Maximizing Efficiency Revisited: Advanced Insights into Dodgeball Strategy
Because of the interest in my previous post I decided to perform additional analyses and present them in this follow-up post.
I’ve written a code for filtering results according to planned vs improvised attack, for synchronized vs unsynchronized attacks, the catch rate for each type of attack and the sex of attacker and defender (to look at nuances arising within the mixed category)
I’ve developed an offensive index which includes the expected conversion rate taking into consideration the risk of catches for each type of attack. This is calculated as 1 x the conversion rate - 2 x the catching rate to identify the expected outcome of each attack
I’ve also developed a method for calculating the expected a priori, or future expected, conversion rate for planned attacks taking into consideration that they may or may not result in asynchronous throws
It is worth noting that the method for identifying multi-ball attacks differs from the previous post and that single-ball attacks have been labeled as synchronized or not depending on timing of pump fakes by non-throwers; see comments at the end of the post for the implications of this.
actionable insights
Limit improvised plays to 1- and 2-ball attacks: the risks associated with 3+ balls do not compensate for the increases in conversion rate
Prioritize single ball attacks for risk mitigation: Planned multi-ball attacks may have a higher conversion rate, but risk being asynchronous with resulting decreases in expected eliminations
Estimation of individual player conversion rates can help identify players with more or less effective synergies in multi-ball attacks: Players that improve the hit percentages of their teammates should be used in planned multi-ball attacks, while those that do not should be coached on improving synergies and used for improvised or single-ball attacks (if that is a strength)
Main analysis
Delving into the analysis, the figure below shows some of the outcomes depending on whether the attack was planned (called by the playmaker) or improvised (decided by the player or players themselves as a reaction to the opponents’ actions), and whether the attack was synchronized (thrown at the same time) or asynchronous/unsynchronized (thrown with delay). Bear in mind that the dataset contains relatively few 4- and 5-ball attacks, making it difficult to draw conclusions beyond 3-ball attacks. I present some of the findings from this plot in subheadings below.
Players relax and reduce focus in multi-ball attacks
The more players are involved in an attack, the lower the hit percentage (the number of balls actually hitting an opponent). This is seen for improvised attacks (for obvious reasons since they are made with short preparations such as counters or post-throw punishes) as well as slightly for unsynchronized planned attacks (which are more likely to occur the more balls are thrown). Despite the conversion rate increasing, each individual player is less likely to hit. This is probably less pronounced for more focused or better players and teams. This finding has a somewhat low certainty due to few attacks with 4 or 5 balls, and requires more data collection.
Improvised attacks should be limited to 1 or 2 balls
For improvised attacks, the hit percentage drastically falls and the catch rate drastically increases, for anything beyond 2-ball attacks, resulting in a lower offensive index. This is because they are difficult to coordinate quickly and without communication, and should only be used sparingly (see third paragraph, two points below). This finding has a low certainty due to few attacks with 3 or more balls, and requires more data collection.
The conversion rate per ball remains stable across multi-ball attacks, but only if the attack is synchronized
This suggests that multi-ball attacks may have more of a role than I suggested in the previous post. However, I cannot stress enough that this is contingent on synchrony and one always risks ending up in an unsynchronized attack. This is particularly a risk when playing against an aggressive wing defender that has good pump fakes or uses pre-throws, since that will disrupt the attackers.
For this reason, as the playmaker, I am more inclined to use multi-ball attacks against passive opponents with poor wing throwers (in addition to using it against uneven opponent lineups as described in the previous post). Against stronger and/or active wingers, I refrain from multi-ball attacks unless there is a very high priority opponent, particularly when leading an inexperienced lineup. I am also much more aggressive, risking my own safety to protect my middle players, when wing-defending against experienced and well synchronized opponents.
The catch rate decreases the more balls are thrown, but is particularly high with 2-ball attacks
It is more difficult to focus on a ball and catch it if one is targeted by many balls. Although there is variability in the data, this is illustrated by the negative slope for the catch rate across all data and planned throws.
There is a caveat though: 2-ball attacks are very risky since even a slight delay or one ball missing the target makes it much more likely that the attack results in a catch (remember that throwers also relax more in 2-ball attacks compared to single ball attacks). Planned 2-ball attacks that are unsynchronized have double the catch rate of synchronized attacks (8% vs 4%).
Improvised 3-ball attacks are more likely to be unsynchronized or result in a slightly delayed/early post-throw, with a catch rate approaching a staggering 10% (requiring an additional 20% conversion rate just to break even). This throw is well known by all dodgeballers as we have all fallen into the trap of thinking the first two misses have distracted the defender and moved it into a position where there is an easy hit, only to result in a simple catch.
As presented in the previous post, the most efficient attack is the one-ball attack
After accounting for the catch rate, one finds that the highest offensive index per ball (true conversion rate) occurs for both planned and improvised single-ball attacks.
This is followed closely by the 2-ball attack, which has the caveat of a high catching risk when unsynchronized, particularly in planned attacks.
Catch and conversion rates can be combined for an offensive index
Since a catch is worth -2, and a hit +1, one can multiply the catch rate by -2 and add it to the conversion rate to get the offensive index, which indicates the number of expected eliminated opponents for a given attack. Since the catch rates are relatively low, the offensive index per ball is not that much different from the conversion rate already presented; the presented patterns and conclusions are the same.
Offensive index and conversion rate per ball are underestimated in the endgame
They are less important when there are less players on court. Giving away 4 balls is less of a problem when there are fewer than 4 opponents left. This decreases the net effect of giving up possession (team conversion rate minus opponent conversion rate in the following attack) and increases the value of multi-ball attacks in the endgame, beyond that indicated by the offensive index and conversion rate. I will try to write the post for expected net effect that I have been talking about for a long time, as it has a huge impact on how to approach the strategy of ball control.
INCORPORATING FUTURE EXPECTATIONS WHEN PLAYMAKING
We have already taken catches into consideration (calculating offensive index from conversion and catch rate). However, as mentioned above, asynchronous attacks also pose a risk and have to be considered when playmaking. I will explain how one can take this into consideration as well.
We can start by looking at the percentage of attacks that result in unsynchronized throws, to know the risk associated with calling a certain play. The following are the probabilities of throws being unsynchronized across planned attacks:
1-ball attack: 11%
2-ball attack: 27%
3-ball attack: 20%
(Not enough data for 4- and 5-ball attacks)
For example, when I, as the playmaker, call for a 2-ball planned attack I have to be aware that there is a 27% chance that the attack will be asynchronous (it is 26.5% for Sweden and there is a rather negligible <2% difference between the best and the worst teams in the dataset). This asynchrony decreases the offensive index per ball from 0.22 (for planned synchronized 2-ball attack) to 0.14 (for planned unsynchronized 2-ball attack) in 27% of all planned attacks. In other words, the expected a priori offensive index per ball, at the time of making the call, is 0.20 eliminated opponents per thrown ball (0.22*0.73 + 0.14*0.27). We can use this reasoning to estimate the actual expected future conversion rate per ball for certain planned attacks, considering both the risk of catches and asynchronous throws, at the time of calling (using the above formula on the offensive indices per ball and respective expected probability for asynchronous throws):
1-ball attack: 0.22 eliminations per ball
2-ball attack: 0.20 eliminations per ball
3-ball attack: 0.20 eliminations per ball
This can be contrasted with the offensive indices for improvised attacks which are 0.31, 0.28 and -0.02 respectively. The conclusion is that 2-ball attacks are much more valuable when improvised (such as during counters or pre-throws) than during planned attacks (for a net increase of 0.08 eliminations per throw).
The risk associated with asynchronous planned attacks is one of the reasons behind my philosophical stance on aggressive/reactive improvization versus ball control. There are many reasons why improvised attacks have a superior expected payout, which will increase winning in the long term. However, when there are few sets left, with fewer potential outcomes, it is more balanced. When playmaking, I prefer ball control and planned attacks only when playing with very experienced players that I can trust and rely upon to execute calls. Any deviation from such execution greatly increases variability in risk, leading to unpredictable outcomes in the long term, such as one player repeatedly giving away the 4th ball. There is much lower variability in risk when employing an aggressive improvised strategy, as one knows the expected rates of conversions, catches and similar (at least when employing clear defensive playmaking). At least I do, since I have analyzed my teammates in great detail and know when to use who based on their profiles of strengths and weaknesses.
SEX BASED ANALYSES
In terms of sex-specific subgroup analyses one can see that males have higher conversion rates and offensive indices per ball in attack (better throwers, against both males and females separately) and hold the opponents to a lower conversion rate per ball (better dodgers/blockers, against both males and females separately) than females, irrespective of the number of balls thrown. Males also have a slightly higher percentage of synchronous 1- and 2-ball attacks (1% and 5% better respectively), while females have better synchrony for 3-ball attacks (3% better). These differences are small and likely reflect prior experience due to differences in play style between men’s and women’s dodgeball (with the former being more single-ball-minded, and the former relying more on multi-ball attacks to minimize risk of catches due to weaker throws).
PLAYER-WISE ANALYSES
Given the wealth of this dataset, there are of course many ways to break down player-wise analyses, to better understand the individual roles specific players have, as well as their strengths and weaknesses, which the coach and playmaker must be aware of when planning lineups and in-game plays. I have presented individual attacking and defensive percentages, as well as tactical and technical skills in previous posts.
For this analysis I looked at many more things but will focus on individual effects on conversion rates. Although each individual player does not necessarily hit their target, their participation in an attack affects both the teammates and the opponents. For the effect on teammates, perhaps I always miss, but my foot-throws cause opponents to move, which increases the probability that my teammates hit. For the effect on opponents, a strong thrower draws a lot of attention which increases the likelihood that other teammates will hit the opponent, while a very weak opponent can be ignored which effectively reduces the attack by one ball (for example from a 3-ball to a 2-ball attack) in terms of efficiency.
To look at this, I found that the team-wise average conversion rate for Sweden was 0.44 eliminations per attack and subtracted that from the individual average conversion rate from all the attacks each player participated in to get a relative player impact. This illustrates the effect the player has on the overall attack. For example, Male3 has a relative impact of -0.12. He participated in 46 attacks, and his participation in those attacks caused him and his teammates to eliminate 5.5 fewer players compared to the average teammate. This dataset does not show why that is the case (although I have my theories, now that I see the results), but knowing this, one can look at attacks that he is part of, which will likely show potential areas of improvement.
This overall average will be skewed for players with high hit percentages participating in attack types with high conversion rates, which is why one can also look at the relative impact for each attack type separately.
These results are more abstract and related to implicit outcomes than that of hit percentages, and likely identify separate aspects of playing, similar to how technical and tactical skills relate to explicit and implicit aspects of eliminating opponents (see the respective posts for explanations on what they quantify and how).
Comments from introduction
Timing for synchronized attacks
In the previous post, multi-ball attacks were identified based on occurring within 1s of each other in the dataset.
In the analysis for this post, synchronized attacks were those occurring at the same time, with no significant delay (reactive or staggered throws). This method is a bit less lenient toward including reactive and early post-throws after the original attack. A 4-ball possession is registered as a 2-ball attack followed by a 1-ball attack if the third ball is significantly delayed (separated by an entire throwing-motion), but an asynchronous 3-ball attack if occurring within a single throwing motion.
The distinction is more philosophical than empirical, since one can consider these throws as part of the same attack or not depending on whether one is interested more in the outcomes of entire possessions or specific attacks. In other words, the previous method is intermediate between looking at outcomes based on ball-possession (presented in a previous post) and the current method of looking at only the primary attack.
Single-ball synchronizations
They were labeled based on the timing of the pump fakes by the teammates. If the teammate next to me pumps at the same time as I throw a single ball attack, it is labeled “synchronized”. One can expect a higher hit percentage when the throws are covered by simultaneous pump fakes.
However, in this dataset a lot of unsynchronized single-ball attacks were made by players with a strong reactive throw, which occurred with a slight delay after the pump fakes had induced movement. This is why the hit percentage is unexpectedly higher than for synchronized pump fakes (which were instead more often thrown by inferior throwers).
Whether single-ball reactive throws after defender movement is better than those covered by synchronized pump fakes is not clear; looking at this would require a randomized controlled data collection since this is not answerable within actual matches.
Let me know if you find any use from these analyses when playing yourself in the comments below…