If you’ve ever wanted an example of how creaky and cumbersome the ancient Dow Jones Industrial Average (^DJI) has become compared with modern market metrics, take a look at this week’s Dow triple play involving Walmart (WMT), Walgreens (WBA), and Amazon (AMZN).

On Monday, the Dow replaced Walgreens with Amazon in reaction to Walmart splitting its stock 3-for-1.

That split, for reasons we’ll get to in a bit, reduced Walmart’s weight in the average — yes, the Dow is an average, not an index — by two-thirds.

Adding Amazon to the Dow, the folks at S&P Dow Jones Indices say, was done to keep retail companies’ weight in the average from falling sharply because of Walmart’s stock split.

Because the Dow has only 30 stocks, adding Amazon meant one of the other components had to go. So Walgreens Boots Alliance, which had the lowest weight in the Dow, got the boot and lost its alliance.

Walgreens being booted from the Dow isn’t exactly a surprise because its share price has fallen around 60% since being added to the average in June 2018, while the Dow has risen about 60%.

Had Walgreens kept pace with the other 29 components, the Dow would be about 400 points higher than it is. With the Dow near 40,000, it’s easy to see what little impact even an at-pace Walgreens would have made.

Amazon, by contrast, has been a hot stock, one of the so-called "Magnificent Seven" that accounted for the bulk of the stock market’s gains last year.

Walgreens’ Dow tenure lasted less than six years — an extraordinarily short time for a market metric that doesn’t change its component stocks very often.

But its exit, S&P Dow Jones Indices senior analyst Howard Silverblatt insisted to me, isn’t because Walgreens has slumped and Amazon has soared.

“We think it’s a better fit,” Silverblatt said. “We’re not saying it’s a better investment.”

Or, as Silverblatt put it on Yahoo Finance Live, Amazon will help the Dow stay “relevant.”

Now, a key question: will being added to the Dow be good for Amazon’s stock price?

My answer, which may surprise you, is no. Based on conversations I’ve had with market mavens over the years, I don’t think that being added to the Dow will make the slightest difference for Amazon shareholders. Just as Walgreens being kicked out won’t make any difference to Walgreens shareholders.

How can I say that when the Dow is such a popular market metric?

It’s because although the Dow has great mindshare, it has almost no financial market share compared with the hugely influential S&P 500 Index (^GSPC).

Let me explain.

The Dow is calculated based on the share prices of its 30 components. That’s why today’s three-for-one split, which reduced Walmart’s share price by two-thirds, reduced its weight in the Dow by two-thirds.