Last week I looked at the horizontal angle of a ball in play as a function of the location in the zone where it was hit. Although there is some trend for lower pitches to be pulled more, most of the trend is dictated by the horizontal location of the pitch. As expected inside pitches tend to be hit to the pull field and outside pitches more to the opposite field.

Below I reproduce the trend for just the horizontal location. I found the average angle of a ball in play as a function of the horizontal location of the pitch. The center of the strike zone is 0 and negative numbers indicate pitches that are inside to right hand batters and positive numbers outside. The strike zone extends from -1 (inside edge to a RHB ) to 1 (outside edge to a RHB). The angle of a ball in play follows the -45/0/45 convention (-45 is the third base line, 0 2nd base and 45 the first base line), so negative numbers indicate the pull field for a righty.

Starting away and moving towards the batter more and more balls are pulled, with the trend slowing and stopping at about the inside edge of the plate. Here you can see the overall pull tendency. At x=0, the middle of the plate, the average ball is hit to about 7.5° to the pull field and at x=1, the outside edge of the plate, the average ball is hit right up the middle.

I was interested in how this varied by pitch type. I expected that slower pitches would be pulled more, as hitter have more time to 'get around' on such pitches.

The results confirm our expectations. The slower a pitch type the more it is pulled, so that through much of the strike zone the average curveball or changeup is pulled 10° more than the average fastball in the same horizontal location. This shows part of the danger of coming inside with breaking and off-speed pitches. These pitches, if they are hit, will tend to be pulled heavily, which is where most hitters have the greatest power.

I also wanted to see how much speed affected pull, regardless of pitch type. Here I plot the average angle of a ball in play by pitch speed for three horizontal locations, away (but in the zone), down the middle and inside (but in the zone).

The effect of pitch speed is strong, nonlinear and interacts with location. So for inside pitches there is not much effect of speed, the pull rate of a very slow and very fast pitch are not that far off. Similarly there is not a lot of difference in the pull rate of very slow pitches across location, they are all pulled heavily. But outside pitches are strongly affected by pitch speed, with slow ones being pulled and fast ones going to the opposite field. And very fast pitches are strongly influenced by location, with inside ones being pulled and outside ones going to the opposite field.

The results here are not that surprising, but nicely confirm long-held baseball expectations.

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This is the third part of what has been a three part series on the MLB Draft. Part one created a model for the expected value of each draft pick, while part two calculated probabilities of becoming a certain caliber player, as well as expanded on the conclusions in part one.

Today's article focuses on individual teams and how much control they have over the draft process. Is drafting more or less a complete crapshoot, or does the success of a draft vary greatly depending on the front office and the team who is doing the drafting (and oftentimes developing the players as well). Is there much to distinguish a great drafting franchise from a poor one, or is the difference mostly due to luck?

To review, the data I had at hand was gleaned from Sean Smith's WAR database and Baseball Reference, and contained overall picks #1-50, as well as a handful of picks after that (every 5th pick through #100, every 10th pick through #500, and every 25th pick through #1000). While not every pick for every team is covered, this data gives each team a sample of well over 100 draft picks, including all of a team's very high selections. Data used in this study, will focus only on each player's "first six year" WAR, since the team only gains from drafting a valuable player during the years in which it does not have to pay market value. The data is also limited to those players drafted in 2001 or earlier, since more recently drafted players have not had a chance to come up and show their full value.

Draft WAR By Team

So, how did the teams fare? For what it's worth, the table below shows team's drafts based on the sample of picks which I have (which includes all top picks and a smattering of picks after that).

As you can see, the Red Sox are the clear #1, while the Padres, Cubs, and Rangers rank near the bottom. As a Cubs fan, the news comes as no surprise, since for nearly all of my first several years of following the team (I started following in 1987), the Cubs never seemed to have a home grown player contribute to meaningfully to the team. Likewise, it seems as though the Red Sox have had an endless array of talent coming up through their farm system.

Of course, this still doesn't account for the fact that teams have undoubtedly changed a great deal since 1965, and the philosophy and scouting behind a team's drafting and development strategy when the draft first began likely bears no resemblance to the operation of today. Additionally, the WAR Above Average per Pick value is tough to extrapolate to the entire draft since the data I have is heavy on top picks and those top picks have higher WAR and a higher variability in WAR.

While the numbers are interesting, and give a snapshot of how teams have done with their past drafts (again, this is only a sample of picks, not all picks - perhaps another study has shown WAR by team for all picks - if so, that would be superior to the above table), we can't fully get at the question of how large a difference there is between a smart drafting organization and a poor drafting organization without fuller data and a more refined unit of analysis.

Draft WAR by General Manager

Perhaps more relevant than a team's drafting record is the record of individual general managers. For study this I compared 10 current general managers with substantial draft records dating to back before the 2001 draft. I went back and obtained all picks (not just the sample I previously had) for each of these GM's during their tenure so that I had a substantial amount of data to work with.

Comparing each GM's actual WAR to the expected WAR from the model and then comparing the GM's to each other, gives us an idea of how successful each GM has been relative to the others. The table below shows each GM and his drafting record.

As you can see, of the 10 GM's studied, Billy Beane is unsurprisingly at the top of the heap, followed closely by Walt Jocketty, former GM of the Cardinals and current GM of the Cincinnati Reds. Bringing up the rear are Brian Cashman of the Yankees and Brian Sabean of the Giants.

So, Beane has had good drafts and the Sabean has had bad drafts. Is this a real difference, or is this a simple artifact of luck? To investigate this, we first calculate the weighted variance of the GM's WAR Above Average per pick. This observed weighted variance is .036. Then we calculate the expected weighted variance if all teams were equally good at drafting (with an expected WAR Above Average value of 0 and a SD of 2.0, which is the SD of WAR Above Average over all picks). This expected variance is .013. Taking the square root of the difference of the two variances gives an estimate of the standard deviation of the true drafting talent across GM's. (Observed Variance - Expected Variance due to Noise = True Variance). Calculating this with our numbers tells us that the true distribution of GM talent (including scouting, development, etc.) has a standard deviation of .150 WAR per pick.

With each team making about 45 picks per year, this means that the SD of the GM talent over an entire draft is a staggering 6.75 WAR. Basically a good GM will net his team an extra 6 or 7 wins above that of an average GM in a single draft. An outstanding GM (top 3% of all GM's) can net his team 13 wins above that of an average GM. Of course the signs can be reversed when talking about poor GM's. This distribution shows just how valuable a good GM can be. As we can see here, the difference in draft quality is more due to skill than chance (though of course, chance plays a major role), and a good GM and scouting system can make all the difference.

According to Moneyball, Billy Beane at one point was to be essentially traded for Kevin Youkilis. While Youkilis has become an outstanding player, the trade would not have been a good one. Beane, in just 4 years of the draft between 1998-2001, brought the A's essentially the equivalent of a Hall of Fame player, giving the A's 46 extra WAR over what the average GM would have been able to acquire. This advantage was gained on his drafting skills alone, not even accounting for his ability to make expert trades or sign free agents. Of course, time will tell how Beane's drafts will turn out during the years that followed the proposed trade, but the point is made - GM's have an enormous impact on a team's successes, even when considering their ability to draft alone.

Even when we scale back the WAR Above Average per Pick by about 25% to account for the regression effect (.15 estimated true standard deviation divided by the .20 observed standard deviation = .75), we still find that Beane is good for about 9 extra WAR per draft, while Sabean and Cashman are losing their teams about 9 WAR per draft.

Unfortunately, because draft picks take so long to develop, it makes it difficult to tell in "real time" how a GM is doing. However, this short study of 10 current long-time GM's shows us just how valuable a good GM can be.

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It's July 1, three months into the baseball season. With another three months remaining, it's a popular time for mainstream media members and basement dwellers alike to look back and determine their respective all-star teams, evaluate trade needs and look forward to what we might be able to expect the rest of the way.

In baseball we have grown accustomed to certain start and end points. The "first half" equals pre-All Star Game. So readily available, monthly splits are now popular. Understandably, the beginning of any given season represents the most widely cited starting point. There have been no shortage of great 10-game stretches by ballplayers in 2009, but remember when Emilio Bonifacio was making an MVP push back in mid-April?

One of many gifts that Fangraphs has given baseball enthusiasts is the ability to sort 365-day leaders in any number of statistics. So at the halfway mark of the 2009 season, I am going to take a different approach and put together an All-MLB team of sorts based on players' performances over the last 365 days - more or less a full season's worth of baseball. The only difference is that I will be using start and end points less commonly cited.

I will list my three top players since July 1st, 2008 at each position, toss in a starting rotation and then three relievers. You will notice that I highlight wOBA, as good a measure of offensive output as any. It combined on-base and slugging, but in a way that more accurately reflects their true respective values. Whereas OPS weights on-base and slugging equally, wOBA makes the proper adjustments. Its creator, Tom Tango, describes it this way:

Do we really need another statistic? Yes, we do. Instead of trying to take two statistics (OBP, SLG) and combine and correct their flaws in the hopes of getting one number, we prefer to start from scratch. Furthermore, by recasting the number onto the OBP scale, it makes it much easier for the reader to get a grasp on the number. wOBA is weighted on-base average (we call it an average rather than a percentage). When you look at wOBA numbers throughout the book, just think OBP, and you’ll be fine. In other words, an average hitter is around 0.340 or so, a great hitter is 0.400 or higher, and a poor hitter would be under 0.300.

Without further ado...

Catcher

             AVG   OBP   SLG   wOBA
Mauer       .356  .434  .547   .420
McCann      .308  .389  .509   .390
Soto        .263  .351  .441   .344

Notes: Joe Mauer is your clear leader here.

1st Base

             AVG   OBP   SLG   wOBA
Pujols      .345  .448  .702   .466
Teixeira    .309  .414  .591   .425
Youkilis    .314  .419  .592   .424

Notes: I can see an argument of Miguel Cabrera over Kevin Youkilis here, since Miggy has played 22 more games than Youk since last July 1.

2nd Base

             AVG   OBP   SLG   wOBA
Utley       .294  .403  .508   .398
Pedroia     .320  .388  .467   .378
Kinsler     .283  .353  .508   .378

Notes: Ben Zobrist didn't play enough games to get in the mix here but in case you had not noticed, he has been ridiculously awesome this season.

3rd Base

             AVG   OBP   SLG   wOBA
Wright      .331  .417  .537   .413
A-Rod       .267  .389  .535   .398
Longoria    .291  .366  .553   .391

Notes: Chipper Jones misses this list by a hair. Given how much more durable he has been than A-Rod, Longoria and Chipper, the extent to which David Wright (at least at the plate) has separated himself from the MLB third base pack is notable.

Shortstop

             AVG   OBP   SLG   wOBA
Ramirez     .325  .412  .559   .414
Jeter       .312  .382  .437   .368
Tulowitzki  .287  .367  .471   .354

Notes: There is a real logjam for that third slot. Jose Reyes did not play enough games, while Michael Young, Stephen Drew and Jhonny Peralta are all right there.

Left Field

             AVG   OBP   SLG   wOBA
Braun       .305  .383  .564   .406
Ibanez      .309  .371  .576   .401
Holliday    .292  .387  .479   .386

Note: Matt Holliday edges Jason Bay and Adam Dunn because the latter two don't play any defense.

Center Field

             AVG   OBP   SLG   wOBA
Beltran     .314  .400  .523   .399
Hunter      .309  .371  .529   .388
Granderson  .266  .361  .486   .372

Notes: Due to his standout defense, Matt Kemp may deserve a slot on this list. No matter how you cut it, these three plus Kemp have really separated themselves.

Right Field

             AVG   OBP   SLG   wOBA
Hawpe       .315  .396  .560   .405
Choo        .306  .403  .508   .398
Ethier      .297  .381  .538   .390

Notes: There are a lot of good right fielders in baseball right now. There are a few more players who may have a justified claim to this list.

Designated Hitter

             AVG   OBP   SLG   wOBA
Thome       .253  .382  .517   .385
Huff        .305  .359  .529   .373
Lind        .306  .361  .501   .369

Note: There is a pretty underwhelming crop of DH's in MLB these days.

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Starting Pitching

               IP     K/BB   ERA
1. Lincecum   231.1   4.10   2.61
2. Greinke    211.2   5.20   2.68
3. Halladay   233.2   5.91   2.50
4. Sabathia   247.2   3.64   2.58
5. Haren      220.1   6.19   2.98

Notes: I leave Johan Santana off because he lags these guys on his fielding independent numbers and has a high strand rate.

Relievers

             K/9    K/BB    ERA
1. Rivera   10.23  12.50    2.45
2. Broxton  13.13   3.89    2.50
3. Nathan   10.52   4.22    1.38

Notes: Look at Mariano Rivera's K/BB!

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There's my All-365 team. What would yours look like? Who's going to make a strong push over the next 365 days and show up on this thing next July 1? A couple of Justins - Verlander and Upton - come to mind.

As we get set for what is shaping up to be one of the most exciting second halfs in a while, whether looking back or ahead, we definitely welcome your take in the comments section on where things stand at the 2009 midway mark.

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"It's a fight, a blow-by-blow verbal battle."

- Vin Scully, June 30, 1959

One of the greatest baseball rhubarbs in my lifetime took place 50 years ago today. The "blow-by-blow verbal battle" occurred between two of the biggest rivals in all sports: the San Francisco Giants and the Los Angeles Dodgers, in just their second year on the west coast.

The game was played on Tuesday, June 30, 1959 at the Los Angeles Memorial Coliseum. The paid attendance of 59,312 was the largest Coliseum crowd since Opening Night when 61,552 fans were on hand to watch the St. Louis Cardinals beat the Dodgers, 6-2, while setting a new attendance record for a National League night game. (Interestingly, the Cardinals and Dodgers had set the previous league record on April 25, 1958 when Stan Musial's first Coliseum appearance attracted 60,635.)

The Giants and Dodgers were in a virtual tie for second place in the National League, 1.5 games behind the Milwaukee Braves. Milwaukee had beaten the New York Yankees, winners of eight of the prior ten World Series, in seven games to win the championship in 1957, then lost the title in seven games to the same Yankees in 1958. San Francisco had snapped the Dodgers' seven-game winning streak the night before when Jim Davenport and Willie Mays led off the 13th inning with back-to-back home runs en route to a 6-4 victory in what my Dad called "the most thrilling game ever played in the Coliseum" to that point.

Mays was to be heard from in more ways than one the following night. Batting second in the lineup, the "Say Hey Kid" slugged his 13th homer of the year (and fifth against the Dodgers) in the third inning to give the Giants a 2-0 lead and, according to Dad's game report in the Press-Telegram the following morning, "almost clouted another in the sixth inning, touching off a 10-minute rhubarb. While the fans hooted and hollered, the umpires changed their ruling twice and finally awarded Mays a ground-rule double. Rigney lodged a protest, but withdrew it after the game."

The batted ball was first ruled foul, then a home run and, finally, a double. I'll let Vin Scully, in what I believe is not only his most descriptive call ever but one of the greatest in the history of the game, take over from here.

Scully details the ensuing rhubarb, mentioning, in order, Drysdale, Mays, Giants manager Bill Rigney, third base coach Salty Parker, third base umpire Dusty Boggess, Dodgers first baseman Gil Hodges, shortstop Don Zimmer, first base umpire and crew chief Tom Gorman, Dodgers manager Walter Alston, left fielder Wally Moon, home plate umpire Ed Sudol, and Dodgers Vice President Buzzie Bavasi. (The fourth umpire was Stan Landes. He was stationed at second base and was never mentioned in Scully's call of the rhubarb.)

Although narrator Steve Bailey says the date was May 30, 1959, the incident actually took place on June 30, 1959. Bailey eloquently introduces the nine-minute clip, "Orchids to Vin Scully for a magnificent description of one of the wildest rhubarbs baseball has ever known."

Here is a word-by-word transcription of my favorite Scully call of all time (and, like everybody else, I love how he reported the ninth inning of Sandy Koufax's perfect game on September 9, 1965):

"Drysdale ready and the 1-1 pitch . . . curveball, cut on, there's a high flyball right down the left field line, right on the line, hits the foul pole and kicks foul. That's just about as foul as you can get without being fair.

Willie Mays hit the foul pole and it kicked off in foul ground. Rigney is telling Mays to trot all the way around. Salty Parker and Bill Rigney appealing to third base umpire Dusty Boggess . . . and now they're gonna wave Mays around and here come the Dodgers after Boggess.

If you know the Coliseum at all and you know the girder that supports the screen right down the left field line, Willie Mays hit a fly ball that actually hit that girder and then kicked off into foul territory. At first, Dusty Boggess called it foul but Rigney told Mays to go around anyway. And after Rigney and Salty Parker got into the discussion, Boggess suddenly ruled home run. The Dodgers came racing out of the dugout . . . a firecracker goes off back of home plate like to scare everybody out of ten years' growth . . . and the argument continues directly back of third base along the line. All four umpires along with a heated group of Dodgers . . . and the rhubarb continues about 30 feet down the line.

So Willie Mays, who is normally causing a lot of noise either at the Coliseum or Seals Stadium, has now really set off a bomb here at the Coliseum.

When you look at that girder down the left field line, there are many cables and wires that make it a very tough spot to look at. No doubt the Dodger contention is the ball hit one of the wires to make it foul.

But Boggess is now sticking to his guns. Drysdale is so mad he almost kicked 20 feet of the Coliseum out of the park. Gil Hodges right now is jaw-to-jaw with Dusty Boggess. Gil pointing first with his left hand, then with his right hand. Drysdale appealing to the gods right now. He just wants to holler at anybody who will listen. Don Zimmer is arguing with Tommy Gorman. The other three umpires now leave Boggess alone, and he is in the midst of lions.

Don Zimmer, Don Drysdale, Walter Alston, Gil Hodges, and Wally Moon are blistering Boggess, and Dusty every now and then seems to punctuate a Dodger's sentence by pointing with his left hand to that left field foul pole. At the very top of the foul pole, there are two slanting guide wires. One goes from the top of the pole to the right, down to the screen. And the other one goes from the top to the left, down toward the stands. The Dodger contention is that the ball hit the guide wire to the left and would be foul. Alston and Hodges and Zimmer and Moon continue to appeal. Gorman now tells Hodges to walk away, but Hodges goes right after Gorman. Zimmer will be hoarse in another two minutes. The veins on each side of his neck bulging out like the cable that actually holds up the left field screen.

Boggess sticking to his guns. The Dodgers continue to appeal, but Mays has touched all the bases and will come in with a home run. Gorman, who is the captain of this umpiring quartet, has now summoned Bill Rigney out of the Giant dugout. And both Gorman and Salty Parker are flanking Bill Rigney and, of course, Gorman doing all the talking.

Meanwhile, the Dodgers are still around Boggess at third. But watching Rigney's reaction, it looks like Gorman is going to call it foul . . . and Rigney is about ready to eat his glasses. Alston has walked away like a Philadelphia lawyer who has just won his case. Rigney slams his hat down and the gray hairs glistening under the lights. Bill is now going jaw-to-jaw with Boggess. Now he kicks at the dirt, hands on his hips, left hand thrown high in the air. Ed Sudol comes in to quiet the Giant manager down. Rigney's left hand, then his right hand up in the air. Now his hat is back on.

So, first the Dodgers appeal and walk away and now it's Rigney's turn to be on the griddle. All four umpires appear to be trying to placate Rigney, presenting their case. The Giant manager now starting to walk around, slamming his hands together, pointing with the right hand, then with the left. Now a big sweeping gesture with the left hand. Gorman comes after him now as if Rigney must have touched a nerve, and Gorman goes chewing right back after the Giant manager. Rigney now goes after Gorman, points with his left hand to that girder. Gorman answers with a right-handed gesture. Rigney bows at the waist with a sweeping right hand. And Gorman and Rigney are really going at it. Boggess comes over and Rigney like a mad traffic cop now with a right hand indicating that all the umpires are mad. Rigney kicks at the dirt, walks away with a hopeless gesture of both hands. Willie Mays comes out. Rigney drapes his left arm around Mays' shoulder and tells him to go to second base, 'I'll meet you halfway and what a riot.'

First it was ruled foul, then it was ruled fair, then the Dodgers won half a case and got Mays to go to second base. As soon as we get the ground rules on this particular play off the back of a batting card, we can pass them along.

Willie Mays hits the loudest double ever heard in Southern California or in the United States, for that matter. Rigney now comes to argue with the plate umpire Ed Sudol. Sudol pointing with his right hand toward the screen. Rigney pointing with his right hand . . . let's say, towards the Dodger dugout. Now Salty Parker comes down, and it's Rigney with his head just jerking a mile a minute, and now Sudol wants to talk to third base umpire Dusty Boggess. It's a fight, a blow-by-blow verbal battle.

Rigney has Boggess on his left and Sudol on his right, and right now Rigney is laying down the law, and the umpires come right back with words and gestures. Salty Parker, third base coach, with his arms folded across his chest, just listening right now. Rigney is concentrating his verbal fire on third base umpire Dusty Boggess. Sudol is now trying to draw some of the wrath of the Giant manager, but Bill wants to stay with Boggess. Rigney now whirls and since Sudol is walking towards the plate, Bill starts to go after him, then turns and goes back after Boggess.

Willie Mays, the cause of it all, at least he hit the ball, standing quietly at second base. Tommy Gorman and Ed Sudol have a meeting halfway between home plate and first base. Boggess has his hands full, with both Rigney and Salty Parker. We will have to wait to get the actual and official clarification. Walter Alston has come out of the Dodger dugout and, in the runway leading back towards the tunnel, he is now talking to Buzzie Bavasi, the Dodgers Vice President.

Rigney is exploding at Boggess so Gorman and Sudol are coming over again, trying to bail out Dusty. Gorman talking to Rigney. Rigney turns and starts to walk away, gives a big gesture with his hands and Gorman comes back with the same gesture. Now, plate umpire Ed Sudol has hollered up to the press box that the Giants will play the ballgame under protest, and it must be announced to the crowd. Listen, here comes the announcement."

After John Ramsey, the public address announcer, informed the crowd, amidst boos, of the protest, Bailey concluded the segment, "San Francisco manager Bill Rigney quickly forgot his protest because Sad Sam Jones pitched a one-hit, 2-0 shutout."

Jim Gilliam had the only hit, a disputed infield single in the eighth inning. According to Dad, "Gilliam's high chop behind the mound was the cheapest of hits, but a hit it was in the opinion of official scorekeeper Charlie Park. 'I hated to call it,' Park told Jones after the game. But Jones, brushing by and refusing to shake hands with Park, answered, 'I don't think it was a hit, whatever you call it.'

"Gilliam's hit bounced over Jones' head and was charged by shortstop Andre Rodgers, who over-ran and fumbled the ball. Park ruled that Gilliam would have beaten the play even if Rodgers had handled the ball cleanly.

"Rodgers and Giants manager Bill Rigney said it should have been called an error. 'I thought he called it too soon,' said Rigney with Park a listener in the clubhouse. 'If he had thought about it, he couldn't have called it that way. We'll never know if Rodgers could have thrown him out, but the way Rodgers throws, I think we had a chance.'

"Jones, who was aware of his no-hitter all the way, said, 'I thought sure the shortstop would get it. Had he caught the ball, he would have got Gilliam.' Then, turning to a group of questioning reporters, Jones said, 'Why don't you buy yourself another scorekeeper.'"

My father was one of the rotating official scorekeepers during his tenure covering the Dodgers and, in fact, was the official scorer during Koufax's perfect game. In an attached piece that accompanied his article, entitled "As Lederer Saw It," he wrote, "It was a hit. Had it happened in the first inning, there would have been no question. It was unfortunate that Jones lost the no-hitter, but it was the right call. I'm happy that I didn't have to make it, but I would have done the same."

Gilliam's high chopper was indeed a hit as was Scully's "blow-by-blow verbal battle" of one of the greatest baseball rhubarbs and calls of the past 50 years.

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