Sports fandom involves some cognitive bias. We assign importance to patterns without real meaning, see signs in events that are essentially random. We hope for the best and steadfastly convince ourselves this is the time things finally work out for the good guys. Long-time Wizards fans are experts at this kind of thing. Our brains are wired for it.
For example, the Wizards won four games in a row before falling to the Clippers and Raptors. Winning streaks are usually interpreted as a sign that a team is good. They’re finding their groove, hitting their stride, getting a rhythm. Right?
Well, no, actually. Long streaks, like Golden State’s (or Philadelphia’s) to start the season provide meaningful information about the relative quality of those teams. But, for virtually every NBA team, including a mediocre one like the Wizards, three- and four-game streaks are inevitable. According to the handy table in Dean Oliver’s 2004 book, Basketball On Paper, a team that wins half its games during an 82-game season has a 99.4% chance of winning four in a row at some point. Naturally, that .500 team has the same odds of losing four in a row. By their 28th game, the Wizards had accomplished both, plus an independent three-game winning streak.
A .400 team — one that would win about 33 games — has an 87% chance of winning at least four in a row during an 82-game season. Even a 25-win team has nearly a 50% chance of at least one four-game winning streak.
Sometimes randomness is fun, like Rasual Butler’s hot streak last season, or Gary Neal’s this year, or Garrett Temple’s binge of three straight games with at least 20 points. Other times, it’s not so fun, like Butler’s second half of the season, or any of Neal’s “non-hot” games, or the dud performances Temple produced in the games preceding and following the scoring outburst.
This is not meant to be a nihilistic “everything is random and therefore meaningless” screed. Some teams and players are better than others. But, the true quality of a team is found by what they do on average, over time.
The Wizards in recent years have been decidedly, consistently, mediocre. I can hear the arguing already: 46 wins last season; 44 wins the year before; trips to the second round of the playoffs both years. These are signs of the Wizards being a team on the rise that’s hoarding cap space for a run at a superstar, and they’ve had some bad luck with injuries this season. Maybe. But, more likely: fan-think.
In an 82-game season, how many games would a truly mediocre team win? The easy answer is 41. That’s exactly half, right in the middle. Therefore, 46 wins is five better than average, which means the Wizards were better than average. This isn’t wrong — just incomplete.
Let’s imagine a team that’s perfectly mediocre in quality. By the end of an 82-game season, it will score exactly as many points as its opponent. How many games will this mediocre team win? They might win 41, but they might win a few more or a few less. Their win total depends on how those points get distributed. Having a 50% chance of winning each individual game doesn’t mean a team will actually win half the games.
For a simple randomness test, google up a coin-flipping simulator or flip a coin yourself. Just for kicks, I ran a coin-flip simulator on 11 sets of 82 trials, one set of 66 trials, and one set of 30 trials. Astute readers might notice the number of “trials” matches the number of regular season games the Wizards have played since Ernie Grunfeld became president.
Of the 998 trials, heads came up 516 times — 51.8% of the time. Variance, right off the bat. If “heads” equals “wins” (and it does here because it’s my blog), that works out to about 42.5 “wins” per 82 games.
Here are the “win” results from each set of the 82 coin-flip trials:
In other words, in a random test where each independent coin flip has identical odds of producing a win or a loss, there’s a low of 35 wins and a high of 53. For the heck of it, I ran the simulation again and got a cumulative “winning percentage” of .454 with a high of 43 and a low of 34. Remember: this is totally random. A perfectly mediocre team could see its actual win total vary significantly from .500.
Which brings me back to the Wizards. There are a few good measures of relative team strength besides record. Chief among these are scoring differential, and efficiency differential, which are basically the same thing, and those same measures adjusted by strength of schedule.
Those differential numbers (adjusted for strength of schedule or not) can be used to estimate how many games each team would be expected to win. Last season, for example, the Wizards’ scoring differential suggested a team that would win 42-43 games. Winning 46 felt good, but was probably more about random outcomes for a mediocre team. The playoff “runs” were hella fun to watch, but represent a small sample size that’s even more prone to random variation. In other words, us fans (and maybe folks in the league as well) overrate results from the first round of playoffs.
Let’s go back to Team Perfectly Mediocre, and let’s say they’ve met their match in the first round of the playoffs. We’ll call the opponent: the Toronto Raptors. Who’s going to win this festival of random mediocrity? It might be a closely-matched, 4-3 series, but maybe not. I replicated 10 seven-game series for Team Mediocre vs. the Raptors, and the “series” went seven games three times, and six games three times. It also had three consecutive “sweeps” and one five-game series. Remember: this is totally random.
Back to the Wizards. Since Grunfeld took over Washington’s basketball operations before the 2003-04 season, the team has been meaningfully worse than mediocre, even allowing for randomness. Under Grunfeld’s leadership — now in its 13th season — Washington has won 417 out of 998 regular season games. That’s a winning percentage of .418. Just to see, I ran the “perfectly mediocre” test of Grunfeld’s 998-game (so far) term with the Wizards 10,000 times and couldn’t come up with a variance close to Washington’s actual performance. This is a fancy way of saying the Wizards have been truly bad under Grunfeld.
Over the course of his 12 full seasons, the Wizards have compiled a record of .500 or better six times, but have managed a positive scoring margin just three times. Grunfeld’s teams in Washington have averaged 34.3 wins per 82 games — slightly outpacing the 33.9 predicted by scoring differential and the 33.3 predicted by adjusted scoring differential.
If the 998 games represented a single, massively long basketball contest, the Wizards have been outscored by 2,467 points with Grunfeld at the helm.
Player Production Average
The ratings below are a metric I developed called Player Production Average (PPA). In PPA, players are credited for things they do that help a team win, and debited for things that don’t, each in proportion to what causes teams to win and lose. PPA is pace neutral, accounts for defense, and includes an adjustment based on the level of competition faced when a player is on the floor. In PPA, average is 100, higher is better, and replacement level is 45.
League-wide PPA scores through games played 12/30/15 are here.
The basic message in the numbers: Wall and Gortat need help. The Wizards don’t have starter-quality players at power forward, shooting guard or (arguably) small forward. Wall remains in the good-not-great range; Gortat’s production is still solid, but diminished significantly from last season.
The other basic message: Wall and Gortat need help fast. Teams in the East have improved, and it’s probably going to take 44-45 wins to make the playoffs. The Wizards are on pace for 38. To reach 45 wins, they’ll need to go 31-21 over their remaining games — about the pace of a 49-win team. Theoretically possible, but not very likely. Barring a major turnaround, the conversation about the Wizards in April won’t be about their matchup in the playoffs, but about their odds of getting the top pick in the draft lottery.