This issue came up in ALAN ROBINSON's article titled Parker wonders if drug use keeps him out of HOF. It compares Parker to recent inductee Jim Rice and others in an attempt to show that Parker might be Hall-worthy. It generally relies on conventionals stats. I don't think Parker has an especially strong case. But it is not bad, either.
Here are some things I came up with. Parker ranks 308th in wins above replacement level among position players with 37.9 at Sean Smith's site Top 500 Position Players. Rice is ranked 257th with 41.5. Neither of those ranks seems impressive.
I have a site which ranks players by the Win Shares Per Plate Appearance. Through 2001, Rice ranked 197th with 20.17 WS per 648 PA among outfielders. Parker was Parker 176th 20.81. Again, not really impressive for either guy.
Baseball Reference has a couple of measures of who is Hall-worthy. One is the "Hall of Fame Monitor." BR says "This is another [Bill] Jamesian creation. It attempts to assess how likely (not how deserving) an active player is to make the Hall of Fame. It's rough scale is 100 means a good possibility and 130 is a virtual cinch. It isn't hard and fast, but it does a pretty good job." Click here to see the rankings. Parker has a score of 124 which ranks 110th while a "Likely HOFer ≈ 100." Rice ranks 90 with a score of 144. So this suggests that both had careers that normally get you in, based on the voters' preferences. Maybe the drug use could be affecting Parker here.
One issue here is that over the years players have gotten in by the BBWAA or the Veteran's committee. The latter has changed its procedures in recent years, so it may not be clear if these patterns will hold in the future and they probably did not always agree with the BBWAA. It would be interesting to have separate formulas for each. Anwyay, if you don't get in by the BBWAA, it usually takes awhile before you are eligible for the Veteran's Committee.
BR also has its Hall of Fame Standards Batting and says "It is used to measure the overall quality of a player's career as opposed to singular brilliance (peak value)." Parker has a score of 41 which ranks him 135th while the "Average HOFer ≈ 50." Rice is ranked 116th with a score of 43. So both guys fall a little short here. But they are close. Parker could argue he is close enough to Rice to get in.
A few months ago, I came up with my own regression based formulas for estimating the % of the votes a player might get in his first year of eligibility or his probability of getting in at all based on voting patterns and the apparent preferences of the voters.
One model was an OLS regression. You can read about that at What Determines Vote Percentage In The First Year Of Hall Of Fame Eligibility? (Part 2). This one estimated first year eligibility vote %. It took into the following variables MVP awards, getting 3000 hits, getting 500 HRs, all-star games, Gold Gloves, getting 500 stolen bases, world series performance and career plate appearances. The model estimated that Parker would get 28.8% while he actually got 17.5%. So a little less than expected but if you read the link you will see that others did even worse.
The other study I did was Predicting Who Makes The Hall Of Fame Using A Logit Model. That model took into account career AVG, number of seasons with 100 RBIs, all-star games, career plate appearances, MVP awards, world series performance, getting 3000 hits and being a catcher. Parker did not do well here but I concluded "If Dave Parker had 8 all-star game instead of 6, he goes from a P of 8% to over 60%." Maybe without the drug use he would have made more all-star games and it would put him in the Hall of Fame. Rice's probability of making the Hall was about 59.5%.
So I don't really see any strong case for Parker. But some evidence supports him.