The Boston Celtics, after whiffing on trades for Jimmy Butler and Paul George, finally got some good news this week when Gordon Hayward announced that he was leaving the Utah Jazz to play for the Celtics. Although Isaiah Thomas would have some beef with this assessment, Hayward’s well-rounded combination of skills will probably make him the best player on the Celtics next year. He’s a good fit with the team’s approach.

And yet, projection systems (including our own CARMELO) are somewhat skeptical of the Celtics, not expecting them to improve on last year’s 53-29 performance or to seriously challenge the Cleveland Cavaliers for Eastern Conference supremacy. Hayward is also fairly expensive; he’ll cost the Celtics $128 million over four years (the fourth season, 2020-21, is a player option). So let’s ask a tough question of Boston and general manager Danny Ainge: If Hayward is the best player on your team, could that team plausibly be good enough to win a championship?

The answer is probably not. Hayward made the All-Star team last season, but he’s a long way from being a superstar. A handful of modern NBA teams — the 1988-89 and 1989-90 Detroit Pistons, the 2003-04 Pistons, and the 2013-14 San Antonio Spurs — won a title with someone about as good as Hayward as their best player. But this is unusual: It requires a team to be constructed almost perfectly, with above-average players at nearly every position, a deep bench, and a cohesive rotation. It sometimes also requires a fair amount of luck.The “Bad Boys” Pistons peaked just as the 1980s Celtics and Lakers were declining, but before Michael Jordan’s Bulls really took off, for example.

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But Hayward can be a building block toward a championship. He’s roughly as good as the second-best player on a typical championship team. That might sound like faint praise, but it’s no small achievement.

Let’s develop some terminology to describe degrees of the stardom in the NBA. I’ll introduce three types of players: Alphas, Betas and Gammas.

• An Alpha is a player who’s as good as the best player on a typical championship-winning team. This is an MVP contender — one of the half-dozen best players in the league.
• A Beta is as good as the second-best player on a typical NBA champion. As I mentioned, Hayward is a good example of a Beta. Betas are usually All-Stars, perhaps even All-Star starters, and they’re among the best players at their position. But they’re not among the very best players in the league.
• And a Gamma is good as third-best player on a typical championship team. A Gamma might be an All-Star, but he usually won’t make one of the three All-NBA teams. He probably has one or two weaknesses (defense, shooting, etc.) along with his obvious strengths. But he’s still a very good player and might be the best player on a non-contending team. Thomas, although he’s somewhat difficult to evaluate because of his defense — various statistical systems rate it anywhere from mediocre to execrableThere’s a big difference between mediocre and execrable. If Thomas’s defense is merely somewhat below average, as the NBA’s opponents’ shooting data suggests, then his offense more than makes up for it and he’d probably qualify as a Beta. If it’s terrible, as RPM suggests, then Thomas is barely even an above-average player overall. Classifying Thomas as a Gamma, as CPM does, is something of a compromise between these assessments.

  ‘>² — is a reasonably good example of a Gamma.

At any given time, only a few dozen players in the league will rated as Alphas, Betas or Gammas. (CARMELO projects that there will be 35 of them in 2017-18, for example.) It’s these players who determine who competes for NBA championships. Doesn’t depth matter also? Well, sure. A well-rounded roster is often the difference between winning a title and losing one. But a team needs its share of star-level talent to compete for a championship in the first place. Otherwise, it’ll usually wind up like last year’s Celtics, a well-constructed team that was overmatched in the playoffs.

Below, you’ll find a table listing the top three players on NBA championship teams since 1984-85 — the first year the league used a salary cap — as rated by a statistic called Consensus Plus-Minus. Consensus Plus-Minus, or CPM, is a statistic I use when I don’t want to get into arguments about the value of individual players. It reflects a combination of four popular statistics — Real Plus-Minus,RPM is available from the 2000-01 season onward. For seasons prior to 2000-01, I use BPM twice in the average.

“>³ Box Plus/Minus, Win Shares and player efficiency rating — equally weighted and translated to the same scale. It also adjusts for the player’s position, which the other metrics do not,CPM measures a player’s value relative to the positional average, rather than relative to the league average. Right now, there’s an excess of good centers and point guards but less depth among small forwards and shooting guards. This adjustment helps Hayward, who plays both those positions.

“>⁴ and it regresses players’ ratings to replacement level if they fall below a certain threshold of playing time.If the player plays less than 20 minutes per team game — or 1640 minutes over an 82-game season — his actual CPM is blended with a replacement-level CPM of -2 points per 100 possessions.

“>⁵ For predictive purposes, we think CPM is liable to be slightly less accurate than the blend of statistics CARMELO uses (a combination of RPM and BPM), but CPM is still a perfectly reasonable stat and much more in line with the consensus view of NBA players. Like BPM and RPM, CPM is expressed in net points added or subtracted per 100 possessions. So a player with a CPM of +2.5, teamed with four average players, would help his team to outscore his opponents by 2.5 points per 100 possessions, for example.

To no one’s surprise, the best players on title-winning teams are usually extraordinary talents. Among the 33 NBA champions since 1985, the top-rated player on the team, according to CPM, was one of the three best players in the league that season on 23 occasions. And the team’s best player was among the top 10 in the league on all but three occasions. The exceptions were Bill Laimbeer of the 1988-89 and 1989-90 Pistons (CPM, perhaps dubiously, rates Laimbeer ahead of his teammate, the other Isiah Thomas) and Ben Wallace of the 2003-04 Pistons. Pretty much all the other No. 1 players are current or future Hall of Famers, however, with the possible exception of Manu Ginobili, who may be a borderline case.

No matter how brightly he shines, however, a superstar usually can’t deliver a title without a good sidekick or two.Take LeBron James’s 2012-13 season, for example, when he had a CPM of +10.6 and played almost 38 minutes per game — about as good as an NBA player can be under modern conditions. A team with that version of LeBron, plus a roster full of replacement-level players, would still project to go only 41-41, according to our forecasting method. A team with that version of LeBron plus a roster full of league-average players (as opposed to replacement-level players) would project to go 59-23, which is closer to being a title contender. League-average players don’t just grow on trees, however.

“>⁶ On average, the second-best player on these championship teams was the 14th-best player in the league, according to CPM. And although not every champ had a classic “Big Three” like LeBron James’s Miami Heat, the third-best player on the championship team rated as the 37th-best player in the league, on average — still very solid.

So let’s get back to the idea of Alpha, Beta and Gamma players, which were meant to correspond to a typical championship team’s best, second-best and third-best players. By looking at the historical data, we can define these classifications as follows:

• An Alpha has a CPM of +6.0 or higher.
• A Beta has a CPM of between +3.5 and +6.0.
• And a Gamma has a CPM of between +2.0 and +3.5.

I re-ran CARMELO using CPM instead of its usual blend of statistics, and it projected the following players to be Alphas, Betas and Gammas for the upcoming NBA season:

This makes for a fairly intuitive list. LeBron, Russell Westbrook, James Harden, Stephen Curry, Kevin Durant and Kawhi Leonard are the league’s six Alphas. Chris Paul falls just short of the Alpha category; instead, he joins players such as Hayward, Giannis Antetokounmpo, Rudy Gobert and Anthony Davis on the Beta list. Gammas include players like Isaiah Thomas, Kyrie Irving, Kevin Love, John Wall, DeAndre Jordan and Paul Millsap.

So then all you need is an Alpha, a Beta and a Gamma and — presto! — you win an NBA championship? Actually, your options are more flexible than that. A team with an Alpha and a Beta — say, this year’s Houston Rockets — could probably skip the Gamma if they had a deep rotation. A team with no Alphas but three Betas — say, Jimmy Butler, Antetokounmpo and Kyle Lowry — would more than likely be good enough to contend for a title. A team with a very strong Alpha could go without a Beta and make up for it with two or more Gammas instead — that’s sort of how the current Cavaliers are constructed.

To help teams think through these decisions, let’s invent one more statistic, which I’ll call star points. The formula is simple: A team gets three star points for each Alpha on its roster, two for each Beta, and one for each Gamma. Next year’s Warriors project to have 9 star points, for example: three each for Curry and Durant, two for Draymond Green and one for Klay Thompson.

Even having that much talent on your roster doesn’t necessarily guarantee a title. But historically, a team’s chances of winning a title are remote if it has four or fewer star points. It has a fighting chance with five or six star points, depending on how the rest of the roster is constructed. And its probability increases rapidly once it acquires seven or more star points.

This system isn’t perfect, but it lines up intuitively with how we evaluate teams. After the Warriors and their nine projected star points next season, the Cavaliers and Rockets are the closest thing the league has to ready-made title contenders, as they’re tied for second at five star points each. They’re followed by the Thunder, Timberwolves and Pelicans at four each; these four-point teams probably need at least one more thing to click (say, George taking the next step in Oklahoma City) to be title-worthy. The Celtics are one of several teams with three star points.

This measure can underrate the importance of team depth; the Spurs, who have only three star points, are rated too low, for instance. The Celtics — although they’re losing a few players to make room for Hayward — are also a deep team, with lots of average or slightly-above-average players and lots of draft picks to keep priming the pump. They could probably compete for a title with five star points, therefore, instead of needing six or seven. Adding another Beta-level player might be enough to do the trick.

It’s hard to see where that player comes from, however. The Celtics lost some of their financial flexibility in signing Hayward. And while they could develop a star player rather than acquiring one, giving more playing time to young players such as Jaylen Brown and rookie Jayson Tatum could make them less competitive in the short run.

If there’s one Celtics move that looks bad in retrospect, it isn’t necessarily trying and failing to acquire Butler or George, it’s trading the No. 1 draft pick for Philadelphia’s No. 3 pick, with which they chose Tatum. While Tatum has a fairly promising projection, he doesn’t have the upside of No. 1 pick Markelle Fultz, whose comparables include players such as Harden, Westbrook and Wall. The trade might have made sense for a team that already had its stars in place and wanted to develop complementary players around them, but the Celtics have plenty of complementary players and are short on stars.

At the same time, it would be easy to underestimate the challenge Ainge faced. The Celtics’ 53-29 record last year was deceptive, in that it came against a weak conference and relied on what were arguably career years from several players, including Thomas.The Celtics also outperformed their 48-34 Pythagorean record by several games.

‘>⁷ In many respects, they were a rebuilding team dressed up as a competing team. And precisely because the Celtics weren’t just one player away from contending for a title, Ainge needed to acquire a player like Hayward or Butler without compromising the Celtics’ ability to acquire or develop another such player down the road. Even if the Celtics are still a star away from seriously contending for a title — maybe even a superstar away — that’s closer than they were last week.