A problem with these analogies (I'll use football here) is that unless the coach actually chooses certain people to be on the team, he has no reason to call the team the "chosen ones." If he simply accepted everyone on the team, there would be no reason to say, "now since you are the chosen ones, put on these pads and go win!"
Yet We are repeatedly called God's chosen one's. What does that mean if we are not actually chosen?
-Colossians 3:12 - Put on then, as God's chosen ones, holy and beloved, compassionate hearts, kindness, humility, meekness, and patience,
-1 Peter 2:9 - But you are a chosen race, a royal priesthood, a holy nation, a people for his own possession, that you may proclaim the excellencies of him who called you out of darkness into his marvelous light
-1 Thess. 1:4-5 For we know, brothers loved by God, that he has chosen you, because our gospel came to you not only in word, but also in power and in the Holy Spirit and with full conviction. You know what kind of men we proved to be among you for your sake.
If you want a good analogy of election, simply look at what is shown in Judges 7.
Jud 7:2 And the LORD said unto Gideon, The people that are with thee are too many for me to give the Midianites into their hands, lest Israel vaunt themselves against me, saying, Mine own hand hath saved me.
3 Now therefore go to, proclaim in the ears of the people, saying, Whosoever is fearful and afraid, let him return and depart early from mount Gilead. And there returned of the people twenty and two thousand; and there remained ten thousand.
4 And the LORD said unto Gideon, The people are yet too many; bring them down unto the water, and I will try them for thee there: and it shall be, that of whom I say unto thee, This shall go with thee, the same shall go with thee; and of whomsoever I say unto thee, This shall not go with thee, the same shall not go.
5 So he brought down the people unto the water: and the LORD said unto Gideon, Every one that lappeth of the water with his tongue, as a dog lappeth, him shalt thou set by himself; likewise every one that boweth down upon his knees to drink.
6 And the number of them that lapped, putting their hand to their mouth, were three hundred men: but all the rest of the people bowed down upon their knees to drink water.
7 And the LORD said unto Gideon, By the three hundred men that lapped will I save you, and deliver the Midianites into thine hand: and let all the other people go every man unto his place.
God knew that only three hundred men would put their hands to their mouth and lap like a dog. It was these three hundred that God chose to fight with Gideon.
Did God cause these three hundred men to drink like a dog? No, God said he would "try" the men. It would be no test if God caused three hundred to drink like a dog and caused the rest to kneel and drink.
Note in verse 2 that God said Israel would not be able to vaunt themselves and say their own hand had saved them.
Note that in verse 4 that God said whosoever he said shall go with Gideon shall go, and whom he said shall not go should not go. God was absolutely in charge and sovereign.
Nevertheless, God chose only those three hundred who drank like a dog. God did not cause this, but he knew beforehand that only three hundred would drink this way. God determined the condition that must be met.
You will not accept it, but this is a figure of both God's foreknowledge and election in scripture.