It sounds like you are doing an excellent job of backing up your partner, whether or not you agree with him. Doing lower level games can be hard sometimes, especially when the quality of some officials is not what some people are used to. In the long run, assignors will have much more respect for you if you back up your partner, than if you repeatedly correct their calls.
If you REALLY miss one bad, and it's obvious to everyone including yourself, it's entirely up to you whether or not you want to tell the coach you kicked it. Most coaches will respect you for admitting that you're not perfect, but you really have to read each coach. If the coach is being a "howler monkey," forget trying to reason with him. If he's merely asking you without creating a scene, let him know you're trying as hard as you can, but you made a mistake.
I had a situation last year where in the last 30 seconds of a 2-point varsity game, my partner made a horrible call, misinterpreting a rule. The coach jumped up and started yelling. I told the coach I would go over the play with my partner, to whom I quickly explained the rule and his error. However, he refused to budge on his call, so I told the coach I had done everything within the rules I could and had offered my opinion to my partner, but ultimately he blew the whistle and felt confident in his call; I was powerless to overrule him. It ended up deciding the game.
A couple of weeks later, the losing coach saw me in a different gym, and made it a point to walk up to me and thank me for doing what I could, even though the call went against him.
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