As the regular season slowly withers to a husk, it is worth revisiting the age-old question: what is the meaning of the regular season? This question has gained new urgency in the wake of the Bucks’ first championship in five decades.
Functionally, the regular season determines which teams make the playoffs and the seeding of those teams. Better seeds enjoy the fruits of home-court advantage and playing relatively worse-off teams in the early rounds. The regular season is also a laboratory where teams can experiment with new players and new schemes. This experimentation can be maximized when teams have a baseline level of quality that assures that they will make the playoffs (or, in contrast, that they will not make the playoffs). Oh, and I suppose it makes folks some money to boot.
Here, I want to emphasize an additional reason to ignore the regular season: luck. Luck (or randomness) plays a bigger role in the regular season than the playoffs. As such, we should be reticent to angrily leap into Bucks Twitter after dropping one or even several regular season games, and remain bullish for the playoffs despite these occasional outcomes. I’ll whip out some combinatorics and simulation data from my math nerd days and pull a little bit of Moneyball into basketball to illustrate how both teams and players are subject to the whims of Lady Luck.
First and foremost, the playoffs are comprised of series rather than one-off games. It is not uncommon to see David beat Goliath; indeed, he did. It is quite uncommon, however, to see David beat Goliath four times out of seven. This relates to the law of large numbers, discussed previously in this venue. If we flip a coin a few times, we might get only heads or tails, but in the long run we should get a similar number of both. Likewise, if a team has a 50% chance of beating another team, they may drop a few games in a row, but in the long run they should win about half of the games.
Let’s crunch some numbers on this. I compared the probabilities that a team wins a single game with the likelihood that, given that probability, that team would win a four-out-of-seven playoff series. (To peek beneath the hood, I calculated the likelihood of all seven game permutations - e.g., WLWLWLW - based on the single-game probability.)
Single-Game vs. Playoff Win Probabilities
First, a sanity check: if a team will never lose a single game (100%), they will never lose a playoff series (100%). Yup! Next, a team that loses 10% of the time in single games has a very low chance of losing a playoff series (.3%). The discrepancy between the two columns wanes but remains stark as the single-game probability drops to 50%. At that point, a toss-up in a single game translates to a toss-up in a playoff series.
The main takeaway here is that playing a playoff series substantially reduces the likelihood of upsets. This makes sense; a team can lose up to three times in a series without being shown the exit. Let’s not forget that the Bucks were 16-7 in last year’s playoffs, and only 12-7 if we forget the series against the Magic (and who hasn’t?).
Like teams, individual players are also subject to the forces of luck. Here, I’ll draw from the work of Bill James made prominent by Michael Lewis’ Moneyball. One example in particular has stuck with me. Consider two baseball players. One bats .275 and the other bats .250. The former is an above-average player and the latter is an average player. Assume that they play five games per week and have four at-bats per game. The difference between these two players - the key to being an above-average player rather than simply an average one - is one hit every two weeks. That’s insane! More importantly, even the most observant batting coach may struggle to see the difference - the underlying truth is revealed in the statistics.
Let’s translate this into basketball terms. The average three-point percentage in the NBA is about .350. Annoyingly, the standard deviation is not readily available, in line with some of our previous discussions. For sake of simplicity, let’s compare the average player who shoots 35% with an above-average player who shoots 40%. If they both play five games and shoot four threes in each, we would expect the above-average player to connect on a single additional three.
And yet, even this difference is more than we would expect from a single game. The combinatorics gets a bit hairy here; instead, I simulated shooting lines for 1,000 games and 1,000 playoff series to compare how often an above-average three-point shooter would outscore an average three-point shooter on a diet of four threes per game. (To peek beneath the hood, I randomly generated numbers between 0 and 1 and categorized them as “make” or “miss” depending on the shooter’s three-point percentage.)
Single-Game vs. Playoffs Probabilities of Outscoring Average Shooter
|Above-Average 3P%||Single-Game||Playoff Series|
|Above-Average 3P%||Single-Game||Playoff Series|
Let’s start at the bottom. When the above-average 3P% is 35% - the same as the average 3P%, so not really above-average, to be fair - the “above-average” player’s likelihood of outscoring the average player in a single game is 36.8% and in a playoff series is 43.4%. It isn’t 50% because players, unlike teams, can tie (the average player would have the same likelihoods of outscoring the above-average player). As more games are played, it becomes less likely for the two players to drain the exact same number of threes, simply due to the increased variability that arises among 28 shots versus 4.
Crucially, this gap widens as the above-average 3P% rises, culminating in a 45% three-point shooter outscoring an average shooter half of the time in a single game yet nearly three-quarters of the time in a playoff series. Over the playoff series, there is more breathing room for the law of large numbers to come to fruition. However, there remains a solid chance for David to emerge victorious (or at least achieve parity) in a playoff series and especially single games. The is because the gap between above-average and average shooting can be quite small, as suggested in Moneyball.
Still, the main takeaway is that playing a playoff series substantially reduces the likelihood of lesser players outperforming better players. There is always variability in player performance, and a playoff series (vs. a single game) will often be more representative of the player overall. The Buck that comes to mind here is Khris Middleton, who may have a subpar performance in a game or two but also a Middleton game every series. Both sides of the Khris coin are valid and can only be captured in a playoff series.
Playoff series are not as long as the regular season. The regular season thus offers more real estate for the law of large numbers to work its magic, suggesting that the regular season is actually meaningful writ large. But narrowing the scope to individual games heightens the chances that Goliath may fall (hence the appeal, or dismay, of March Madness).
As we prepare for the playoffs, I am focusing on our new additions and schemes and enjoying the ride with one of our best teams ever, with only a lazy eye lolled towards seeding. Last year showed that this team is above the luck-laden morass of the regular season; let’s look forward to the playoffs.