Where the weight
goes

This page
discusses the effect of adding weight in various places in a croquet mallet

Where is it best to insert weight?

The answer to
this is easy: as near to the extremities of the mallet head as possible.

In theory, the
perfect configuration would be to place the weights in eight equal, tiny
packets: one at each corner of each face.
But in practice, of course, no material has an infinite density, and so
the required weights are bound to have some volume. The material with the highest density that is
practical (note)
is tungsten, which has a density of about 17.
Other materials are as follows:

Tungsten |
19 |

Lead |
11 |

Brass |
9 |

Steel |
8 |

Water |
1 |

Hardwood (typical) |
.8 |

Softwood (typical) |
.4 |

Balsa wood |
.12 |

Are there downsides in placing the
weight immediately behind the striking face?

Not in terms of
moment of inertia. But placing the
weights hard up behind a striking face can mean that it is harder to achieve a
satisfactory bond between the striking face and a wooden head material.

Does it help to put the weight on the
sides?

From
the point of view of moment of inertia, a little, but not much.
Depending on the materials used, a more important advantage of putting
the weights at the side is that it facilitates a more efficient transfer of the
shock wave through the mallet head if the material(s) immediately behind the
strike point is/are as homogeneous as possible.

What happens if the weight is placed
away from the extremities?

The weights need
to be at 57% of the way from the shaft to the face before they start doing
anything useful at all; see note
for the calculation of this.