## FATS Model

Wouldn’t it be useful to have a system that allows you to plug in the numbers for an NBA team in the middle of a playoff push and see how the most historically similar teams in the relatively modern years of the Association have fared? Not the most similar in terms of roster construction, but the most congruent when looking at the underlying stats that represent the teams’ levels of effectiveness.

That’s what the FATS (factor adjusted team similarities) projection model does, and it’s important for you to understand exactly how it’s derived. In order to explain, I’ll not only go over the methodology, but also show the steps necessary to calculate the 2014-15 Golden State Warriors’ projection, as they were the league’s No. 1 team (in terms of record) at the time of this metric’s inception.

## The Four Factors

In his seminal basketball text, Basketball on Paper, Dean Oliver first came up with the “Four Factors of Basketball Success,” which have since been shortened and are simply known as the Four Factors. There’s nothing too complicated about the reasoning behind them, as they’re meant to provide an overview of what affects performance on the court—shooting, turnovers, rebounding and free throws.

Shooting is measured by looking at effective field-goal percentage (eFG%), which factors in the extra point earned when making a shot from beyond the arc. Essentially, two teams with identical field-goal percentages will differ in eFG% if one makes more three-point shots than the other.

Next are turnovers, which are analyzed through turnover percentage (TOV%). Quite simply, the metric estimates how many turnovers a team records per 100 possessions.

The third factor is a bit more complicated, but only because there are two different sub-factors, if you will.

While we refer to these stats as the Four Factors, there are technically eight of them, as we analyze teams on both ends of the court. So for rebounding, we have to look at offensive rebounding percentage (ORB%) and defensive rebounding percentage (DRB%), both of which show the percentage of possible boards the squad in question grabs on that respective side of the floor. For the others, we can simply say we’re looking at the opponents’ [insert metric here].

Finally, there’s free throws per field-goal attempt (FT/FGA). This shows both how well a team shoots free throws—as it looks at free-throw makes, not attempts—and how often it gets to the line. The squads that fare best in this category are the ones that not only draw plenty of whistles, but also convert their attempts at the charity stripe.

Heading into their Dec. 22, 2014 game against the Sacramento Kings, here’s how the 22-3 Warriors stacked up in the eight relevant statistics:

When making historical comparisons, it’s not enough just to look at the raw data, and that’s the first way that FATS differentiates itself from similar models used elsewhere.

Up to the date in question, the Warriors had produced an ORB% of 23.7. That’s the same exact mark that was earned by two other teams in NBA history: the 2010-11 Phoenix Suns and the 2004-05 Toronto Raptors. But those scores shouldn’t be treated as equivalents, and that’s the reason for adjustments.

League averages change over time, and we’re most interested in how the teams fare relative to those averages. The specifics are irrelevant, as the relative strength of the team in that category is what truly matters.

Even though all three aforementioned teams produced identical offensive rebounding percentages, it’s the current Dubs who reign supreme in this category. In fact, the team most similar in this category from the 2010-11 season would actually be the Milwaukee Bucks, and they hauled in 24.7 percent of their offensive-rebounding chances. Again, the raw numbers don’t matter nearly as much as what they say about the team’s strength in that category compared to the league as a whole.

The differences in league-wide averages are only slight when comparing teams separated by just a few years. But this gets significantly more important when working across decades. The league-average ORB% in 1980-81, for example, was 33.5 percent. That same 33.5 percent would currently be the best mark in the league with room to spare, as the Houston Rockets and Sacramento Kings are pacing the Association at 28.8 percent, as of Dec. 22.

The adjusted scores that you can see in the final column of the above table are formatted so that a score of 100 means the team was perfectly in line with the league average. For categories in which a higher score is better, the adjusted score is formed by dividing the raw number by the league average and multiplying by 100. For categories in which a lower raw score is better, the adjusted score is derived by dividing the league average by the raw score and then, once more, multiplying by 100. In both cases, adjusted numbers above 100 are superior to adjusted numbers below the triple-digit barrier.

Essentially, it’s the same process previously used for calculating adjusted offensive efficiency (ORtng+) and adjusted defensive efficiency (DRtng+).

Now, let’s adjust for the Warriors:

## Team Similarities

Once we’ve calculated those numbers, the real fun begins.

Over the last year or so, I’ve compiled a database with information on literally every team that has suited up while affiliated with the NBA. Since 1974, we have numbers that show the Four Factors for each squad, so we’re comparing the modern teams to the adjusted numbers of those from the last four decades. In total, that gives us 1,073 squads to form comparisons with.

It’s also important to note that not every one of the eight categories counts the same.

In Oliver’s original work, he estimated that shooting, turnovers, rebounding and free throws should be weighted 40 percent, 25 percent, 20 percent and 15 percent, respectively. And that’s for each side of the ball. There was no differentiation made between offensive rebounding percentage and defensive rebounding percentage, for example.

Obviously, rounded and generalized numbers like that—and Neil Paine used these same numbers while working on his own model for Basketball-Reference.com in 2010—aren’t going to be perfect, and we’re trying to be as exact as possible with these projections. To be as accurate as can be, we regressed wins (prorated to 82 games when necessary, primarily because of lockout-shortened seasons) on the eight categories and based the category weights on the strengths of the correlations found in the multiple regression.

Here are the results:

If you combine the two related factors to form overarching percentages, as both Oliver and Paine have done, here’s how my results compare with theirs, just to satiate your curiosity:

Ever wondered why I tend to harp about efficiency? This would be the answer.

When looking at winning, it turns out that the forefather of the Four Factors didn’t account for shooting nearly enough. That’s the biggest difference between the two systems, and it comes from all three of the other categories.

With those weights in mind, we can move on to the actual similarities between current teams and their historical counterparts. Everything centers around percent error, as we want to know how far off the modern team is from the older one in each category. Whether they’re above or below the mark doesn’t matter; only the absolute value of the difference comes into play.

So, let’s see how the Warriors compare to their top match—the 1980-81 Philadelphia 76ers:

To get from the penultimate column to the final one, we need only multiply by the percentage weights given in the earlier table. That’s why, despite the major difference between the two teams, the gap in FT/FGA is fairly inconsequential. It’s much more crucial for the squads to have similar shooting profiles, though everything is obviously important.

So, because the total weighted percent error is 2.71, we can give the 1980-81 Sixers a final grade. In this case, there are some rounding errors in the table up above, and that early squad is actually a 97.3 percent match in our model. No other team was in the 97s, though many came close.

Now, how does that turn into a win-loss projection?

Projected Pace

We don’t just find the best match for each team; instead, we look at the percent match for each of the 1,073 squads that have played since the 1973-74 season began. Next year, the model will be even stronger, as we’ll have data on 1,103 teams, factoring in those who are currently playing out the 2014-15 campaign.

The 1980-81 Sixers were the top match, but the analysis goes all the way down to the 1990-91 Denver Nuggets, who were the worst fit for this team (87.37 percent). That may seem like a high number, but remember just how much each difference is being depressed by those category weights.

For this model, we’re interested in the 10 best fits. Then, based on the strength of their match with the team in question, we can find a weighted average of how many wins they earned (again, prorating to 82-game seasons when necessary).

Here’s how it works for the current Dubs:

The numbers in the last column are calculated by multiplying the team’s number of wins (or prorated wins) by the team’s percent error, then dividing by the sum of the percent error for the 10 squads in question. That weights the 10 comparisons properly, giving the most influence to the one that’s the best match. The sum of that final column is the pace that our current team is playing at.

Based on historical data, the Warriors are playing at a 56.5-win pace, even if their current winning percentage indicates that they’re tracking toward 72 wins and have a distinct shot at tying Michael Jordan’s Chicago Bulls for the NBA’s best single-season record.

But that’s not the last step. After all, we’ve calculated the pace they’re playing at, not their final projected record.