By now, you've probably heard that the Dow Jones Industrial Average (DJINDICES:^DJI) is getting a makeover. Three of the venerable index's weakest tickers get the boot on September 23, replaced by fresher blood. But do you know how these changes will change the Dow?

First of all, the Dow's total score won't suddenly soar or plummet when the new tickers take their seats. Instead, the Dow will adjust its "Dow divisor," which is an adjustment that keeps the index stable through ticker changes, stock splits, dividend payments, and coffee-stained stock certificates.

For some context, the divisor has decreased by 1.5% over the last year, including the single-ticker replacement in September of 2012. Total share prices will increase by 19% this time, so the divisor will make a bigger adjustment to keep the Dow's bottom-line score stable.

But some things will change. Right now, IBM (NYSE:IBM) is far and away the most influential Dow stock since its nearly $200 share price stands head-and-shoulders above runner-up Chevron.

Losing the weakest share prices from the price-weighted index, and adding two stocks that play in IBM's ball park, will change the Dow's relative weighting. Play around with these interactive charts to see what I mean.

Old and New Dow Jones Weights | Infographics

The hefty share prices of Visa (NYSE:V) and Goldman Sachs (NYSE:GS) will reduce IBM's market-moving powers. Today, IBM accounts for 9.4% of the Dow's combined share prices -- and, therefore, 9.4% of the total index weight. Chevron runs a distant second, at 6.2%.

The oil giant's shares would have to move 3% to affect the Dow's total value as much as a 2% move by Big Blue. Bank of America, which is moving out due to low share prices, and stands for just 0.7% of total Dow values, must record gains or losses more than 13 times larger than IBM's in order to make a similar difference to the index.

Less than two weeks from now, IBM will stand shoulder to shoulder with Visa, each owning 7.9% of Dow weightings. Goldman isn't far behind, at 7%. Nike (NYSE:NKE) runs in the middle of the Dow pack with a more modest share price, but is still a significant upgrade from the stocks it will replace.

The distance from top to bottom shrinks; the triplets at the bottom of the revised 30-ticker list will each stand for 1% of the Dow. That's down from 1.2% today as the rising combined share prices dilute the value of all the current members. Play around with the pie chart above to see how this works.

IBM and Visa may be eight times as important to the index, but that's still far closer than the 13-fold multiplier we discussed earlier. That's not to mention the even greater 23-fold difference between IBM and (soon-to-be former Dow member) Alcoa today.

The Dow will also gain some fundamental quality by folding a few weak hands. The combined trailing revenues of all 30 Dow members will decline by 4.8%, but total earnings will rise 4.3%. In other words, the new members run more effective businesses than the ousted tickers do.