## Friday, May 15, 2009

### The Marginal Impact Statistics Have on Hall of Fame Voting

A couple of weeks ago I presented a binary (logit) model of Hall of Fame voting. I looked at all players whose first year of eligibility was from 1990-2009 (except for Pete Rose). The model's equation estimates the probability that a player would be elected to the Hall of Fame (though not necessarily in his first year of eligibility). Of course, there are coefficient estimates and what I do here is give the change in the probability of being elected due to a change in a hypothetical player's stats.

I made up a player who had a 0.290 career AVG, had 6 100 RBI seasons, won 1 MVP award, played in 8 all-star games and had 8,894 career plate appearances. This player was not a catcher and did not achieve 3,000 hits. He had a world series impact of 18 (that is, his world series PAs times his world series OPS). It is like he had a .750 OPS in 24 world series PAs.

The first line in the table below shows that his probability of being elected was .50 or 50%. The rest of the table shows what his probability would be if his stats changed. For instance, if his career average had been .300 instead of .290 (with nothing else changing), his probability (or PR) rises to .663. Another 10 point gain in average brings it to .795. But if he had only hit .280, the PR is just .337. Of course, other things might have changed if his averaged had changed. Maybe 100 RBI seasons or all-star games played would have been different. But I will have to assume that they did not. The different cases for AVG are in red. More discussion follows the table. You can see a larger version of the table if you click on it.

Adding 1 100 RBI seasons raises PR to .638. Taking 1 away lowers it to .362. So the 100 RBI seasons has a powerful impact, like AVG. Adding an MVP award raises PR to .59.But all-star games played in (AS) might have the strongest effect. Going from 8 to 9 all-star games raises the PR to .80. If all-star games falls to 7, PR is just .20.

Having 3000 hits, not surprisingly, raises the PR to 1.00 or 100% (actually its a little less but it is above 99.99%). If the player had been a catcher (see the 1 in the C column), it jumps to .973. The WS or world series impact is very slight. Adding or subtracting 500 career PAs matters alot. Adding 500 PAs bumps PR up to .657 and taking 500 away drops it to .343.

I also did the same test for an actual player, Jim Rice. His predicted PR was the closest of any of the players in the study to .50 at .595. The next table has the marginal changes like the one above. Maybe the biggest impact for Rice is all-star games. If he had just one less, his PR falls to .269. In general, his table looks similar to that of the hypothetical player.