Origin and details of -10 to +10 model of becoming a Christian

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It is the Engel Scale. Originally it went from -8 "Awareness of supreme being, no knowledge of Gospel" to +5 "Stewardship" but now it is often shown as going from -10 to +10 (see eg Bill Hybel's Just Walk Across The Room).

A quick Google search will reveal multiple variations, see eg this YWAM variant:

YWAM version of Engel

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What is described in this link does seem to me to be a model for becoming a Christian but a means of describing where someone is on the spectrum of belief/faith. In particular, this document seems to employ the scale as a means of comparing some beliefs of different Christian groups.

I don't think a model such as you're describing exists. To use a fleshed-out scale as a means of plotting a person's progress would suggest that a person must go through certain stages, and except for the fundamental stages (listed as -1 and 0, perhaps corresponding to recognition of sin, confession, repentence, and belief), there may not be predictable stages through which any one person would pass.

There are some passages (or some popular exegeses of them) that suggest an ordered progression. The Beatitutes (Mt 5:1-12) is one. I don't know if it would be feasible to assign numbers to these as if the number implied some meaningful relative closeness to a goal.

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