A criminal defendant's best chance of winning, or at least getting a good deal, has already passed. Most appeals end with the conviction being affirmed (upheld).
In California, the recent reversal rate for state criminal convictions was about 4%. That means of all the defendants who got convicted and appealed, only 4% got their case sent back to the trial court. Defendants convicted in federal court had a slightly better chance, with about a 6% reversal rate. That rate is closer to 7% in the Ninth Circuit, which includes California's federal courts.
Of course, getting a case reversed doesn't mean the defendant was innocent. Many reversals are because there was a serious problem with the way the trial was conducted, or to correct a problem with the sentence. The defendant may not be any better off at the end of the day.