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The battle for the Senate is heating up, with most favoring Republicans to win the upper chamber, but Senate Majority Leader Harry Reid (D-Nev.) saying Democrats would hold the Senate, as of today.

One thing we do know: Whoever wins the Senate come November (or December), it's quite possible we won't know where most of the ad money that won it came from.

According to an analysis by the pro-transparency Brennan Center for Justice, 51 percent of the funds spent in the top nine Senate races so far comes from groups that don't disclose or that partially disclose donors.

Here's how that looks:

Brennan Center for Justice

And here's the breakdown in the top nine Senate races.

Brennan Center for Justice

These numbers also significantly undersell the impact of so-called "dark money" groups, because they do not include so-called "issue advertisements." These are often thinly veiled attempts to sway voters against a candidate, without expressly saying not to vote for him or her. Such ads don't need to be disclosed in the same way ads expressly for or against a candidate do.

Down the stretch, we could see groups that have to disclose their donors assert themselves more; after all, party committees generally hold most of their fire for the final weeks of the campaign.

As of now, though, "dark-money" groups appear to be the dominant force in the race for the Senate.