindbergh used it, calculated in groups by horizontal hit trajectory, to illustrate the improvement in the quality of Major League fielders over many decades. Considering an emphasis on defense (it’s said that it’s cheaper to prevent a run than to score one), the rise of the infield shift, and more athletic and able players, it’s certainly conceivable that defenses today are better than they were in the 1970s.

However, that’s not particularly useful for the task of roster construction today. Sure, Manny Machado may be a better third baseman than most of the professionals 50 years ago, but how much better than his active peers is he? And how much is he worth to the Orioles in run prevention and ultimately revenue generation (i.e., as the General Manager, how much I should pay him)?

To begin to answer these questions in a new way - good but volatile defensive metrics exist, remember - I sought to categorize balls in play by horizontal angle as Ben and partner Rob Arthur did, but also to build in the ability to separate fielding teams from one another. This would allow me to strip out BABIP against the Orioles (or any team) by horizontal angle - absolving Manny of balls hit to areas of the field that he isn’t responsible for, and better indicating which hits came in his domain - and compare it to other teams or the league generally. As such, we are able to see which teams are best at fielding in which locations around the diamond, and better ascribe that to specific players.

The wonderful and regularly-updated PITCHf/x database produced by Baseball Heat Maps was my primary source of information, as it included coordinates for the location of every ball in play since PITCHf/x was introduced in 2007. One thing to note - the coordinates are for where the ball was played by a fielder, not where the ball first hit the ground. A liner that hits the grass and reaches the outfield wall before being picked up in the warning track is shown as having a y-coordinate of the warning track, not of the grass. That’s a big issue if you’re measuring hit distances, but not so much if you’re measuring hit angle; rarely do balls take sharp turns in the field of play before being played.

The other critical source that needs recognition is this Hardball Times article by Peter Jensen from 2009. The PITCHf/x data contains no information to put hit coordinates into context, and the coordinates make little sense to someone used to the normal four-quadrant coordinate plane. Home runs typically have a y-coordinate of less than 20, while bunts have a y-coordinate of around 200. Peter Jensen answered a ton of questions by publishing his normalized estimates of home plate coordinates in each stadium, which allowed me to manipulate the data to orient the field of play in a way that made sense with a regular plane - and to calculate the horizontal angle of each ball in play.
If you visit that Hardball Times link, you’ll notice that the home plate coordinates were from 2008, before the Marlins, Yankees, and Mets began playing in their new stadiums. To avoid complicating things even further, I elected to use the 2008 context for all of the PITCHf/x information. The home plate in most stadiums is just about at the y-coordinate 200.0, so I can’t imagine the MLB Gameday scorekeepers would deviate much from that in three parks.

With all of this information (plus hits and outs) properly paired and grouped, we can see how well the Orioles do in the field against balls batted to different parts of the park:

They are, in this case, very much average. In fact, most teams are:

There just isn’t much variation in BABIP by hit angle across Major League Baseball, likely because certain balls in play are going to be hits nearlyall of the time. It doesn’t matter who’s on your team; a grounder to the shortstop is always going to be an out (or an error, which isn’t counted here), and a liner to shallow left center is always going to be out of reach of everyone running towards it.

Since Manny Machado’s call-up, we might expect to see the Orioles leading Major League Baseball in BABIP allowed by hit angle. He is, after all, one of the best fielding third basemen in baseball, with stellar range and a cannon for an arm - all while playing shortstop throughout the minors. Surely a player of Manny’s caliber in the field would hurt the ability of a batter to reach base safely if he were to put the ball into play, right?

Actually, Manny’s call up hasn’t materially affected the Orioles’ ability to prevent hits once the ball is in play.

To get a better sense of the Orioles’ ability to prevent hits when a ball in play might be expected to be played by their third baseman, I pared down the data to only include a hit distance inside or just out of the infield - ones that are played by the third baseman or by the outfielder rushing in to back up the third baseman once a ball gets through his area - and balls hit between -55 degrees (which is just foul) and -22.5 degrees (which is halfway between the foul line and second base). This seems like a good set of balls in play to assign as the responsibility of the third baseman. I included balls past -45 degrees because MLB’s data tracks where the ball is played, not where it lands, so a live ball that gets picked up in foul territory would be played at a less than -45 degree angle.

I calculated the league average BABIP using this set of data that could reasonably considered specific to third basemen, as well as the BABIP of each of the thirty teams in order to determine the standard deviation from that average. The data follows a roughly normal distribution, although Toronto is apparently so bad at third base as to be a significant outlier that made me think I had very heavy skewed data.

League average BABIP on balls to third base and in the infield is 0.117 - very low! Which is to be expected, given that those are balls played in the infield and therefore did not get past the third baseman. The Orioles, since Manny’s callup, have allowed a batting average of 0.122 on similar balls, or about 0.41 standard deviations above average. This is well within the range of possibilities via random chance, meaning that there might not be any cause for alarm regarding infield defense.

Rather, what this means to me is that the dazzling, rangy plays that it seems like Manny makes on a regular basis might not have a material affect on outcomes. Even though Manny can field a bunt on the grass and fire to first from an impossible angle to garner a putput, he doesn’t do so with enough regularity to dramatically affect the Orioles’ ability to suppress batting average on balls hit to him - and really, nobody in Major League Baseball does.

But wait - that was only on balls fielded in the infield. Perhaps Manny is unusually good at stopping balls hit towards him from reaching the outfield, and makes more outs on those than normal. In fact, the Orioles fare slightly worse in this category, with a BABIP allowed of 0.335, a full standard deviation above the league average of 0.322. Here, again, I have to consider the possibility that despite his incredible range, Manny doesn’t have supernatural talent at preventing an unusually high number of balls in play hit towards him from becoming hits.

There is one final way to slice the data that might shed a more optimistic light on Machado’s fielding. Since his callup on August 9, 2012, Manny has missed large chunks of time for two separate knee injuries. By limiting the sample further to include not only games since Manny’s callup but also only games in which Manny was an active player, we see exactly how his presence on the field has affected the Orioles’ defense. At the same time, this limits the sample size significantly, the information is far more prone to drastic swings, and our conclusions should be couched to recognize that our understanding of Manny’s defensive ability is still developing.

The first thing I notice is that the Orioles are about as adept at preventing balls in play from becoming hits with and without Machado on the field - and they’re about league average at it. Minor fluctuations visible in this chart are more than likely the result of small samples rather than Manny being better or worse than fielding balls in play than average.

Remember, this is not to say that Machado is somehow overrated or that we should reevaluate our understanding of defensive ability. Not one team was noticeably well above average in preventing hits on balls in play - but some were noticeably worse, particularly at first base. Manny’s greatness comes from many things, and although he can snag a hard grounder up the third base line arguably better than most players, those web gems are few and far between for a reason: they’re incredibly difficult plays to make. Turning them once in a while is awesome, and proves that the ability is there, but doesn’t materially affect how often a player who hits them gets on base against the Orioles. Some balls in play are just impossible to turn into outs.

* * *

In addition to slicing this data up by pitching team, it’s possible to examine in-play occurrences in each park. The results of doing so are expected to be pretty similar to splitting the data up by pitching team - after all, nobody plays at Camden Yards without the Orioles, so roughly half of the balls in play in Camden Yards occur with Adam Jones, Manny Machado, and J.J. Hardy on the field.

Where this is interesting is on the margins. All Major League infields are identical in shape and size, but outfield corners can be in any variety of shapes and any distance from home plate.

For instance, the right field corner in Fenway Park, where the outfield continues past the foul pole, seems to cause fielders some trouble. There’s even evidence that BABIP is unusually high when the ball is hit at a 20- to 30- degree angle, which for alignment is about where the second baseman would usually play. Whether that abnormality is due to liners over the second baseman’s head dropping in because the right fielder is in position to cover Pesky’s Pole, or due to teams rarely shifting at Fenway (doubtful, seeing as how the Red Sox are among league leaders in runs saved via the shift, the Orioles and Yankees are two of the teams that most commonly employ the shift and play in Fenway often, and because the Red Sox employ David Ortiz, one of the most shiftable players in baseball).

Unlike Fenway, Yankee Stadium features a below-average BABIP on balls hit sharply to right field. Perhaps the very plain dimensions of Yankee Stadium are easier to play than the quirky ones of Fenway - or perhaps long fly balls that would fall on the grass or hit the wall in most stadiums carry into the right field bleachers in the Bronx, lowing the number of hits and at bats considered in the BABIP calculation while leaving the balls in play that are easily fielded.