What have I got in my pocket?
when the sperm is halfway into the egg
duh
No, in fact it takes a swarm of sperm to get past the egg's defenses & fertilize the egg. That's why sperm aren't produced singly; in the case of sperm, it actually does take a village.
See
Human fertilization - Wikipedia
"Sperm preparation
"Further information: Acrosome reaction
"At the beginning of the process, the
sperm undergoes a series of changes, as
freshly ejaculated sperm is unable or poorly able to fertilize.[9] The sperm must undergo
capacitation in the female's reproductive tract over several hours, which increases its motility and destabilizes its membrane, preparing it for the acrosome reaction, the
enzymatic penetration of the egg's tough membrane, the zona pellucida, which surrounds the oocyte.
"Zona pellucida
"After binding to the corona radiata the sperm reaches the zona pellucida, which is an extra-cellular matrix of glycoproteins. A special complementary molecule on the surface of the sperm head binds to a ZP3 glycoprotein in the zona pellucida. This binding triggers the acrosome to burst, releasing enzymes that help the sperm get through the zona pellucida.
"Some sperm cells consume their acrosome prematurely on the surface of the egg cell,
facilitating the penetration by other sperm cells. As a population, sperm cells have on average 50% genome similarity so the premature acrosomal reactions aid fertilization by a member of the same cohort.[10] It may be regarded as a mechanism of kin selection.
"Recent studies have shown that the egg is not passive during this process.[11][12]
"Cortical reaction
"Once the sperm cells find their way past the zona pellucida, the
cortical reaction occurs. Cortical granules inside the secondary oocyte fuse with the plasma membrane of the cell, causing enzymes inside these granules to be expelled by exocytosis to the zona pellucida. This in turn causes the glyco-proteins in the zona pellucida to cross-link with each other — i.e. the enzymes cause the ZP2 to hydrolyse into ZP2f — making the whole matrix hard and impermeable to sperm. This prevents fertilization of an egg by more than one sperm. The cortical reaction and acrosome reaction are both essential to ensure that only one sperm will fertilize an egg.[13]"
(My emphasis - more info @ the URL)
This is an excerpt, of course. There are other considerations, & more ramifications to the process.