NBA Analysis: What Impact Can a Single Player Have on Winning Championships?

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“If my team wins 15 more games next year, what are the odds that it will win a championship?”

Many fans ask questions like these, and while it’s easy to conceptualize “15 more wins,” it’s harder for them to understand what they means when they postseason rolls around. When a player joins a team, his “impact” can be seen in the Wins column…but that’s a reflection of scoring more net points, which is captured by SRS. (SRS is a simple rating system that looks at points — margin of victory — and adjusts for schedule.)

We know if a player improves SRS by 5 points, the team is expected to win an extra 14 games or so. But how does that change their odds of winning a title? How much does an average all-star help? Do superstar players guarantee titles? Is one year of Bill Walton better than 10 years of Reggie Miller?

To answer these questions, we need to know a few things. First, we need to calculate the odds of a team winning a game based on SRS differential.  We can do this by looking at actual games — let’s use games from 2010 to 2012 — to determine the odds of a home team winning based on SRS differential. Once we do that, we can calculate the odds of a team winning a 7-game series based on SRS differential. When we do, we get something like this:

First, note that the reason the results aren’t smooth is that they are based on actual results, so there is some variability at the extremes. Such variance is acceptable here as it will not affect the results in any noticeable way. Second, note that one in every 200 times we should expect to see the largest of underdogs (-15 points) spring an upset simply based on the variability of a basketball game. Third, notice what happens as the team’s grow closer in strength: Home-Court becomes a large factor, and for teams within +/-2 SRS points of each other, the odds are close to a coin flip. The truly “better” team will never be decided in a 7-game series. C’est la vie.

So what does this mean for our original question? Well, if a player can come in and shift a team up by enough SRS points, that team will suddenly go from a near 50-50 proposition to a considerable favorite to win. Taking into account the different opponent strengths in each round based on SRS (eg higher seeds face weaker opponents), the results look like this...

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