Volleyball is not a game that can be won with just one player, everyone knows that! While that may be the case, sometimes you find a hitter that just seems so efficient and you think to yourself, “Do their setters really need to set anyone else?” Diversifying an offense is one of the setter’s most important jobs, and I have certainly heard that yelled at me a few times. With that being said, offensive strategy differs from team to team, and some teams are more reliant on a single player to get their kills than others. But how does a team’s distribution of kills affect their ability to win games? Luckily for us, this is something we can look at in the data! Let’s take a look at how widely dispersed the kills a team has over the course of a season are. While this article will be looking at the bigger picture surrounding kill distribution, in later articles I’ll dig into some more specific details of the hitting distributions within games and across positions.
When looking at a team’s offense, one way to look at its concentration is by looking at the percent of kills your best scorer has on the team. On average, the leading attacker on a collegiate volleyball team takes 25% of the swings and gets 25% of the kills. This number certainly varies across teams, however, as you can see from the distribution for both D1 and D3 volleyball teams in the graphs below.
While the overall average and distributions are pretty similar across D1 and D3, it is worth noting that the outliers in D3 are more extreme. In particular, while the highest percentage of team kills by a single player in Division 1 is 47%, the highest in Division 3 is 64%. That means that more than half of the kills a team had in a single season came from one player!
While focusing on the percentage of kills going to the top player is interesting, it doesn’t capture the full distribution of kills across all players on the team. For example, a team’s offense looks very different if there are two outsides each getting 40% of kills along with a right side getting the remaining 20% of kills, with no middles or any other player getting any kills, as opposed to a situation in which there is one player getting 40% of kills and six other players each getting 10% of the kills–even though the two situations would look the same in the charts above!
To capture this difference, I generated a measure called the “effective number” of hitters for each team-year in the dataset to measure how concentrated the kills are for each team. If one player had all the kills, the effective number of hitters would be exactly 1.00, since only one player had any kills that year. If there were only two players that generated all the kills that year, and they split the kills equally, the effective number would be exactly 2.00. If one of them has 99% of the kills and the other player only has 1% of the kills, however, the effective number of hitters would be about 1.01. On the other hand, if one of the hitters had 80% of the kills and the other had 20%, the effective number would be about 1.5. The effective number generalizes beyond just two–if three players split the kills equally, the effective number would be exactly 3.00. Most volleyball teams, however, rely on more than just 3 hitters, and as you’ll see in the graph below, the lowest effective number of hitters in a D1 season is around 3.5.
The effective number of hitters in collegiate volleyball varies, but most teams dish the ball out fairly well over the course of a season, as most teams average between 5 and 7 effective hitters. The effective number of hitters is usually lower for individual games. In the championship game between Texas and Nebraska, Texas had 3.72 effective hitters, and Nebraska had 4.54 effective hitters. Throughout the season, however, Texas had an effective number of 4.73 hitters, and Nebraska had 5.55. While the overall pattern in D1 and D3 is similar, the effective number of hitters in Division 3 is slightly more dispersed, as there are more outliers in D3, with some teams being more reliant on fewer hitters.
In another article, I’ll look at how the effective number of hitters relates to other volleyball statistics, but for now, I’ll just mention that there is an interesting pattern relating the effective number of hitters to team success. Teams with an extremely low (3.5 or fewer effective hitters) and extremely high effective number of hitters (8 or more) tend to perform markedly worse than teams with a more typical effective number of hitters. Let’s check out why that is the case!
Well, to those familiar with volleyball, the fact that teams with a less diversified offense perform worse seems fairly self-explanatory: if a team is reliant on just a few hitters, their offense may be more predictable, making them easier to read, easier to block, and easier to dig. This is why coaches and teams often work so hard to develop a diversified offense.
Less intuitive, however, is that an over-diversified offense is also less successful. If the effective number of hitters across a season is 8 or more, this often suggests that players missed time with injuries, or the team is having rotational issues in which they cannot get their hitters in rhythm and scoring.
While these numbers show a general idea of what usually works and does not work offensively, every team runs their offense differently, and there is not just one right way to run an offense! Everyone says serve and pass wins games, and while I wholeheartedly believe that, they win games because they allow a team to be in-system so they can effectively run their offense!
Data Notes:
- For the stats geeks: the ‘Effective Number’ is equivalent to the inverse of the Herfindahl-Hirschman Index of market concentration (when using the decimal form of market share) or the Simpson diversity index used in biology. The HHI is used to measure how much an industry is dominated by a few companies or market power is broadly dispersed amongst many companies in the same industry.
- While in this post I look at the effective number of hitters weighting them by kills, the story is the same if we normalize the effective number of hitters by all hit attempts.
- Imagine an idealized team running a 6-2 with the same players all season, and that their kills were divided equally across the two middles, two outsides and two right sides (assume there is no back-row hitting or setter dumping). That team would have exactly 6 effective hitters. Normally the distribution of kills isn’t equal across players, which would push the effective number lower than 6. In a 5-1, you’d also probably expect a lower effective number of hitters (depending on how often the setter gets kills). But to the extent that a team brings in its bench hitters over the course of the season, the effective number would go up. So, teams that have an effective number of hitters above 6.0 are either changing starters over the course of the season or relying on their bench more.
- While I’ve introduced the ‘effective number’ in the context of looking at balance in hitting, you can use the effective number to summarize distributions for other volleyball stats as well. For example, the variation in the effective number of setters is in many ways more pronounced than the variation in the effective number of hitters, because of the difference between teams running 5-1s and 6-2s. I’ll be writing about that more in future articles.
- I’ll also dig more into the relationship between balanced hitting, distribution of hitting by position, and team success. You might think, for example, that teams with higher effective number of hitters are more successful at running their middles, but looking at the data, that’s not always the case. More to come soon!
- Photo Credit: Header image photo from Charleston Southern Athletics (CSUSports.com)