I decided to do the research myself. Over time, we would expect the value of the player selected versus the slot selected will form a continuous distribution curve where the players selected earlier will have more value than those selected later. Here is an old article about draft picks: MLB Draft and WAR. It shows a drop over the major leagues (for its time period) between the average protected pick (1-10) 1.417 WAR/year and the next ten (11-20) 1.115 WAR/year.
Looking up draft picks for the Angels in particular. We have had 2 first over all Picks Danny Goodwin –1.7 career WAR over small parts of 7 seasons (basically a bad player who was given a lot of chances to prove himself.) Darin Erstad 32.4 WAR over 14 years, OPS over 100 in 3 of those years. Small sample size, but if we could get an Erstad 1 out of 2 times, I would say screw the values that we are teaching our kids and lose every game. But it is unlikely that we would receive the first overall pick this year.
We have had 19 2-10 Overall Picks, including Troy Glaus and Jim Abbott. Also 4 with negative WAR. This is a total of 123.7 career WAR or average of 6.51 per player. Or more importantly to me, 5 played at the Kenny Landreaux level or better.
We have had 16 11-20 Overall Picks, including Jim Spencer, Frank Tanana, Jered Weaver, and Tom Brunansky. (4 with negative WAR.) Eliminating recent picks Cowart and Cron, leaves 14. This is a total of 162.6 career WAR or average of 11.61 per player. In this group, 5 played better than the Kenny Landreaux mark.
So by any WAR standard (peak or distributed), the Angels did better with the 11-20 picks than the 2-10 picks. This is a small sample with a number of variables (better scouts at different times, better farm developmental system, focus on high school versus college, etc.) But the conclusion is that there is no indication that a ‘protected pick’ will perform better than the next 10.
Looking farther down, we have had 13 21-30 picks, many of whom are still playing including Hank Conger and Mike Trout (both supplemental picks.) 2 have had negative WAR including Brandon Wood’s -3.8. Really not enough data here.
Round 2 (including supplements.) 40 players drafted including John Lackey, Bruce Bochte, and Dave Kingman. 18 played in the majors with 110.8 career WAR, 6.2 per major leaguer.
Round 3 (including supplements.) 52 players drafted including Tim Salmon, Wally Joyner, and Carney Lansford. 21 played in the majors with 156.5 career WAR, 7.5 per major leaguer.
Round 4. 48 players drafted including Garret Anderson and Mike Witt. 18 played in the majors with 84.2 career WAR, 4.7 per major leaguer.
Round 5. 48 players drafted including Bobby Jenks. 13 played in the majors with 5.7 career WAR, .4 per major leaguer.
Round 6. 49 players drafted including Troy Percival, Devon White, and Clyde Wright. 12 played in the majors with 99.5 career WAR, 8.3 per major leaguer.
In conclusion, the baseball draft is such an inexact science that after 52 years of the Angels existence that the distribution of good players in the first 10 has not yet caught up to the second 10. And the distribution of good players in the second round has not caught up to the seventh round.