Here's a pop quiz for you--don't worry, it's a short one...
1) What do you think the average winning percentage is for a team in games in which its hitters hit no home runs? When they hit exactly one home run? Two HRs? Three or more HRs?
2) And what do you think the distribution of such games might be? What's the percentage of games in which a team--a single team, mind you, not both teams in a game--fails to hit a HR? Exactly one HR? Two HRs? Three or more HRs?
Or take a crack at the answer, on the off-chance that it might lead somewhere you haven't been--inside a context that hasn't been examined because it didn't contain enough nuance, or examining a framework that's been ignored because it seems to have way too much empty space in it.
OK, before you pull a set of numbers out of thin air, consider whether those numbers are fixed or mutable. How uniform might the sequence or progression be? Those who remember their baseball history will know that prior to 1920, these figures will all be a helluva lot different, simply because almost no one hit homers and it would thus be a lot easier to win games without hitting any.
So it's probable, then, that hitting no homers in a game is becoming a less successful strategy (that word might be a little strong...let's revise that simply to less successful result) in a time when hitting homers has reached historical levels of frequency.
Pondering it this way, and looking at the history of home run hitting as represented by the chart above, we can see that if no one hit any homers at all, we'd have a .500 WPCT. How much will a league that averages half a homer a game depress that WPCT for teams that don't hit a homer in a single game? Is it a straightforward mathematical function?
To answer the question, we need to break out all those winning percentages by team for every year, based on results sorted by homers/game. Now, as you might suspect, this breakout has yet to be performed, though you can do it (by hand) from the data available at Forman et fil. (We will have to take some of our leftover "nice pills" and ask Sean to write a query that will do this, but it's the Labor Day weekend and we know he's got much better things to do that read our e-mail.)
So we've done it just for a few years to give you a taste--and supply those of you who can't help but want to know the answer despite all instincts and inclinations to the contrary. The table below shows these breakouts for the AL in 2012 (a year where teams are hitting in excess of a homer per game); the AL in 1975 (when they hit about three-fifths of a homer/game); the 2011 NL (just under nine-tenths of a homer/game, the lowest average in twenty years), and the 1950 NL (about four-fifths of a HR/game).
What we see in the AL this year is a distribution very similar to how things have been in baseball for the past twenty years. Without the entire dataset, we can't be sure where that percentage of games with two or more HRs ranks in history, but when you compare it to the totals in the 2011 NL it's still quite a large difference. And comparing it to the 1975 AL is pretty revelatory.
Note how the WPCT in zero-homer games is so low in this year's AL (just .317) compared to the other years. This is where the game's escalating problem of two-dimensionality really stands out: it's simply impossible to be a winning team without hitting a lot of HRs. In 1975, the AL champion Red Sox were barely over the league average in HRs, and the league doormat (Detroit, 55-107) hit nearly as many HRs as the league champs. That type of run-scoring flexibility has decreased markedly over the last twenty years to the point where only one offensive style is possible.
Of course, there is still variation in WPCT for individual teams across this distribution. Teams that do better in games where they don't hit any homers, however, tend to be the best teams.
However, this trend can be bucked when the percentage of no-homer games gets as low as it is in the AL this year. Astonishingly, the two teams currently fighting it out for the AL East (the Yankees and those mind-blowing Orioles) are both doing terribly in games when they don't hit HRs. (At last count, the Yankees were only 3-17 in such games; the Orioles were only 8-25. By way of contrast, the Rangers were 17-22.)
It would be interesting to track the fluctuations in those 2-HR games; it seems that in certain years, there are events that conspire to create anomalous results (that 1950 NL average is awfully low, possibly skewed by the Whiz Kid Phillies winning so many one-HR games that year, including a bunch against teams who hit 2 HRs in a game against them). Another way to track all this would be to calculate the average runs/game when teams hit 0, 1, 2... HRs and see how this has fluctuated with respect to HR/G averages. Relative to the overall league run scoring, this average may well be lower now than at any other time in baseball history.
We'll need to fill in all of this data to be absolutely sure, but based on what we see here, it will take a lot of work to make offenses three-dimensional. It's possible that it simply can't be done. It's also possible that folks simply won't like it if it actually can happen. But there's got to be a better way than what we have right now...