On Thursday Carlos Delgado hit four home runs in four consecutive at-bats to become just the 15th man to collect four homers in a game and just the sixth man to hit four consecutive in one game.
Given the rarity of the event, it got me to thinking about the odds of such an accomplishment. Given that Delgado had 42 home runs and 704 plate appearances on the season, the odds in any plate appearance of hitting a home run are 5.97%. The odds of him jacking one out of the park four times in a row are equal to the odds above multiplied four times or 0.0013%, pretty remote. Given that Delago played 160 games, the odds of his hitting a home run in his first four plate appearances in any one of those games are .20% (160 x .0013%) or one in five hundred. Given that he averaged about 4.4 plate appearances a game, he often had the opportunity to hit four home runs in more than 4 plate appearances, increasing the four-homer odds fivefold and doubling the odds of hitting four consecutively. His odds of hitting four straight in one game improve to .28% and of hitting 4 in a game increase to .53% given this approach (96 games at 4 plate appearances and 64 at 5óOf course Delgado did not just have four- and five-PA games but this is as close an approximation as possible without delving into each box score and it will also jibe with the historic research that follows).
So at best, Delgado had a one-in-200 chance of hitting four home runs in a game this year. The fact that he was facing the Tampa Devil Rays didnít hurt his odds much though.
Actually, using this methodology revealed that Delgado's odds of hitting 4 dingers in a game were second all-time to Barry Bonds great 2001 season (.5274 to .5270). Though the odds don't seem to have panned out for anyone besides Delgado and Willie Mays, whose 1955 season ranked 31st (he hit 4 homers in a 1961 game though and his odds were 280th all-time that year).
By the way, using this method for setting the odds for 4-HR games predicts that there would only by about six all-time (6.222654872 actually). The year with the best odds was 2001 in the NL with a one-in-five shot and the worst was 1878 in the NL with a 0.00060% chance.
Given that Delgado was the fifteenth man to hit 4 homers in a game, one can either declare that the probabilities based on estimated plate appearances per game don't accurately reflect reality or that players can affect their own performance when such a feat is theirs for the taking. Take your pick. Given that a 6-plate appearance game (such as Bobby Lowe's 4-HR game in 1894) improves your odds greatly (30-fold over four plate appearances), the estimates are surely just that. However, I like to think that great performances require great effort not just favorable odds and that 4-home-run games are no exception.