How Possible Is a Five-Homer Game?

by
December 11, 2020

A recent post in the Effectively Wild Facebook group sparked my curiosity. A poster named Tim wrote: “Record I’d like to see set that isn’t inconceivable: Player gets 5 HR in a single game.” That record is not inconceivable, because it has been accomplished at least five times in the minor leagues.

In fact, the professional baseball record is eight home runs in a single game, set by catcher Jay Clarke of the Corsicana Oil Cities in a 51-3 win over the Texarkana Casketmakers in a Texas League contest in 1902. The last minor leaguer to hit five homers in a single game was Dick Lane of the Muskegon Clippers in 1948.

Known Five-Homer Games
Date Player Team Opponent Outcome League HRs Hit
6/15/1902 Jay “Nig” Clarke Corsicana Oil Cities Texarkana Casketmakers W, 51-3 Texas League 8
5/11/1923 Pete Schneider Vernon Tigers Salt Lake City Bees W, 35-11 Pacific Coast League 5
5/30/1934 Lou Frierson Paris Pirates Jacksonville Jax L, 17-12 West Dixie League 5
4/29/1936 Cecil Dunn Alexandria Aces Lake Charles Skippers W, 28-5 Evangeline League 5
7/3/1948 Dick Lane Muskegon Clippers Fort Wayne Generals W, 28-6 Central League 5

But of course the poster was in all likelihood talking about the MLB record of four in a game, which has stood since 1894. But it was a commenter on the post that really piqued my interest. They simply asked: “Would a team really continue pitching to a guy who’s already had 4 HR in a game though?”

It’s a valid question to ask, and it set me down a rabbit hole of seeing just how many players had a plate appearance with four homers already in a game, and how those plate appearances went. Looking back at history isn’t necessarily the best way to predict future behavior, but it is a fun exercise if nothing else, because frankly, before conducting this research I had no idea how many players ever had a crack at a fifth home run.

Before we get into that, I have a couple of quirky observations. The Atlanta Braves franchise has been involved in five of these games, more than any other team (Bobby Lowe, Gil Hodges, Joe Adcock, Willie Mays, Bob Horner). That includes having a player hit four homers in a single game in all three of the franchise’s homes (Boston, Milwaukee and Atlanta). Three teams — the Philadelphia Phillies (3; Ed Delahanty, Chuck Klein and Mike Schmidt), Boston/Milwaukee/Atlanta Braves (3; Lowe, Adcock, Horner), and Brooklyn/Los Angeles Dodgers (2; Hodges, Shawn Green) — have seen players hit four homers in a game more than once.

All-Time Four-Homer Games in MLB
Date Player Team Opponent Outcome Chance at 5th HR?
5/30/1894 Bobby Lowe Boston Beaneaters Cincinnati Reds W, 20-11 Yes
6/13/1896 Ed Delahanty Philadelphia Phillies Chicago Colts L, 9-8 No
6/3/1932 Lou Gehrig New York Yankees Philadelphia Athletics W, 20-13 Yes, twice
7/10/1936 Chuck Klein Philadelphia Phillies Pittsburgh Pirates W, 9-6 (10) No
7/18/1948 Pat Seerey Chicago White Sox Philadelphia Athletics W, 12-11 (11) No
8/31/1950 Gil Hodges Brooklyn Dodgers Boston Braves W, 19-3 No
7/31/1954 Joe Adcock Milwaukee Braves Brooklyn Dodgers W 15-7 No
6/10/1959 Rocky Colavito Cleveland Indians Baltimore Orioles W, 11-8 No
4/30/1961 Willie Mays San Francisco Giants Milwaukee Braves W, 14-4 No
4/17/1976 Mike Schmidt Philadelphia Phillies Chicago Cubs W, 18-16 (10) No
7/6/1986 Bob Horner Atlanta Braves Montreal Expos L, 11-8 No
9/7/1993 Mark Whiten St. Louis Cardinals Cincinnati Reds W, 15-2 No
5/2/2002 Mike Cameron Seattle Mariners Chicago White Sox W, 15-4 Yes, twice
5/23/2002 Shawn Green Los Angeles Dodgers Milwaukee Brewers W, 16-3 No
9/25/2003 Carlos Delgado Toronto Blue Jays Tampa Bay Devil Rays W, 10-8 No
5/8/2012 Josh Hamilton Texas Rangers Baltimore Orioles W, 10-3 No
6/6/2017 Scooter Gennett Cincinnati Reds St. Louis Cardinals W, 13-1 No
9/4/2017 J.D. Martinez Arizona Diamondbacks Los Angeles Dodgers W, 13-1 No

Of the more than 19,900 players in MLB history, only three of them have ever taken a turn at bat with a chance for a fifth home run in an MLB game. Amazingly, Lou Gehrig and Mike Cameron both came to the plate twice with a chance for a fifth homer, giving us a total of five plate appearances to consider:

May 30, 1894 — Lowe — bottom of the eighth.

June 3, 1932 — Gehrig — top of the eighth.

June 3, 1932 — Gehrig — top of the ninth.

May 2, 2002 — Cameron — top of the seventh.

May 2, 2002 — Cameron — top of the ninth.

Bobby Lowe

Bobby Lowe was a hard hitter who could play all over the field. He was playing second base the day he became the first major leaguer to ever hit four home runs in a single game. Lowe made an out in the first inning, but then homered twice in the third and once in the fifth and sixth innings of the second game of a Memorial Day doubleheader at the Congress Street Grounds in Boston.

Following his fourth home run of the day, Boston fans showered the field in coins as tribute to Lowe, an amount totaling $160, the equivalent of more than $4,800 in 2020. He came to bat once more in the game, singling in the bottom of the eighth. He set a record of 17 total bases in a game, which stood until Ty Cobb’s 6-hit, 3-homer game in 1925. So the Cincinnati pitcher did give Lowe a chance to hit again after his four homers, but of course pitching was a fundamentally different exercise in 1894.

Lou Gehrig

The Iron Horse matched Lowe in hitting home runs in four straight at-bats, but he did so in his first four of the day. Gehrig homered in the first, fourth, fifth and seventh innings in one of the wildest offensive games of the 1930s. The Yankees hit seven home runs in the effort, which tied the MLB record at the time. Tony Lazzeri also hit for the cycle, the only instance of a four-homer game and a cycle happening in the same contest in MLB (it happened at least once in the minor leagues in 2019, as Yasmany Tomás hit four homers and Matt Szczur hit for the cycle for Reno on May 20).

Gehrig came to bat twice after hitting his fourth home run, grounding out in the eighth inning before a dramatic at-bat in the ninth. At the time, Shibe Park’s center field measured 468 feet from home plate. In his ninth inning at-bat, Gehrig launched a ball toward this remote area, which A’s center fielder Al Simmons caught “only a few steps from the furthest corner of the park. A little variance to either side of its actual line of flight would have sent the ball over the fence or into the stands.”

Mike Cameron

It was nearly 70 years until a player had a chance at a five-homer game again. Mike Cameron had been struggling at the plate and had visited an eye doctor the week before. The Seattle center fielder started this game with a bang, hitting back-to-back home runs with Bret Boone in a 10-run top of the first inning. Cameron and Boone are the only teammates to ever hit two homers in the same inning. But his record-setting day was not done as he homered in the third and fifth innings as well. Cameron was the first AL player to hit four in a game since Rocky Colavito in 1959, and he got a standing ovation from the Comiskey Park crowd.

Cameron’s first crack at a fifth home run came in the seventh. Mike Porzio hit him with a pitch on the back of his left thigh, causing the South Side crowd to boo. In the ninth inning against Porzio again, Cameron hit a long drive to right field which was tracked down on the run by Jeff Liefer in front of the warning track for an out. Like Gehrig, he was close to a fifth home run on the night but came up just short. Perhaps a consolation was that he robbed a potential grand slam from Magglio Ordoñez in the game as well.

So there you have it. All five plate appearances in MLB history in which a player had a chance to hit a fifth home run in a game, and opposing pitchers pitched to the batter just about each time. But just because they did in the past doesn’t mean that in the future that would still occur. All five of these PAs came during blowout games, and at least in the case of Cameron’s game, that almost definitely factored into the decision. In a closer contest, maybe that decision doesn’t get made.

The upshot is that in the five times players have batted with a chance to hit a fifth home run, the batter has flown out to the warning track twice. That gives us a hope that as unlikely as it seems, yes, someone someday might just hit five over the fence in a single game.

Joe Vasile is a broadcaster for the Scranton/Wilkes-Barre RailRiders and hosts the baseball history podcast Secondary Lead.

Sources:

Armour, Nancy. “Four Play: Mariners’ Cameron Ties Homer Record Vs. White Sox.” Pittsburgh Post-Gazette. May 3, 2002.

Brandt, William E. “Equals Two Marks in 20 to 13 Victory.” New York Times. June 4, 1932.

New York Times. “Bobby Lowe Dead: Baseball Star, 83.” December 10, 1951.

https://officialdata.org/us/inflation

https://sabr.org/research/article/four-homers-one-game

Baseball-Almanac.com





 

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Jimmember
3 years ago

This was interesting and fun. Thank you!

5
Joe Vasile
3 years ago
Reply to  Jim

Thanks! This has been something I’ve been meaning to look into and write about for a while now and I’m happy that I finally got around to it and you like it!

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Justin
3 years ago

Awesome stuff…thanks for this one!

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WARrior
3 years ago

I submitted to CR a lengthy analysis of the probability of hitting three HR in a game. This was more than two months ago, so I don’t hold out much hope that it will be published (I have another article still languishing there after nearly two years). I didn’t address the question of 5 HR, but the formulas I used can be adapted to that issue.

The probability of a player hitting 5 HR in a game, p5HRG, is:

p5HRG = pHRexp5*(1-pHR)exp(AB/G-5) *F(5)

where pHR is the probability of hitting a HR in any random AB (career HR/career AB); AB/G is the player’s career average AB per game; and F(5) is a fractional factorial, necessary because AB/G values are generally not whole integers. I go into great detail in this paper on how to calculate fractional factorials, but basically, it works like this:

If a player has fewer than 5 AB in any particular game, he of course can’t hit 5 HR in that game. If he has exactly 5 AB, there is just one way he can hit 5 HR, by hitting a HR in every one of his AB. If he has 6 AB, there are six ways he can hit 5 HR, given by:

6*5*4*3*2/5!

For 7 AB, there are 21 ways, and for 8 AB, usually the maximum number of AB in any game in any player’s career, there are 56 ways.

I determine the number of games in a player’s career in which he has 5 AB, games with 6 AB, and so on. I multiply the 5 AB games by 1, the 6 AB games by 6, the 7 AB games by 21, and the 8 AB games by 52. I add these totals—each of which represents the number of ways a player could hit 5 HR in that game–to get a total F(5) value, and divide by the total number of games to get an average F(5) value per game. This is the value which goes into the formula above. The validity of this approach has been validated by a lot of data, which I present in that full article.

Here are a couple of examples, using the two most prolific HR hitters of all time, Babe Ruth and Mark McGwire. Ruth’s career F(5) was 0.279, while McGwire’s was 0.147. I’ll mention in passing these are relatively low values, reflecting that these hitters walked a lot, and thus had relatively few games with 5 or more AB. Plugging these and the other relevant values into the formula above, it turns out that both hitters had a very similar probability of a 5HR game (5HRG), about 1.4 x 10-6 for Ruth, and 1.3 x 10-6 for McGwire, or about one in a million. In other words, either one of these all-time sluggers would have had to play about one million games, on average, to have a single 5HRG.

We can use the same formula to estimate the probability that anyone would hit 5 HR in a game. We begin with a league average player. Using data from 1922-2020, the average HR/AB is 0.0245, the average AB/G is 3.80, and the average F(5) is 0.436. Plugging these values into the formula, we find that the probability of an average player having a 5HRG is about 4 x 10-9, or about one in 250 million. There have been a total of a little more than 3 million player games during this period (determined by dividing the total number of AB by the average number of AB/G), so the probability of a 5HRG during that span is about 12 x 10-3, or one in eighty. This is a rough calculation, I have made some simplifying assumptions about league averages, but for our purposes they don’t matter.

Fractional factorials, or F-values, can also be used to determine the average number of AB a player will have to hit an additional HR in a game in which he has already hit one or more. The formula is F(n+1)/F(n), or for a 5 HRG, it’s F(5)/F(4). E.g., for Ruth, it’s about 0.225. That is, if he had managed to hit 4 HR in game, on average, he would have about a quarter of AB left. Or over a very long period, in which he had enough time to have some 4HRG, he would get a fifth AB about one-fourth of the time.

I will close by noting that calculations like these assume randomness. E.g., it’s assumed that if a player hits multiple HR in a game, he’s just as likely to get an additional AB as if he didn’t hit those HR, and just as likely to hit a HR in any additional AB as in any other AB. I have discussed this issue in the full analysis, but I’ll just point out first, that players who hit 2, 3 or 4 HR in a game have on average more AB in that game than their career average (about 0.5 AB more per HR). As you note, multiple HRG often are blowouts. We expect this, because a) a player hitting several HR contributes to that blowout, and since his HR might be partly due to poor pitching, his teammates also may create a lot of offense; and b) when a team generates a lot of offense, its players come to the plate more often, giving the player an extra AB.

Second, the number of career 3HRG by all players is more than would be expected based on randomness. This does not appear to be the case with career multi-hit games, the number of which can be predicted by a formula similar to that above, using BA in place of pHR. So perhaps a 5HRG is more possible than a simple calculation concludes.

A final note: Very improbable things do happen in baseball. In my analysis, I found that Mookie Betts had a probability of about one in half a million of six 3HRG in his first 800 or so games. That is by far the lowest probability of any player with multiple 3 HRG. The most improbable accomplishment I’ve found is Fernando Tatis (the father, not the son), hitting 2 GS in one inning. That comes in at about 1.4 * 10-8, or about one in 70 million.

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tmthjdbmember
3 years ago
Reply to  WARrior

Wouldn’t you want to do this based on PA not AB? Or maybe PA-IBB? (Though I don’t think they tracked IBB in Ruth’s day.) Until it’s a walk it coulda been a dinger!

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WARrior
3 years ago
Reply to  tmthjdb

It doesn’t make much difference. Either AB or PA can be used, because they are simply.a vehicle for estimating the probability of doing something in a game. For any player, the probability of hitting a HR per PA is always going to be lower than the probability of hitting a HR per AB, but the average PA per game is greater.

E.g., if you go through the Ruth calculation using AB, you get 1.28 * 10-6. If you use PA, you get 1.29 * 10-6. For McGwire, AB yields 1.29 * 10-6, PA gives 1.48 * 10-6. And these are outliers, in the sense of having very high walk rates. For a more typical player, e.g., Steve Finley, the numbers are essentially identical, 1.66 * 10-8.

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WARrior
3 years ago

Here’s another way to look at it. There have been 291,973 HR hit from 1922-2020. There have been about 15,000 2HR (no more, no less) games (I don’t have the exact number, but it’s close to that). There have been 615 3HRG, and 15 4HRG. From these figures, we can calculate that there have been about 260,000 HRG, that is, games in which a player hit one or more HR. The fraction of those games in which the player hit 2 or more HRG is 6.01%. The fraction of the latter games in which 3 or more HR were hit is 4.03%. The fraction of games in which 3 or more HR were hit in which 4 HR were hit is 2.38%.

The fractions decrease, because the more HR a player hits in a game, the fewer AB he will have, on average, to hit another. The fraction of 4HRG in which a player would be expected to hit a fifth HR is thus less than 2.38%. If it were 2%, one would expect 0.3 5HRG; if it were 1%, one would expect 0.15 5HRG. There have been 3,132,363 player games in the 1922-2020 period. The first value, 0.3 5HRG, would correspond to one 5HRG in about ten million player games; the second value, 0.15 5HRG, would correspond to one 5HRG in about twenty million player games.

Those estimates are probably better than the one I posted above, because the latter is based on a league average player. But using league average players skews the result, because most multi-HR games are hit by players who are above average in HR/AB. The probability of hitting 2 HR in a game, other things equal, increases with the square of HR/AB, and for a 3HRG, with the cube of HR/AB, and so on. So more multi-HR games are recorded than would be predicted based on league average HR/AB.

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jrogersmember
3 years ago

I was at the Josh Hamilton game at Camden Yards, and I will say that despite not having an at-bat after the 4th, he was very close to 5 HR. In his 2nd or 3rd at-bat, he hit a double off the wall, about 3 feet shy of going over. His 4th HR could have then been his 5th HR if the rest went the same.

The O’s were not pitching around him (they left in Darren O’Day with the platoon disadvantage), and a lot of the small crowd that day was rooting for him to hit #3 and #4.

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