# Binary logistic regression: interpretation of regression coefficients

I have performed a logistic regression with whether or not an athlete was re-contracted by their sports team as the DV. One of the significant predictors of the final model was draft order (OR 0.888).

Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept)                     -120.69457   46.78377  -2.580 0.009885 **
Debut.first.year                   0.67977    0.21772   3.122 0.001795 **
Grouped.by.fives                  -0.11849    0.02361  -5.019 5.21e-07 ***
Draft.year                         0.06109    0.02334   2.617 0.008863 **
Maturity                          -0.65844    0.40981  -1.607 0.108118
Games.second.season.DC             1.87716    0.34011   5.519 3.40e-08 ***
Interstate.vic.team                0.47625    0.19390   2.456 0.014044 *
Rising.star                        1.50635    0.44429   3.390 0.000698 ***
Team.EOS.ladder.second.year.raw   -0.04403    0.02062  -2.135 0.032728 *


I understand that this indicates that being selected later in the draft results in a reduced odds of being re-contracted. There are 8 predictors overall therefore my question is, does this indicate that being selected later in the draft results in a reduced odds of being re-contracted when all other predictors are held constant? Does this then mean that draft order is associated with being re-contracted irrespective of rising star nomination, maturity, draft year etc?

The text books I have read and online forums are quite vague and I am struggling to understand the relationship between the regression coefficients.

Thank you!