Archive for November, 2016

2017 Team WAR Projections and Playoff WAR Targets

Now that the World Series is over and the offseason upon us, our view of baseball begins to shift. For the last six months we have been laser-focused on the outcomes on the field. Now we begin to focus on the process of team-building and the chase to taste October Glory.

This exercise is an attempt to figure out how close teams may be and what they need to add in in the offseason to reach the playoffs. To do this, I looked at the latest FanGraphs depth charts, and the WAR landscape looks something like this:

Team 2017 Projected WAR

Cubs 50.1
Dodgers 48.7
Nationals 45.3
Indians 43.2
Red Sox 42.5
Giants 41.1
Astros 40.2
Cardinals 39.1
Angels 38.3
Mets 37.5
Mariners 37.2
Yankees 36.9
Pirates 36.6
Tigers 34.2
Rays 33.8
Rangers 33.5
Blue Jays 32.5
Marlins 32
Orioles 31.9
White Sox 31.1
Royals 30.7
Athletics 30.7
Diamondbacks 30.3
Rockies 27.7
Twins 27.7
Reds 26.5
Phillies 26.1
Padres 23
Braves 22.9
Brewers 21.6

To the surprise of no one, the Cubs lead in projected WAR due to the excellent core in place, with the Dodgers and Nationals taking second and third, respectively. The Indians and Red Sox rank fourth and fifth on this list and represent the top of the American League.

Now, to get a feel for what it is likely going to take to make the playoffs in 2017, I approximated how much team WAR will be needed to make the 2017 playoffs by averaging the WARs of playoff qualifiers going back to 2012 and came up with this:

AL WAR Target: 42.0
NL WAR Target: 44.6

American League teams, when assessing whether they are a realistic playoff contender, should project for a team WAR of 42, and National League teams thinking the same should project for closer to 45. Next, I took the projected WAR from each team and subtracted it from the respective league’s WAR target to determine how close teams may or may not be:

Team Target WAR +/-

Cubs 5.5
Dodgers 4.1
Indians 1.2
Nationals 0.7
Red Sox 0.5
Astros -1.8
Giants -3.5
Angels -3.7
Mariners -4.8
Yankees -5.1
Cardinals -5.5
Mets -7.1
Tigers -7.8
Pirates -8.0
Rays -8.2
Rangers -8.5
Blue Jays -9.5
Orioles -10.1
White Sox -10.9
Royals -11.3
Athletics -11.3
Marlins -12.6
Diamondbacks -14.3
Twins -14.3
Rockies -16.9
Reds -18.1
Phillies -18.5
Padres -21.6
Braves -21.7
Brewers -23.0

We see that only five teams exceed the arbitrary threshold of projecting above an average playoff contender. For a team like the Astros and Giants the decision to go for it is obvious. The Giants and Astros have payroll available and solid player development. Interestingly enough, the Angels are closer than one might initially think, but that has more to do with Mike Trout than the cast around him.

Moving toward the middle of the graph is where things begin to get intriguing. With the cost of 1 WAR on the open market approximately $8 million and the trade market expected to be active and expensive, teams need to be realistic with how much they are willing to spend, in cash or prospects, in order to reach the projected WAR threshold. Fringe contenders like the Pirates, Blue Jays and White Sox need to look in the mirror and recognize the uphill battle they have. The Blue Jays are losing key pieces to free agency and they could potentially cripple their flexibility with ill-advised moves. The Pirates are staring up at the Cubs dynasty in the making and you wonder if it is time to shop Andrew McCutchen and other short-term pieces. Lastly, the White Sox have Chris Sale, Jose Quintana, Todd Frazier and other quality pieces around the diamond. Given the AL Central, the Sox could blow it up and return to contention sooner rather than later, with the Royals and Tigers’ windows closing and the Indians representing the class of the division.

As we know, it rarely plays out this cleanly on the field, but from a pure projections standpoint, this serves as a gauge to where teams currently are. Some teams have very easy decisions and the choice to contend or rebuild is obvious. For other teams, the decision is less clear, and failure to capitalize could leave them stirring in mediocrity. The Cubs and Indians will fortify their rosters to chase down another pennant. For teams like the Pirates and White Sox, it just might be time to hit the red button.

Jose Bautista Might Be the Most Interesting Free Agent

It’s safe to say 2016 was a disappointing year for Jose Bautista. After posting three consecutive seasons with a WAR greater than 4, Bautista posted his lowest mark since 2008. The Toronto Blue Jays were ousted in the American League Championship Series for the second consecutive year and have looming decisions on how to go forward. Bautista is a polarizing figure in the baseball world and is a free agent in a relatively weak class. The big question teams will be asking is whether Bautista’s 2016 was more indicative of further decline or if there is a chance he rebounds. The 36-year-old will be looking for his last big payday.

Bautista’s defensive game continued to deteriorate. After posting a -12.5 UZR/150 in 2015, Bautista had a -9.3 UZR/150 this past season. Moreover, he finished second to J.D. Martinez for the right field Iron Glove. The main takeaway here is that Bautista is no longer good defensively and we shouldn’t expect him to get better. Unless a team wants him playing in the outfield, his future likely rests at first base or in the DH role. That’s not say a team cannot be playoff contenders with a poor right fielder. The aforementioned J.D. Martinez and Mark Trumbo were both below-average fielders this past season and both teams were in the thick of the playoff race. Moreover, being a good base-runner has never been part of Bautista’s game. Which brings us to his offensive value.

Jose Bautista will be paid on the basis of his bat. With his bad defence and sub-par base-running, teams will be lining up for Bautista due to the offensive numbers he has put up since his breakout in September of 2009. Since 2010, only three players have had a higher wRC+, and nobody has more home runs. On the surface, Bautista’s 34-point drop in wOBA and 26-point drop in wRC+ show a declining bat. Factor in his age, and things aren’t looking so rosy. Digging deeper, it is possible this was somewhat of an anomaly and Bautista will have a better offensive season in 2017. This is what makes Jose Bautista the winter’s most intriguing free agent.

Jose Bautista Walk and Strikeout Rate

Bautista’s walk rate remained elite. The Dominican slugger is one of the more selective hitters in the league, having the tenth-lowest swing percentage since 2014. The strikeouts rose, becoming much closer to the league-average 20.6% strikeout rate. Since 2014, Bautista has the 65th-best swinging strike rate at 7.3%, tied with notable players such as Adrian Beltre and Joey Votto. Bautista’s swinging strike rate in 2016 was 7.2%. This suggests his strikeout rate has more to do with an increase in called strikes than swinging strikes.

It’s been said that when a player can no longer catch up to a fastball, the end is nigh. The swing is slower, leading to more swinging strikeouts and an increase in weak contact.

FB SwStr%: League and Bautista

Bautista’s been below league average at swinging and missing on fastballs throughout his career. He saw an uptick in 2016, but it was still better that most. Moreover, among players to see at least 1000 pitches, Bautista ranked 11th in the league in average fastball exit velocity on line drives and fly balls, at 97.8 MPH against. Overall, Bautista can still hit the fastball.

In a similar method as shown here by Andrew Perpetua, I took a look to see if Bautista was getting lucky or unlucky.

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As you can see, Bautista’s slugging was fairly close to its expected value. Bautista’s lowest slugging percentage over the past five years was .498. There is a big difference in batting average, likely due to the big difference between expected BABIP and actual BABIP. To look into this disparity further, I looked at Alex Chamberlain’s expected BABIP formula. Using that formula, the xBABIP was .287, a lot closer to Bautista’s batting average. Bautista has been a career .260 BABIP hitter. Some of that is due to him popping out a lot and a lack of speed. Lastly, by taking a look at xISO, Bautista also underperformed by both metrics. Through Chamberlain’s formula, Bautista’s expected Isolated Power would be .265, and under the work of Andrew Dominijanni, his expected ISO would be .257. Bautista’s .217 ISO was his lowest mark since 2009. It is likely that Bautista was a tad unlucky in regards to outcomes. The story told by the multiple variants of xBABIP, xISO, and xAVG all point toward a better fortune for the Dominican slugger.

Another potential concerning issue with Bautista was the drop in contact on pitches outside the zone. With a career 64.7% O-Contact percentage, this number dropped to 60.4%, the lowest since 2009. You can see the difference between 2012-2015 and his 2016 contact percentages in various parts of the zone below.

Bautista Contact% 2012-2015

Bautista Contact% 2016

While his zone contact rate looks consistent, his contact made outside the zone away from Bautista decreased. To compensate for this, Bautista swung slightly less on pitches outside the strike zone. If he continues to struggle to make contact on pitches outside, then Bautista will continue to take more chances on borderline calls. The overall contact rate remained solid and he continued to pull the ball at the same rate, showing that Bautista still has good bat speed.

Another riveting aspect of Jose Bautista is that over his career, he hasn’t had a platoon split. Against right-handers, the six-time All-Star has a career 131 wRC+, and against southpaws he owns a 135 wRC+. The current Steamer Projections peg Bautista to be worth 2.9 Wins Above Replacement, with a 128 wRC+.

Jose Bautista showed some signs of decline. He made less contact on outside pitches, and he saw a decrease in offensive stats such as wRC+ and Isolated Power. The three-time Silver Slugger however continued to show strong plate discipline, and continued to hit the ball hard, using the same approach he has over the past few years. Furthermore, many expected stats point toward Bautista being somewhat unlucky with balls in play. With a wRC+ of 122, it is clear he can still hit and a rebound in offensive numbers isn’t out of the question. With the sub-par season he had, he could very well be one of the better value sluggers in the market. ­It will be a fascinating offseason for the Dominican slugger.

Joe Morgan’s Secret Socialist Baseball Regime

A popular theme this preseason was parity.  Truth be told, it’s been quite popular since the 2014 preseason projections forecast the smallest disparity between the best and worst teams at least going back to 2005Since then, the term has been so worn out that BuzzFeed included it on their end-of-the-year list of “words that need to be stricken from the Saber community” (source needed).

While the AL was the main driver of parity-related conversation, it might be worth mentioning that the results show that the AL was more lopsided than it was in 2015 while the NL’s gap was more compressed compared to the previous season despite the existence of the Chicago Cubs World Champion Chicago Cubs.  It’s not that that’s incredible — projection systems are conservative and variables such as sequencing and luck are still unpredictable.  Reflections of these points can be seen in Texas’ record in one-run games, or the Phillies and Braves performing better than they expected, or the Twins performing more like the Phillies and Braves were expected to.

It’s possibly reasonable to think that, as front offices skew more towards advanced analytics, the trend of increased parity will continue.  Of course that’s too simple of a statement as revenue sharing and luxury-tax measures have played their part in balancing out the competitive environment as well.  But as front offices progress it’s more likely that the true-talent level at the major-league level will span a smaller range, fewer and fewer at-bats will go to poor players, and the top players should be more evenly distributed throughout the league, speaking in terms of true talent.

This article, however, is not really about anything based in analytics or reality and I don’t know how to segue from my intro into delivering to you what I set out to do any better than asking you to assume some truly ridiculous prerequisites:

  1. MLB and the owners of all the teams only care about the viewer’s experience
  2. Unpredictable variables have become somewhat predictable. This includes some luck, breakouts, injuries, and rapid declines or dips based on smaller injuries.  This does not mean, however, that Runs and RBIs are predictable; it just works out perfectly by FanGraphs WAR
  3. The public is unaware of the predictability of baseball and there is an Illuminati-type presence in baseball headed by a board of trustees that includes, ironically, but obviously, Joe Morgan
  4. Payrolls are dictated by the outcomes that MLB knows will happen and are strictly performance-based – by FanGraphs WAR
  5. Rosters are reconstructed every single year
  6. Reconstructing rosters has no effect on luck or sequencing or ballpark effects (maybe all ballparks have the same dimensions)
  7. The DH is in both leagues but is only reserved for a portion of games throughout the year; teams are required to allocate at least 140 PA to pitchers
  8. Dave Stewart somehow managed to mess up his last season as the Diamondbacks GM (They just happened to be the last team I constructed and there wasn’t enough WAR left to make them as good as the other teams — the Cubs got dinged by this, too.)

What I did was export all the data I felt was relevant from the leaderboards and build 30 rosters based on the average number of Plate Appearances, Games Started, Innings Pitched, and WAR.  The numbers for the league break down like this:


PA (Non Pitchers): 179,218 (5,974.93/team)

WAR (Non Pitchers): 572 (19.07/team)

PA (Pitchers): 5,366 (178.87/team)

WAR (Pitchers): -2.6 (-0.09/team)


GS: 4856 (161.87/team)

IP: 43306.3 (1443.54/team)

WAR: 429.5 (14.32/team)

The only other things I wanted to be consistent with reality were the distribution of plate appearances by position and accounting for the IP by position players.  The first caveat doesn’t work out perfectly, but you’re not going to find a team that received 1,500 PA from their catchers and only 900 from all three outfield positions combined.  The second one, however, I believe I perfected.

After I had built the 30 rosters I realized they were only distinguished by a roster number, so in order to assign each roster a team, I simply took an alphabetical list of the team names and went down one by one with a random number generator and matched that team and random number to the roster with the corresponding number.

Here’s a link!

Who was on your favorite team?  Considering the public doesn’t know about the basically flawless projection systems, how did your team do compared to how you thought they would do? How much would this affect the way you watch the game?  How much would this affect your team loyalty?  Would you enjoy this?  Is this the dumbest exercise you’ve ever seen?  Is Joe Morgan a genius for complaining about the lack of dynasties while he secretly pulled strings to get all teams to be perfectly balanced, competitively, thereby creating a socialist baseball regime?



I’ll do this again when the 2017 rosters and projections are set so we can follow up on “equal” roster construction.

Hardball Retrospective – What Might Have Been – The “Original” 1921 Tigers

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. 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 teams with the biggest single-season difference in the WAR and Win Shares for the “Original” vs. “Actual” rosters for every Major League organization. “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

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.


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

AWAR – Wins Above Replacement for players on “actual” teams

AWS – Win Shares for players on “actual” teams

APW% – Pythagorean Won-Loss record for the “actual” teams


The 1921 Detroit Tigers 

OWAR: 49.3     OWS: 289     OPW%: .553     (85-69)

AWAR: 40.4      AWS: 212     APW%: .464     (71-82)

WARdiff: 8.9                        WSdiff: 77  

The “Original” 1921 Tigers paced the Junior Circuit in OWAR and OWS. Detroit finished third in the American League, ten games in arrears to the Red Sox. Harry “Slug” Heilmann (.394/19/139) collected his first batting title, smashed 43 two-baggers and topped the leader boards with 237 safeties. Ty Cobb (.389/12/101) continued to mash opposition offerings. “The Georgia Peach” tallied 197 base knocks, 124 runs, 37 doubles and 16 triples while recording an OBP of .452 and a .596 SLG. Baby Doll Jacobson (.352/5/90) contributed 211 base hits, 38 doubles and 14 triples to Detroit’s powerful lineup. Ray “Rabbit” Powell (.306/12/74) legged out 18 three-base hits to lead the League and scored 114 runs. Powell and outfield mate Bobby Veach (.338/16/128) established personal-bests in almost every major offensive category. Lu Blue supplied a .308 BA with 103 runs scored and 33 two-baggers in his inaugural campaign while fellow first-sacker Wally Pipp (.296/8/103) drilled 35 doubles.

Ty Cobb placed runner-up to Willie Mays among center fielders in the “The New Bill James Historical Baseball Abstract” top 100 player rankings. “Original” Tigers teammates registered in the “NBJHBA” top 100 ratings include Harry Heilmann (16th-RF), Bobby Veach (33rd-LF), Carl Mays (38th-P), Donie Bush (51st-SS), Lu Blue (77th-1B), George H. Burns (79th-1B), Wally Pipp (83rd-1B) and Baby Doll Jacobson (85th-CF).

“Actuals” backstop Johnny Bassler rated forty-seventh.

  Original 1921 Tigers                                Actual 1921 Tigers

Bobby Veach LF 5.23 22.64 Bobby Veach LF 5.23 22.64
Ty Cobb CF 5.74 25.77 Ty Cobb CF 5.74 25.77
Harry Heilmann RF 4.1 28.09 Harry Heilmann RF 4.1 28.09
Lu Blue 1B 1.61 16.87 Lu Blue 1B 1.61 16.87
Joe Sargent 2B 0.04 3.37 Ralph Young 2B -0.3 8.76
Donie Bush SS -2.03 6.82 Ira Flagstead SS 0.4 5.92
Eddie Foster 3B 1.78 13.05 Bob Jones 3B 1.22 12
Frank Gibson C 0.34 4.11 Johnny Bassler C 2.38 12.73
Baby Doll Jacobson CF 3.64 25.11 Donie Bush SS -1.41 5.77
Ray Powell CF 3.17 24.19 Joe Sargent 2B 0.04 3.37
Wally Pipp 1B 1.49 14.75 Chick Shorten CF -0.39 3.06
Bob Jones 3B 1.22 12 Larry Woodall C 0.38 2.48
Charlie Deal 3B 0.66 11.21 Eddie Ainsmith C 0.22 2.38
Fred Nicholson LF 1.52 10.17 Herm Merritt SS 0.32 1.45
George H. Burns 1B 1.5 8.58 Sam Barnes 2B -0.02 0.17
Ira Flagstead SS 0.4 5.92 Clyde Manion C -0.01 0.13
Ossie Vitt 3B -0.37 3.6 Jackie Tavener SS -0.05 0.04
John Peters C -0.21 2.59 George Cunningham RF -0.01 0.01
Larry Woodall C 0.38 2.48 Clarence Huber 3B 0 0.01
Herm Merritt SS 0.32 1.45 Sammy Hale -0.04 0
Frank Walker CF -0.37 0.63
Sam Barnes 2B -0.02 0.17
Clyde Manion C -0.01 0.13
Jackie Tavener SS -0.05 0.04
George Cunningham RF -0.01 0.01
Clarence Huber 3B 0 0.01
Sammy Hale -0.04 0

Carl “Sub” Mays (27-9, 3.05) topped the American League in victories, games (49), saves (7) and innings pitched (336.2). Clarence Mitchell fashioned a 2.89 ERA and notched 11 wins while splitting time among the bullpen and starting rotation. Dutch H. Leonard contributed a 3.75 ERA with an 11-13 record for the “Actuals”.

  Original 1921 Tigers                                Actual 1921 Tigers 

Carl Mays SP 7.27 34.42 Dutch H. Leonard SP 3.02 13.14
Clarence Mitchell SP 2.59 16.23 Red Oldham SP 2.13 10.76
Red Oldham SP 2.13 10.76 Hooks Dauss SP 1.3 9.82
Hooks Dauss SP 1.3 9.82 Howard Ehmke SP 0.65 8.14
Lou North RP 0.41 6.23 Jim Middleton SW -0.73 4.25
Slicker Parks RP -0.18 0.85 Slicker Parks RP -0.18 0.85
Jim Walsh RP 0.04 0.25 Jim Walsh RP 0.04 0.25
George Boehler RP 0.06 0.15 Dan Boone RP 0.01 0.16
Lefty Stewart RP -0.58 0
Bert Cole SP 0.75 5.71 Bert Cole SP 0.75 5.71
Carl Holling SP -0.65 4.81 Carl Holling SP -0.65 4.81
Suds Sutherland SP -0.17 2.87 Suds Sutherland SP -0.17 2.87
Bernie Boland SP -1.58 0 Pol Perritt SP -0.02 0.59
Doc Ayers SP -0.29 0
Lefty Stewart RP -0.58 0


Notable Transactions

Carl Mays 

Before 1914 Season: Returned to Providence (International) by the Detroit Tigers after expiration of minor league working agreement.

Before 1914 Season: Obtained by the Boston Red Sox from Providence (International) as part of a minor league working agreement.

July 30, 1919: the Boston Red Sox sent Carl Mays to the New York Yankees to complete an earlier deal made on July 29, 1919. July 29, 1919: The Boston Red Sox sent a player to be named later to the New York Yankees for Bob McGraw, Allen Russell and $40,000. 

Baby Doll Jacobson 

Before 1915 Season: Purchased by the Detroit Tigers from Chattanooga (Southern Association).

August 18, 1915: Traded by the Detroit Tigers with $15,000 to the St. Louis Browns for Bill James. 

Ray Powell 

July 10, 1917: Purchased with Wally Rehg by the Boston Braves from Providence (International).

Clarence Mitchell

October 16, 1917: Selected off waivers by the Brooklyn Robins from the Cincinnati Reds.

Wally Pipp

August, 1912: Purchased by the Detroit Tigers from Kalamazoo (Southern Michigan). (Date given is approximate. Exact date is uncertain.)

February 4, 1915: Purchased with Hugh High by the New York Yankees from the Detroit Tigers.

Honorable Mention

The 2003 Detroit Tigers 

OWAR: 14.8     OWS: 195     OPW%: .400     (65-97)

AWAR: 7.1       AWS: 129      APW%: .265    (43-119)

WARdiff: 7.7                        WSdiff: 66


The “Original” 2003 Tigers finished last in the AL Central, 17 games behind the White Sox. However the “Actuals” finished 47 games off the pace with a ghastly 43-119 record.

Juan Encarnacion (.270/19/94) established career-highs in RBI and doubles (37). Frank Catalanotto contributed a .299 BA with 34 two-base knocks. Robert Fick registered a personal-best with 80 ribbies and Dave R. Roberts pilfered 40 bags. The bullpen featured John Smoltz (1.12, 45 SV) and Francisco Cordero (2.94, 15 SV).

On Deck

What Might Have Been – The “Original” 1979 Mets

References and Resources

Baseball America – Executive Database


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

The information used here was obtained free of charge from and is copyrighted by Retrosheet. Interested parties may contact Retrosheet at “”.

Seamheads – Baseball Gauge

Sean Lahman Baseball Archive

The State of the Yankees

As a Yankees fan (albeit one that has only witnessed their 2009 World Series), I have never been more excited about the team’s present and future. With the MLB roster slowly filling with good, young talent, and with even more stirring circumstances in the minors, the Yankees have the potential to be another powerhouse team.

The Team

Right now, the Yankees are in the midst of a revolution. Out with the old (A-Rod and Teixeira) and in with the new (Sanchez, Judge and Austin). Despite missing out on the playoffs, they will feature a well-rounded lineup at the start of next year.

It’s safe to say that Gary Sanchez won’t enjoy quite the success he did in the last two months of this season. Actually, he won’t come close. This isn’t to say he will play poorly, it’s just that he played so well that he can’t come back to those levels. However, Sanchez will no doubt still be one of the better-hitting catchers in the MLB with average to plus defense behind the dish, so they will already be better in that position in 2017 than they were in 2016.

The Yankees infield is the most likely to change the least with only Greg Bird slotting in at first base. Didi Gregorious, Starlin Castro and Chase Headley are each under team control until at least 2018, and there isn’t anyone challenging them for their spots at the moment. At first base, though, I say it is most likely that Bird gets the spot because it is possible that Tyler Austin beats him out in spring training. Austin is more likely to be used as a quasi-utility player as he can play at first, in right field and DH.

In the outfield everything could remain the same as the end of the season with Hicks or Judge in right, Ellsbury in center and Gardner in left. It could also see some changes. Gardner and Ellsbury both have the potential to be traded over the offseason with Gardner the more likely of the two. There are options to fill those gaps if trades do happen. Mason Williams could fill in until Clint Frazier is (hopefully) ready later in the season. Hicks, Austin and Judge could also fill the holes if needed.

The Yankees pitching is the most worrisome issue. The starting pitching, that is. Masahiro Tanaka performed well in 2016, so there is no reason to think otherwise for the next year. Beyond that, though, are question marks. Nate Eovaldi will probably be a non-tender after his Tommy John surgery. Pineda had his usual ups and downs. Sabathia is still getting older. Then there are numerous options in Luis Severino, Chad Green, Luis Cessa and Bryan Mitchell. Severino will be given the longest look because of his end to the 2015 season, but it’s a toss-up from there.

The bullpen in New York is still a quality one despite trading away Aroldis Chapman and Andrew Miller. Dellin Betances is one of the best in the game, so that’s a good start. Tyler Clippard, Adam Warren and whoever misses out on the rotation gig will presumably fill in the rest with a lefty thrown in.

The Minors

Now comes the most exciting part of the Yankees. With a system that starts with four top-30 prospects despite Sanchez already graduating, the Bombers are on their way to a good future. Frazier is in AAA and still needs to put up good at-bats before he gets the call to the majors, but that time will come soon enough. Gleyber Torres and Jorge Mateo will likely start the year in AA, so they won’t be seen until 2018 most likely, especially with the likes of Gregorious and Castro blocking them. Beyond their top three guys, the Yankees still have plenty of players who could make a major-league impact once it’s their time. Simply, there is a lot to be excited about when it comes to the team’s future.

The Yankees will have the 17th overall pick in next year’s draft, so they will be in familiar position after having the 16th and 18th picks in the two previous years. Their first-round picks in recent years have both been ones that I personally like, but who wouldn’t? James Kaprielian is shining in the Arizona Fall League and Blake Rutherford looks like a steal at the 18th pick, especially after his hot start to his pro career. This year will hopefully prove to be another that produces some good picks.

The Offseason

With the Yankees pretty much set with position players, there’s no reason to add any pricey free agents. It also wouldn’t be wise to block some of their young players out to prove themselves or ones that are close to ready in the minors. Pitching is another story.

As I stated before, their starting pitching has question marks when it comes to Sabathia’s age, Pineda’s consistency and Severino bouncing back. There also aren’t many pitchers on the free-agent market that stand out. Overpaying for Rich Hill would be contradictory to what the Yankees are trying to do in becoming younger, but his dominance when healthy is something that can’t be questioned. It wouldn’t be a bad move to sign him, but it would add yet another question mark to their rotation due to his injury history. Signing him also wouldn’t help any towards getting under the luxury tax, which Steinbrenner would like to do.

The only free-agent acquisition that I would like to see is a top-notch reliever, which means one of Chapman, Kenley Jansen or Mark Melancon. Jansen is likely going back to the Dodgers and Melancon would be yet another righty for the bullpen. A reunion with Chapman would be the best move. Pairing him with Betances again would put the bullpen in great shape. It’s just that it will cost a lot.

In terms of trading, I am one that is all for trading Gardner, Ellsbury and/or Brian McCann. Ellsbury’s contract probably means he’s staying, but Gardner will be easy to move if Brian Cashman can get the right return. Some reports have said that a swap of him for a middle-of-the-rotation pitcher could work, and that would be just what the Yankees need. McCann will have high demand this offseason with multiple teams needing catchers and not enough free agents to go around. The Yankees will have to eat a good chunk of his contract to get anything of value in return, but it shouldn’t be a problem as they’d be shedding a good portion of his $17-million-per-year contract. It would also give younger players like Bird, Austin and Judge a chance to DH.

The Braves have been said to want a reunion with McCann but won’t trade Mike Foltynewicz for him. The Yankees will do well if they can eat about half of his contract and get a couple middling prospects with some upside.

With such a deep farm, the Yankees also have the ability to trade for a front-of-the-rotation starter. Landing one of the top guys on the trade market probably isn’t in their best interests, though. To get one of Chris Sale, Chris Archer or Sonny Gray will cost a good portion of what the Yankees were able to get for Chapman and Miller. Instead, they should look to trade from depth for a guy that is a step down from the others. With Torres looking like the better middle-infield prospect, trading Mateo as the headliner of a package for a starter would be a good move and won’t impact the team’s future too much.

In Summary

In an ideal scenario, the Yankees will sign one of the top relievers to pair with Betances, stand pat on other free agents and see how Cashman can work the trade market for a third straight offseason. The Yankees likely aren’t a top contender next season, but the potential is there. If things break right with Judge, Bird, Sanchez and the rotation, they could find themselves at the top of the A.L. East. Right now, though, they should look to continue development of their top-three farm system and look at 2018 as the year to really contend.

The Home Run Conundrum, Part II: Less Is More

In Part I, one of the major observations was that a group of smaller-statured players seemed to be using backspin as a distance tool. I was curious how the increase in home runs would look when broken down by physical size. In addition to using Statcast data from Baseball Savant, I downloaded player heights and weights from MLB rosters and created size quintiles. While I expected to see significant contribution from smaller-sized players, the magnitude of what is occurring was quite surprising:

Size Quintile Home Runs
 (1= smallest) 2015 2016 Change
1 410 522 112
2 714 1,025 311
3 1,036 1,132 96
4 1,277 1,420 143
5 1,469 1,512 43
Totals 4,906 5,611 705

Note: Size based on height * weight. Since pitchers skewed the quintiles due to their above-average size, they were excluded in making the quintile groups; however, their HRs are included in order to tie back to HR totals.

Now that is democratization of power! While interesting, the obvious question is: How are the smaller players hitting all the additional home runs? Is it more distance through exit velocity (EV) and/or launch angle (LA), more pulled balls, more fly balls, or just better-hit fly balls? Let’s take a look:

Distance, EV and LA

Change from 2015 to 2016
Balls Hit >=90 MPH, >=15 Deg.
Quintile EV (MPH) LA Distance (ft)
1 0.08 -0.09 -0.96
2 0.26 0.32 2.99
3 0.54 -0.56 3.75
4 0.44 0.16 3.88
5 0.58 0.46 3.06

Note: Balls hit at Coors Field excluded

Although the data above would support a slight increase in homers overall, there is no smoking gun as to what might be happening within the smaller player groups. If smaller players are not hitting the ball that much harder or further, maybe it could be that they are hitting more homers to the pull side.

Pulled HR and Hits

Pulled Home Runs Change and Mix
Quintile            Change 2015 2016
1                   63 85% 78%
2                242 77% 77%
3                   69 77% 77%
4                153 68% 71%
5                   18 65% 64%
Total/Avg                545 71.8% 72.2%

Although the location mix of homers did not change significantly from the prior year, smaller players in both years hit a much higher percentage of their homers to the pull side than average. The more important metric to consider with respect with the pull factor is what is happening to the mix of well-hit fly balls.

            Pulled Balls Hit >=90 MPH And >=15 Deg
Quintile 2015 2016 Change
1 35.7% 36.2% 0.5%
2 36.3% 38.4% 2.1%
3 38.1% 40.3% 2.2%
4 35.0% 37.0% 2.0%
5 35.6% 36.7% 1.1%

Again, more data supporting a slight overall increase in homers – More well-hit fly balls hit to the pull side and more of those balls going for homers. No real support here for what might be happening with the smaller players. What about well-hit fly balls in general:

Size Quintile Well Hit Fly Balls >=90 MPH + >=15 Deg.)
 (1= smallest) Change % Change
1 442 16%
2 881 22%
3 -175 -3%
4 66 1%
5 13 0%

Now we’re getting somewhere! Smaller players experienced a significant increase in well-hit fly balls in 2016. What about fly balls in general, not just those of the well-hit variety:

Change in Total Fly Balls

2015 – 2016

Quintile Change % Chng
1 385 10.4%
2 979 20.5%
3 -146 -2.5%
4 127 2.1%
5 199 3.4%

The last two charts kind of sum it up – smaller players are hitting more fly balls in general as well as more well-hit fly balls that are going for homers. Before closing, I’d like to show two other tables which I believe are meaningful for both the home-run question as well as hitting in general. In a certain respect, it appears hitters are making better contact. The following chart shows the volatility (via standard deviation) for EV, LA, and Distance.

Changes in Volatility
Changes in Std. Dev.    2015-2016
Quintile EV LA Distance
1 -0.65 0.18 -5.44
2 -0.31 0.60 -4.56
3 -0.36 0.46 -5.22
4 -0.21 0.56 -5.77
5 -0.18 0.67 -5.43

Since EV is up in terms of MPH but down in terms of volatility, this would indicate players in general are making better contact. The same is true for distance – higher average distance but lower volatility. However, the increase in volatility of launch angle would seem to indicate quite the opposite – that players are using a lower ball-contact point in order to achieve the higher number of fly balls. Take a look at pop-ups over the past two seasons:

Change in Pop-Ups
Quintile Change % Chng
1 59 4.9%
2 211 13.7%
3 -34 -1.8%
4 41 2.2%
5 -8 -0.4%

While not up across the board, it is very interesting that there is a significant increase in pop-ups in the group responsible for the largest increase in homers.

After considering the data above, I was curious how the homers looked broken down by age. The increase in homers of the younger players was equally surprising:

         HR Breakdown By Age
Age 2015 2016 Change
21-23 125 285 160
24-26 905 1,474 569
27-29 1,321 1,352 31
>=30 2,555 2,500 -55

I checked for the obvious relationship between size and age; however, the 24-26 age group was reasonably well distributed in terms of size so there is likely something additional going on with the younger players. Whether it is a power focus earlier in their development, a selection bias through the draft or some other factor I’m not sure. Maybe I’ll get into that another time.


This is a very interesting issue to consider and while I’m sure there will be much more written on the topic, it certainly takes some possibilities such as a juiced ball completely out of consideration. Now that would be a conspiracy! That umpires are throwing out juiced balls for the little guys! Except that the balls would have to be so stealthy that they don’t get hit significantly harder or further – they just hit bats of the smaller players for well-hit fly balls more often.

For me, the really interesting part is the underpinning driver – that advanced metrics have changed the market which values the players. Whether consciously or not, players are changing to align with the market to maximize their value. Even more interesting is what the future holds – what is the cost of the hyper-focus on power and loft and what are the unintended consequences that have yet to come to light?  As far as the home-run issue, at least in terms of player size and age, less certainly has been more.

The Future of the Angels

Any fan that is somewhat invested in the game of baseball understands the importance of putting both a good team on the field at the MLB level while also sustaining an adequate farm system. The Angels have done neither.

This is a hard thing to do when the best player in baseball plays for you, but Arte Moreno and the Angels have managed to do that. Let’s take a look at how they ended up in this dire situation.

MLB Team

One thing the Angels do have (sorta) is a good core of players. They have Mike Trout, Kole Calhoun, Andrelton Simmons and Garrett Richards. Trout and Simmons play at premium positions, Calhoun is a good two-way player and Richards has ace potential (given his arm doesn’t snap). They even have quality players in Yunel Escobar and C.J. Cron who are quietly productive. With the exception of Escobar, each of those players are controllable for the next several years. The team isn’t devoid of talent behind Mike Trout like some believe. They also have a few starting pitchers who have either shown success or are promising in Matt Shoemaker, Tyler Skaggs, and Andrew Heaney. The only problem is that Heaney is done for next year already and Skaggs may be too if his stem-cell therapy doesn’t work.

The holes in the team are at second base, left field, starting pitching spots that aren’t guaranteed and the bullpen. Especially the bullpen. The only true bright spot of their bullpen is Cam Bedrosian while everyone else is expendable at best (unless Huston Street can return to form).

Now that we’ve looked at their roster heading into next season, how can they fix it?

Win-Now Options

Moreno has to let Billy Eppler spend some money this offseason. He isn’t paying Jered Weaver or C.J. Wilson anymore. That leaves them with roughly $30 million to spend before hitting the luxury tax, which Moreno has made clear he won’t go over. One thing this offseason is sure to provide is offense.

Obvious fixes would be to sign Yoenis Cespedes and one of Justin Turner — which would move either him or Escobar to second — or Neil Walker. The Angels can’t go another year with below-replacement-level players at those positions if they truly want to win. The smart route for them would be to avoid what are likely to be excessive bidding wars for Cespedes and Turner. Walker is a great fit at second for them. He offers good offense from the left side to couple with their righty-heavy lineup as well as average defense to a team that has seen paltry turnouts at the position.

As for left field, their are plenty of corner outfielders on the market. However, instead of paying too much for a reunion with Mark Trumbo, the Angels should look at Ian Desmond, Dexter Fowler and Carlos Gomez. Desmond and Fowler failed to garner much interest last offseason, so an offense-heavy free-agent class should keep their price tags down. As for Gomez, he was DFA’d by the Astros before playing somewhat better with the Rangers. Gomez is the higher risk/reward player while Fowler is the closest to a sure bet to perform consistently. Desmond is a wild card since he just converted to the outfield and profiled as below average in center. Shifting him to left with Trout in center could improve his defense, so he is also a viable option. The Angels took huge risks in the past that didn’t turn out well, so Fowler is probably their best option. Plus he adds another lefty bat against righties.

If the Angels can manage to add both Walker and Fowler, their offense would actually fill the basic requirements for a successful team. They would have a leadoff hitter in Fowler, and a number two in Calhoun, with Trout in the three slot. Either Cron or Pujols will bat fourth and fifth with Walker behind them. Then some mix of Escobar, Simmons and their catcher in the 7-9 spots.

As for fixing the rotation, that will be much harder, and they might just have to wait out the storm or go over the luxury tax. Overpaying for Jeremy Hellickson or Ivan Nova would be a bad move and Rich Hill isn’t a good fit for a fairly old roster that already has its risks. Henderson Alvarez could be a good bounce-back candidate after missing 2016 following a shoulder surgery. Andrew Cashner could be an option in a pitcher-friendly park in Anaheim, though the one in San Diego didn’t do him much good. Going into the season with Richards, Shoemaker, Skaggs, Nolasco and one of Alex Meyer, Nate Smith or Daniel Wright isn’t the end of the world. It just has its risks.

What about the farm?

Minor Leagues

According to, the Angels have 11 home-grown players on their 40-man roster. That’s definitely on the lighter side compared to most teams, but it isn’t quite as extreme as the Padres’ six. They also only have six free-agent signings, which isn’t too large of an amount. The part of their roster that stands out is their eight waiver claims. The fact is that the Angels didn’t have the depth to fill their own roster with players already within their organization.

Going back to the team’s free-agent signings, six isn’t a large amount as I stated before. However, some of their more recent signings have been very costly (both in terms of monetary and baseball value). In the offseason prior to the 2012 and 2013 regular seasons, they signed Albert Pujols, C.J. Wilson and Josh Hamilton. Each of these players cost north of $15 million per season. Each also cost the team draft picks. They lost two first-round picks and a second-round pick.

The teams’ most recent top picks most likely aren’t going to make an impact with the MLB team. For one, Sean Newcomb definitely won’t since he’s on the Braves now. Taylor Ward and Matt Thaiss were both very weak first-round picks. Ward won’t hit and Thaiss is basically limited to first base.

This isn’t to say the Angels have nothing in the minors. Jahmai Jones is promising but very young and a few of their other 2016 picks could develop into good MLB players, including Brandon Marsh and Nonie Williams. Their farm isn’t deep enough to trade for any key pieces though, and they shouldn’t do that even if they did have the pieces. Eppler has a chance to use a top-10 pick this year as well as future picks to try and build the strong farm that the Angels have lacked for so long, so he can’t waste that opportunity on a middling team.

In Summary

I feel that I’ve laid out the best-case scenario for the Angels next year with potential signings of Walker and Fowler, who would fit in very nicely with their current lineup. Any team with Mike Trout has a chance to be successful after all. They will need to sign those two players first, and then the rotation needs to have luck on its side with the injury situations. The bullpen is a clear gap in the roster, so safe signings over the offseason could complement Bedrosian and possibly Street. Their farm system is also a clear work in progress, but it isn’t empty in terms of talent. That talent is just a little ways off at the moment. Overall the future of the Angels seems dreadful, but if things break right they can be a contender next year. Their overall run differential was only 18 apart from the first-place Rangers, so they at least played in close games. Now all that needs to be done is execution by the players and by the front office to bring a winner back to Anaheim.

The Small Things Do Matter: Lack of Hustle by the Cubs

Despite their World Series Game 5 win, the Cubs came under fire Monday morning for their lack of hustle. On Mike & Mike ESPN Radio, Mike Greenberg commented that the Cubs seem to be lacking hustle, as evidenced by slow home-plate-to-first-base times by Jorge Soler on his Game 3 triple and Anthony Rizzo on his Game 5 double. Soler assumed a fly out or foul ball, and Rizzo assumed a go-ahead home run. Buster Olney added, “It’s interesting you say that, because I had a conversation with one of the veterans in this World Series…and that’s exactly what he said. ‘This is the World Series, how can that happen? It’s a different generation.’”

That’s right, this is the World Series, the biggest baseball stage, the postseason when even average fans tune in to watch and learn from some of the best players in the game. In today’s baseball market worth billions, where players in their late teens and early twenties are paid 10 or more times the average American salary, maybe a lapse in hustle or a hard 90-time is acceptable, if not necessary, during the regular season of 162 games in order to avoid injury or excessive exhaustion. You wouldn’t want your star player pulling a hamstring on a routine infield groundball in August, would you? Of course not. But c’mon, this is the World Series! Most of these players have never played for higher stakes. Is the “lack of hustle” a generational problem? What ever happened to the commitment Joe DiMaggio had to playing hard just in case someone was watching for the first or last time?

Your organization hasn’t won a title in 108 years. Why wouldn’t you approach every play as if it was the last? You’d think they would in the World Series; especially given Game 5 could have been the last. Greenberg and Olney failed to even mention Javier Baez’s Game 5, second-inning strikeout where he refused to run to first base on a dropped third strike, looking increasingly frustrated with his World Series offense (2 for 18 with 7 strikeouts, and 16 runners left on base after that at bat).

Let’s take a look at some numbers by analyzing the Win Expectancy (WE) for the Cubs before and after each of these three plays (Soler’s triple, Baez’s strikeout, and Rizzo’s double) to show the importance of maximizing every opportunity and play. These three players were caught up in the moment and took things for granted on the biggest stage of their sport, a time when small mental errors could make the ultimate difference in winning a game and the championship. We’ll also look at the WE if each play had ended with a different outcome. All WE are obtained from The Book: Playing the Percentages in Baseball, by Tom Tango, Mitchel Lichtman and Andrew Dolphin.

Jorge Soler (Age 24)

Game 3, Series tied 1-1

Bottom 7th, Cubs trailing 1-0 with 2 outs

Triple to right field

WE before at bat: 29.1%

WE after triple: 35.0%

WE after next batter ends inning 26.5%

For the sake of this article, let’s assume (which is assuming a lot with an inside-the-park home run) Soler runs hard out of the batter’s box and rounds the bases for an inside-the-park home run, tying the game. The WE for the Cubs would have jumped to 52.2%, a major swing (nearly double) from where that inning ended. The Cubs lost that game 1-0 to give the Indians a 2-1 series lead.

Javier Baez (Age 23)

Game 5, Indians leading series 3-1, Cubs one loss from elimination

Bottom 2nd, Cubs trailing 1-0 with 2 outs and a runner on 1st

Strikeout, dropped third strike (ball in dirt), Baez does not run to 1st base

WE before at bat: 41.9%

WE after strikeout: 39.4%

Again, for the sake of this article, let’s assume Baez runs hard to first on the dropped third strike and reaches base, which rarely ever happens in Major League Baseball. However, this is the World Series and Game 5 is an elimination game. You never know what can happen. Though the data for the number of baserunners reaching on a dropped third strike isn’t available, such instance would be scored with either a passed ball or wild pitch on the play (a battery error). Take a look at the number of passed balls and wild pitches in MLB over the past 10 seasons, as provided by Baseball Reference.

Year Passed Ball (per game) Wild Pitch (per game)
2016 0.08 0.37
2015 0.07 0.36
2014 0.07 0.35
2013 0.07 0.36
2012 0.08 0.32
2011 0.07 0.32
2010 0.06 0.34
2009 0.06 0.33
2008 0.06 0.32
2007 0.07 0.31
Average 0.069 0.338

A catcher is scored with a passed ball on average every 14-15 games, while a pitcher is scored with a wild pitch on average every third game. If anyone can provide data for the number of times a batter has reached base on a dropped third strike, it would only strengthen the claim that Baez’s chances of reaching base were slim. Regardless, remember it’s an elimination game in the World Series. For the sake of proving a point, let’s look at the scenarios if Baez had reached base.

The ball did skip quite a distance from catcher Robert Perez, so let’s take a look at WE if Baez reached first, leaving the Cubs with runners on first and second with 2 outs: 44.1%.

How about if Roberto Perez threw the ball away into right field, causing a 1st and 3rd situation (let’s note that catcher errors are also very rare): 45%.

Even though Baez reaching first base on a dropped third strike (which was far from guaranteed by running) would have only added about 5-6% to the Cubs WE, there is no excuse for Baez to have a lapse of effort and allow Perez an easy, no-pressure throw to first base because there was no runner hustling down the line. At the very least, run hard and make it look good for the millions of people watching. Not to mention the thousands of people who spent a week’s wage on tickets to Wrigley. They, along with your teammates, want to see you running to first base instead of walking back to the dugout.

Instead, the Cubs were left with their two weakest hitters (David Ross and Jon Lester) to lead off the next inning, which resulted in a 1-2-3 inning for Indians starting pitcher Trevor Bauer, who took a 1-0 lead into the fourth inning.

Anthony Rizzo (Age 27)

Game 5, Indians leading series 3-1, Cubs one loss from elimination

Bottom 4th, game tied 1-1, 0 outs, first batter after Kris Bryant game-tying home run

Double to right field

WE before at bat (after Bryant home run): 56.3%

WE after double: 63.4%

The back-to-back extra-base hits certainly turned the momentum of the game in the Cubs’ favor. Two batters (Bryant and Rizzo) increased the Cubs’ WE from 43.7% to 63.4%, a major increase in a game they eventually won 3-2 to force a trip back to Cleveland for Game 6.

A better throw from right field would have made a very close play at second base, so let’s look at the WE for the Cubs had Rizzo been thrown out at second base on his hit off the right-field ivy: 53.4%. His lack of hustle from home plate to first base, as he admired what he thought was a go-ahead home run, could have cost the Cubs 10% on their WE.


There is certainly no guarantee that any individual exertion of hustle will lead to a different outcome in a baseball game. Running out a groundball will not guarantee an infield hit, but it puts pressure on the fielder to make a clean play. Running hard on a fly ball has no measurable effect on whether a fielder will catch it or not, but it puts the runner in the best possible position to advance an extra base on a rare dropped ball. Running hard to first base after a dropped third strike does not make a difference in the outcome of the play 99% of the time, and it certainly doesn’t change the 0-for-1 with a strikeout in the box score. But it puts pressure on the catcher to retrieve the ball in a clean manner and make an accurate throw to first base. Let’s not forget that hustle is the right thing to do. It’s more about the precedent, not the result. It’s about the example we want MLB players on the biggest stage to set for younger players worldwide. DiMaggio likely wouldn’t recognize some aspects of today’s game. He, like many other players, never took anything for granted. Despite the fact that Soler and Rizzo still ended up with extra-base hits, and Baez most likely would have been thrown out at first base anyway, shouldn’t we hope that on this kind of stage the very best will play the game to its absolute potential?

Linearization and Fantasy Baseball

Among the astounding phenomena abundant throughout calculus, linearization remains one of the least glamorous. It’s incredibly simple, taught in less than a day, and a more precise (and more complicated) method can often be substituted for it. On the other hand, it’s an incredibly powerful tool and one with weighty implications for fantasy baseball. Because of the concept’s relative simplicity, a reader with even the most basic inkling of what calculus actually is should be able to understand the idea of it, so don’t let a fear of mathematics deter you.

First, let’s think about graphs, functions, and derivatives. Put simply, continuous functions, whether they’re linear, quadratic, or exponential, will generally experience some rate of change — slope. Think of it as the change in the y direction per unit change in the x direction between two points. This is considered a secant line, or the average rate of change between two points. More interesting, however, is the concept of the tangent line, or the instantaneous rate of change at a given point. Note that the tangent line only touches the function at one point rather than two, meaning that we can easily evaluate and analyze the rate of change when comparing two points on a curve. Importantly, the magnitude of the slope of the tangent line tells us the rate by which the function is increasing or decreasing. So the greater the slope, the faster it is increasing (perhaps indicating an exponential function), and the lesser the slope, the more it is decreasing (a negative quadratic).

In calculus, the formula for linearization is:

L(x) = f(a) – f'(a)(x – a)

Here, given some value of a, we get a y-value, or f(a). From there, we subtract the product of the derivative of f(a) and the difference between the value we are estimating, x, and the value we already have, a. This gives the linear approximation and we get a pretty good estimate.

When rendered down to its most basic essence, linearization is a glorified form of estimation that gives credence to gut instinct through a formula. Using the tangent line at a certain point, one can make very incremental estimations, but it’s important to note that they must be very small. The farther from the initial point a that one travels to find an approximation of y, the less accurate the result will be.

It seems that this would have little application to baseball, but that’s incorrect. Recently, I started toying with a couple of formulas that could actually have some importance in the realm of amateur fantasy baseball with the usage of a regression line for an entire player’s career in pretty much any statistic.

L(x) = f(k) – f'(a)(x – a)

Here, f(k) is the actual value at the known point (k), f'(a) is the derivative of the predicted point on the regression line, x is the point for which we are predicting the value, and a is the value we start from.

L(x) = f(a) – f'(a)(x – a)

Differing here, f(a) is the predicted value at the regression line, f'(a) is the derivative of the predicted point on the regression line, x is the point for which we are predicting the value, and a is the value we start from.

I don’t know which would work best, but my guess is that first formula would be most accurate due to its mix of actual and predicted values. Neither of them would be terribly precise, but it’s a heck of a lot better than relying on what you feel might be best.

Regardless of which formula you might prefer, the implications of the linearization idea as applied to fantasy baseball are apparent. Probably best used for 10-day predictions, linearization mixes short-term performance with long-term talent to assess how well a player might perform for a short period of time — whether he’s likely to continue streaking, slumping, or somewhere in between. Rather than having to rely on gut instinct or dated and/or biased statistical analysis, a fantasy player could rely on some concrete math to make short-term decisions. This would be especially helpful in leagues that play for only a month, or can only alter their rosters once a week, or even at the end of a highly competitive season (perhaps making the risky move of dropping a slumping MVP for the streaking rookie).

It’s understandable if it’s unclear how to use one of the formulas at this point. To simplify matters, let’s use formula 1 to demonstrate how this might work in regard to something as simple as batting average. So what you might have is a regression line for a player of rolling 10-game predicted batting averages plotted along with actual values. In this case, x-values are 10-game rolling averages by each 0.01 (the intervals are arbitrary). So 1.1 is the x-value at 110 games played, while 1.2 is the x-value at 120 games. Let’s just say for simplicity that the player has played 110 games in his career, had an actual average of .264 during the last 10-game stretch, and the derivative of the regression line at this point is 0.12. We want to guess his average for the next 10 games, up to career game number 120.

L(1.2) = .264 – (0.12)(1.2 – 1.1)

L(1.2) = .254

We’d expect him to hit .254 over the next 10 games. Hopefully that makes some sense. Obviously it’s still in development and I haven’t done a whole lot of research yet, but expect some to come out later along with some clarifying material if necessary. Confusion is to be expected, but with some explanation applied linearization could potentially help a lot of people out next season in fantasy.