Golf ball having an over-indexed thermoplastic polyurethane elastomer cover and having a soft feeling when hit

1. A golf ball comprising:

a golf ball precursor, the precursor comprising at least one preselected golf ball layer but not an outer cover layer, and

an outer cover layer that:

(1) comprises a moisture-cured, crosslinked, thermoplastic polyurethane elastomer formed by reacting a mixture of (a) an unsaturated diol having two primary hydroxyl groups and at least one allyl ether group of the formula

in which R 1 is a substituted or unsubstituted alkyl group, substituted or unsubstituted aryl group, substituted or unsubstituted alkyl-aryl group, substituted or unsubstituted ether group, substituted or unsubstituted ester group, a combination of these, or H, and optionally includes an unsaturated bond in any main chain or side chain of any group; R 2 comprises an allyl group optionally attached by a substituted or unsubstituted alkylene group, substituted or unsubstituted arylene group, substituted or unsubstituted alkylarylene group, substituted or unsubstituted ether group, or substituted or unsubstituted ester group; and x and y are integers independently having a value from 1 to 10, (b) a polyisocyanate, (c) a polyol having a molecular weight between about 500 and about 4000, and—optionally (d) a chain extender having at least two isocyanate-reactive sites and a molecular weight less than about 450; wherein a free radical initiator induces crosslinking of the allyl group and, if present, the optional unsaturated bond of R 1 , the mixture having an NCO index of from about 1.06 to about 1.18;

and

(2) has a 100% modulus of from about 80 to about 130 kg/cm 2 .

2. The golf ball according to claim 1 , wherein the outer cover layer has a flexural modulus of less than about 1,000 psi.

3. The golf ball according to claim 1 , wherein the golf ball precursor comprises

an inner core layer, the inner core layer comprising at least a thermoplastic material;

an outer core layer substantially surrounding the inner core layer, the outer core layer comprising a thermoset rubber composition; and

an inner cover layer substantially surrounding the outer core layer, the inner cover layer having a surface Shore D hardness of at least about 60.

4. The golf ball according to claim 3 , wherein the thermoplastic material of the inner core layer comprises a blend of two highly neutralized acid polymers.

5. The golf ball according to claim 4 , wherein the inner core layer has a diameter of from about 21 mm to about 28 mm and a compression deformation of from about 3.4 mm to about 4.2 mm.

6. The golf ball according to claim 5 , wherein the outer core layer has a thickness of from about 5 mm to about 9 mm.

7. The golf ball according to claim 6 , wherein the outer core layer has a surface Shore D hardness of from about 50 to about 60.

8. The golf ball according to claim 7 , wherein the inner core layer has a coefficient of restitution that is lower than the coefficient of restitution of the outer core layer.

9. The golf ball according to claim 8 , wherein the golf ball has a coefficient of restitution of less than about 0.8.

10. The golf ball according to claim 7 , wherein the outer cover layer has a surface Shore D hardness of from about 53 to about 57 and the inner cover layer has a surface Shore D hardness of from about 60 to about 70.

11. The golf ball according to claim 1 , wherein the inner cover layer has a thickness of less than about 1.2 mm.

12. The golf ball according to claim 11 , wherein the outer cover layer has a surface Shore D hardness of from about 53 to about 57.

13. The golf ball according to claim 1 , wherein the unsaturated diol is trimethylolpropane monoallyl ether.

14. The golf ball according to claim 13 , wherein the outer cover layer has a flexural modulus of less than about 800 psi.