Efficiency Bandwidth Product (EBP) is a number which shows the trade-off between efficiency and bandwidth of a driver. It is useful in determining if a driver is suited for a sealed or vented box and is also used to determine suitability for horn loading.
EBP = fs / Qes
As a general rule:
EBP < 50 - use only for a sealed box
EBP 50 - 100 - can be used in either
EBP > 100 - vented box only
Efficiency and bandwidth
These two parameters are inversely related. For maximum possibly efficiency, the bandwidth must be narrow. For maximum possible bandwidth, the efficiency then becomes less. Due to the assistance of the vent, a vented driver can have higher efficiency. Many pro woofers will reach 40 Hz with a vented box with around 95 db 1w1m. To achieve this with a sealed box requires an fs one octave lower (20 Hz), and in a 12" size this would be a subwoofer driver with about 85 db 1w1m.
Beyma SM 212 is a pro 12" woofer with an EBP of 102. Placed in a 110L vented box it achieves a -3 db point around 45 Hz. Efficiency is 96 db 1w1m.
Exodus Audio Shiva X2 is a home theatre 12" subwoofer with an EBP of 47, suggesting a sealed box. A sealed box with 45L volume has the same cut off but the efficiency is 85 db 1w1m.
The two illustrate two very different ways of getting a result. The Shiva has high excursion and needs about 1kw to achieve it's full potential output of 112 db. The Beyma can achieve 118 db with only 150 w of input, and higher output can be achieved if tuned a little higher. The Shiva, however, has more output below 30 Hz as expected, being a home theatre sub driver.
What happens if we break the rules?
Since these two drivers are not far from the 50 - 100 range, we can stretch things a little. The Shiva does just fine in a vented box and gains more LFE output. The Beyma doesn't do quite as well because it starts rolling off at 80 Hz. We could still make it work if it had sufficient excursion, but that isn't the case. In other words, it fails to work well for other reasons.