Joe Posnanski

Stacking Martinez up against history

Stacking Martinez up against history

Let's have some fun with math. On Monday, J.D. Martinez became just the 18th player in baseball history -- and the 16th in the last 100 years -- to hit four home runs in a game.

Martinez is a good hitter; it was good for him to have this game to remind people of that. He worked his way up the hard way; he was a 20th-round pick out of Nova Southeastern University. Even after winning the New York Penn League batting title in his first Minor League season and crushing the ball in his second, the Baseball America diagnosis was that he "profiles as a second-division regular," which seems less a scouting report than a grumpy curse someone throws at you when you try to squeeze 15 items into the 10-items-and-under supermarket line.

But they were right: Martinez was a second-division semi-regular for some dreadful Astros teams before being released and picked up by Detroit. He was given an actual regular job with a good Tigers' team, and he responded by hitting .315 with some power. The next year, he hit 38 home runs, made the American League All-Star team and got an MVP vote or two. Last year, again, he hit .300 and slugged over .500, but by various metrics struggled so much in the outfield that it overshadowed much of his hitting.

Then in July this year, the Tigers dealt Martinez to Arizona, where he had been struggling somewhat until Monday -- four homer games do tend to end slumps.

So to the math, I asked Statcast™ guru Tom Tango to whip up a fairly quick, easy and unscientific formula to determine just how unlikely it is for a good hitter like J.D. Martinez to hit four home runs in a game. The math, I think, leads us to interesting places.

First, we need to come up with a rough home run percentage for Martinez. Tango did this the easy way, by dividing Martinez's home runs in recent years by his at-bats. He came up with 6.85 percent. Martinez's home run rate this year is higher than that, but let's be honest -- even that 6.85 percent rate is ridiculously high. Babe Ruth hit home runs 6.7 percent of the time. Barry Bonds hit homers 6.1 percent of the time. So we're being more than fair to J.D. Martinez.

Now, are we saying that Martinez's home run stays constant at around seven percent? Of course not. It's so much more complicated than that -- home runs depend on stadium, wind, altitude, health, age, who is pitching and countless other factors. We can't come up with a true home run percentage for Martinez, but the 6.85 percent seems as reasonable as anything else.

Anyway, let's go with it. It's all for fun, anyway.

Next, it comes down to plate appearances. With just four plate appearances, the mathematical chances that Martinez would hit four home runs are very slim -- 45,000-to-1 according to Tango's calculations (77,000-to-1 if you put Martinez's home run chances at a more realistic six percent). Only one player in baseball history (Carlos Delgado in 2003) has hit four home runs in a four-plate-appearance game.

But it turns out that Martinez got five plate appearances Monday -- and that's a whole different thing. With five PAs, the odds drop significantly, to 9,000-to-1. If he would have happened to get six plate appearances, the odds drop much more, down to 3,000-to-1.

If these odds sound low to you -- they did to me -- you have to consider that plate-appearance thing. Truth is, more often than not, hitters (and especially middle-of-the-lineup hitters) do not get five-or-more plate appearances.

Look: I would say only 10 true power hitters got even 1,000 games career with five-or-more plate appearances: Alex Rodriguez, Henry Aaron, Barry Bonds, Rafael Palmeiro, Babe Ruth, Lou Gehrig, Willie Mays, Ken Griffey, Albert Pujols and Stan Musial. So using the odds, 9,000-to-1, that means at least one of those should have had a four-homer game.

Two of them did: Gehrig and Mays.

See? Isn't math fun?

Anyways, what the math tells us is this: Hitting four home runs in a game takes a perfect storm. Ruth never did it. Bonds never did it. Mark McGwire ... Jim Thome ... Harmon Killebrew ... Sammy Sosa ... it never happened.

For 16 others, though, it all came together. All but a couple of them were big power hitters (for an exception, see blog post on Pat Seerey), and they got five-or-more at-bats (Seerey got seven at-bats), and conditions were ripe (Gil Hodges and Joe Adcock did it at cozy Ebbets Field; Josh Hamilton did it at home run friendly Camden Yards).

So, no, we can't come up with real odds for Martinez to do it ... especially at Dodger Stadium ... especially off four different pitchers ... especially against a team that until a few days ago we were calling potentially the best of all time. But he did get five plate appearances. And he is hitting home runs at a career-high rate. And sometimes, when the tumblers click into place, magic happens.

Joe Posnanski is a No. 1 New York Times best-selling author, an Emmy Award-winning writer and has been awarded National Sportswriter of the Year. This story was not subject to the approval of Major League Baseball or its clubs.