Thanks Mike for reminding me.
I do need to clarify a bit the difference between the HOF program, yearbook, and scorecard. Unfortunately, due to a lack of understanding, these words are often used interchangeably and incorrectly.
The HOF program is a fairly new publication for the BBHOF. As far as I can tell the HOF started making induction ceremony programs beginning in 1982. These commemorate and are distributed at the induction ceremonies themselves. They are usually very thin in comparison to the Yearbook. The cover and contents are different from the Yearbook. I believe these are usually freely distributed.
This is the 1984 HOF YEARBOOK.
This is the program (not mine. I got the pic off of ebay)
The scorecard is a third publication which is sold at the HOF Game played at Doubleday field. It is truly a scorecard with the grids in place for scoring of the game. Neither the HOF yearbook nor the program have ever had grids for scoring a game. Most of the scorecards are very thin and sometimes even a one page folded cardboard material. I believe these are also free to those attending the game.
Scorecards appear to have been produced starting in 1939. I can't confirm whether or not they have been produced every year. I would assume they would've been made every year there was a HOF game played.
The 1939 scorecard is a little different from the other years. It is listed as a program for Doubleday field, and is more along the lines of what a regular season game program would be like. There are multiple pages with ads and article. Towards the center are the scoring grids, without team names.
As I have never handled any of the scorecards from the 1940's I can't say when the HOF switched to the thinner format. The earliest one on ebay is 1943 which appears to be one page. Perhaps the 1939 edition is the only one like that as it was the first HOF game and 1939 was the centennial celebration of baseball.
Here is my copy.
Here is the 1943 edition I found on ebay
Hope that clears any confusion.
Best,
Mark