Well, it turns out there is a very useful report in Statsplus to do this: for any year's draft picks, it shows what their total WAR is: (e.g. https://statspl.us/brewster/draftyear?y ... league=100 for 2021).
But in order to do this effectively, we need to look at players whose career is essentially complete. So what I did was to download the CSV for each of the years between 2018 and 2027 (i.e. almost every player here will have retired already, and the few that haven't aren't likely to get many more WAR), and paste it into a spreadsheet with a separate tab for every year. Then I created formulas (using SUMIFS() and COUNTIFS()) to calculate the total number of players that were drafted and then signed to a minor league contract by each team (note that a player might be drafted but not signed), the total (and percentage) that had at least 1 WAR in BBA over their career, those players' total BBA WAR (I excluded any UMEBA WAR for this analysis), and the average war per pick.
Then I did totals across all ten of those years, the result shown in the table below:
| Rnd | # | #>1 | pct. | total war | avg war/pick |
|---|---|---|---|---|---|
| 1 | 270 | 156 | 57.8% | 2564.7 | 9.499 |
| 2 | 285 | 44 | 15.4% | 420.7 | 1.476 |
| 3 | 236 | 15 | 6.4% | 107.8 | 0.457 |
| 4 | 184 | 8 | 4.3% | 33.5 | 0.182 |
| 5 | 157 | 9 | 5.7% | 31.3 | 0.199 |
| 6 | 187 | 4 | 2.1% | 24.9 | 0.133 |
| 7 | 183 | 2 | 1.1% | 2.8 | 0.015 |
| 8 | 175 | 5 | 2.9% | 37.8 | 0.216 |
| 9 | 162 | 3 | 1.9% | 17.5 | 0.108 |
| 10 | 171 | 2 | 1.2% | 2.8 | 0.016 |
| 11 | 161 | 4 | 2.5% | 26.9 | 0.167 |
| 12 | 154 | 2 | 1.3% | 71.8 | 0.466 |
| 13 | 142 | 0 | 0.0% | 0 | 0.000 |
| 14 | 138 | 0 | 0.0% | 0 | 0.000 |
| 15 | 145 | 0 | 0.0% | 0 | 0.000 |
| 16 | 152 | 3 | 2.0% | 9.8 | 0.064 |
| 17 | 137 | 1 | 0.7% | 7.1 | 0.052 |
| 18 | 146 | 2 | 1.4% | 45.5 | 0.312 |
| 19 | 138 | 0 | 0.0% | 0 | 0.000 |
| 20 | 143 | 0 | 0.0% | 0 | 0.000 |
| 6:10 | 878 | 16 | 1.8% | 85.8 | 0.098 |
| 11:20 | 1456 | 12 | 0.8% | 161.1 | 0.111 |
The second-to-last row totals all players drafted between rounds 6 and 10, and the last row totals all players between rounds 11 and 20. During the last few years of this analysis the draft was expanded to 25 rounds, but I only tracked through round 20 since those were the only ones available for every year.
To be frank, the results to me are quite different than I expected. I thought there would be a lot of early round flubs as well as a lot of later round gems thrown in but there is little evidence of that. A whopping 58% of all first-round signed picks had at least 1 WAR through their major league career , and the average signed first-rounder had 9.5 WAR over their major league career. In fact, 75% of the total WAR by all draft picks was by first rounders, with more than 90% of the total by draft picks in the first three rounds.
In fact, after the third round (average < .5 WAR per signed pick; 6.4% > 1 WAR), there is not a lot of utility gained by picks. The fourth and fifth round does show about 5% chance of getting at least 1 WAR in majors, but the average WAR is still only .19 between fourth and fifth round, not much more than the .106 WAR from rounds 6 to 20 total.
This result was very surprising to me. Thoughts?
