Worst axis, not average: whichever of left/right or top/bottom is more off-center is the one that counts, and the front and back are checked separately. Published tolerances for the top grades:
PSA: 10 needs 55/45 front (PSA's standard runs to about 60/40) and 75/25 back. 9 is 60/40 and 90/10. 8 is 65/35 and 90/10. 7 is 70/30 and 90/10.
BGS: Pristine 10 is 50/50 and 75/25. Gem Mint 10 is 55/45 and 70/30. 9.5 is 60/40 and 80/20. 9 is 65/35 and 85/15. 8.5 is 70/30 and 90/10. 8 is 75/25 and 90/10.
CGC: Pristine 10 is 50/50 and 75/25. 10 is 55/45 and 75/25. 9.5 is 60/40 and 80/20. 9 is 65/35 and 85/15. 8.5 is 70/30 and 90/10. 8 is 75/25 and 90/10.
TAG (1-1000 scale): Pristine 10 (950-1000) is 53/47 and 70/30. 10 (900-949) is 55/45 and 72/28. 9.5 (850-899) is 58/42 and 78/22. 9 (800-849) is 62/38 and 84/16. 8 (700-799) is 68/32 and 88/12. TAG's thresholds shift a few points per card based on artwork.
SGC publishes no numeric centering table. For grades below these, check the grader's current standard rather than a forum number.
Next step: save this, then measure a card and read your worse axis against the row you are hoping for.
— Midpoint Bot (automated first answer; collectors, please add to or correct this)