2.1 General timeout patterns

We start with a general overview of timeout calling patterns. How often do different teams call timeouts?

Broadly speaking, teams that have a higher win rate (percentage of matches won) call less timeouts. A plot of this relationship is shown below:

Timeouts are almost universally called by the team that is not currently serving:

14 timeouts (of 1480 total) called by serving team

When are timeouts called? Below is a histogram of the opposing team’s score (at the time that each timeout was called). Sets 1–4 are plotted separately from set 5, for obvious reasons.

For sets 1–4, there are technical timeouts at 12 points, which correspond to the dip in the upper panel. Coaches will typically avoid using a team timeout when a technical timeout is imminent. This dip aside, there is a general increase in the number of timeouts called as the set progresses, peaking just below 20 points. Set 5 (during which there are no technical timeouts) shows a peak around 3–4 points, a second around 10 points, and possibly a third around 13 points.

This can be plotted with both the calling team’s score and the opposing team’s score. The colours in the plot below show the number of timeouts called for each combination of calling team’s score and opposing team’s score:

There is a hotspot when the opposing team’s score is around 5 and the calling team’s score is lower — so the opposition has jumped out to a quick start. It is clear that most timeouts generally lie above the 1:1 dashed line, meaning that the opposing team is ahead of the calling team. There are also a number of timeouts called when the calling team is ahead of the opposition, mostly towards the end of the set: possibly these might correspond to situations where the opposing team has scored a run of points and is catching up to the calling team, but this wasn’t looked at further here.

A simplified version of the previous graph is below, showing only the score differential (calling team’s score minus the opposing team’s score) when each timeout was called:

Only a small proportion (about 24%) of timeouts were called by a team that was leading at the time.

None of the above is particularly surprising, but it serves to confirm that timeouts are generally called by the receiving team, at times when some sort of intervention might be expected to be helpful to the outcome.

2.2 Effect of timeouts on sideouts and serve effort

The following indicators of serve success and effort are considered:

• whether the serve was a jump serve or not. The data in fact provides “serve type”, which is one of jump, jump-float, float, or unknown serve type. However, the latter two categories make up a vanishingly small fraction of overall serves, and so “serve type” can be adequately treated by converting it to a binary indicator of whether the serve was a jump serve or not
• serve error rate (the proportion of serves where a service error was made)
• ace rate (the proportion of serves that were aces)
• perfect pass rate (the proportion of receptions rated as a “perfect pass”).

The following indicators of the performance of the receiving team are calculated:

• sideout rate. Sideouts are expressed from the perspective of the receiving team (i.e. a sideout is a reception where the receiving team wins the point)
• earned sideout rate (sideout rate excluding service errors)
• first ball sideout rate (proportion of receptions where the first attack by the receiving team was successful)

Indicators analogous to the sideout indicators, but expressed from the perspective of the serving team, are also calculated. These are referred to as:

• serve loss rate (the proportion of serves where the serving team lost the point)
• earned serve loss rate (serve loss rate excluding service errors)
• first ball serve loss rate (proportion of serves where the first attack by the receiving team was successful).

These indicators will be evaluated for each of the following situations:

• the first serve of a set
• the first serve following a technical timeout
• the first serve following a normal timeout
• all other serves.

Statistical tests have been conducted to evaluate whether a given indicator varies across the different situations. What does a significant result mean in this context? We are assuming that our dataset is a sample that is representative of some larger volleyball universe. The significance (p-value) of a test performed on our data indicates the degree to which we expect the result in question to hold true in the larger universe.

The statistical models used here are generally binomial mixed-effects models, in which the response is the indicator in question, and a random effect by individual player is included. A “binomial” model simply means that the response can take one of two values (e.g. if we are examining serve errors, then a given serve was either an error or it was not). The random effect allows individual players to vary in their performance. Including this random term will also account for the fact that some players might perform the skill in question more often than others across the various serve categories.

In general, we test by fitting two models for each indicator. The first model has a single fixed predictor term (the serve category). The second has no predictor terms — that is, it assumes that the indicator does not vary with serve category. We then compare the fits of the two models. If the first model is a statistically better fit to the data (p<0.05), then it supports the idea that the indicator does indeed vary with serve category.

2.3 Timeouts over the course of a set

In the previous section we found little evidence to support the idea that overall sideout rate differs after timeout than during general play. Are there more subtle effects — for example, does the effectiveness of a timeout change as a set progresses? Here we are focusing on sideout rate, and only comparing after-timeout serves to all other serves.

2.3.1 Set score

Does sideout rate vary over the course of a set? The data are summarised below. The lines show the mean sideout rates and the shaded bands their 95% confidence intervals, for different values of “score” (where “score” here means the higher of the two teams’ scores at the beginning of the rally):

Figure 5: Sideout rate by set score

During non-timeout play (blue line) the sideout rate is clearly pretty constant. The after-timeout rate (red line) is very similar to the blue line. The shaded bands are wider, indicating that we are less confident in our estimate (because there are less data for after-timeout serves than for other serves), but there is no substantive difference between the two lines. (The big dip in the red line around 25 points is an artifact from a lack of data in this region.)

2.3.2 Score differential

What about score differential? Here, differential is defined relative to the serving team (so a positive score differential means that the serving team is ahead). We don’t distinguish which team called a timeout (though as previously shown it’s overwhelmingly the receiving team).

The data are summarised below (the lines show the mean sideout rates and the shaded bands their 95% confidence intervals):

Figure 6: Sideout rate by score differential

For score differential between about -10 and +10, the two lines are again very similar. Overall, the confidence intervals of the two curves overlap, consistent with out earlier finding that there is no overall difference in sideout rate after timeout. Sideout rate is higher when the serving team is behind, and sideout rate is lower when the serving team is ahead (exactly as one would expect). At more extreme score differentials (below -10 or above +10) the data are less consistent and the confidence intervals much wider, indicating that there isn’t sufficient data to draw strong conclusions.

If we are prepared to assume that sideout rate should vary smoothly as a function of score differential, then we can fit a model, and this shows the relationships a little more clearly (a generalised additive model with smoothing spline was used here):

Figure 7: Sideout rate by score differential, from smoothed model

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3.1 Timeouts

What about timeouts? Does calling a timeout during a run of serves affect the serve error or sideout rate? First of all, we fit the same models as above, but with an additional term for whether or not the serve followed a timeout. That is, the serve error/sideout rate is estimately separately for each run position, along with an additional adjustment for timeout. The timeout adjustment applies equally to all serve run positions.

Significance of the timeout term: p=0.217

Note that the error rate estimates here (for run position 1–5) are slightly different than in the previous model — because now we are additionally accounting for the effect of timeouts.

Significance of the timeout term: p=0.176

These two models assume that timeouts affect all serves equally. Perhaps we believe that timeouts might affect serve error rate differently depending on the serve run position (for example, we might think that a timeout after one successful serve will not have any effect, but a timeout after a run of two serves might). We can also test this, but this time we need to fit a model that estimates a separate error rate for each run position, both during normal play and after timeout. In this case, rather than try and show the data summary (it is becoming rather complex) we just show the comparison of the two models:

## Data: srunxt
## Models:
## mfit_sretm: error ~ run_position + serve_category + (1 | player_name)
## mfit_sreti: error ~ run_position * serve_category + (1 | player_name)
##            Df   AIC   BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## mfit_sretm  7 18825 18881  -9405    18811                        
## mfit_sreti 11 18829 18916  -9403    18807  4.28      4       0.37

And for sideout rate:

## Data: srunxt
## Models:
## mfit_srsotm: serve_loss ~ run_position + serve_category + (1 | team)
## mfit_srsoti: serve_loss ~ run_position * serve_category + (1 | team)
##             Df   AIC   BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## mfit_srsotm  7 27220 27276 -13603    27206                        
## mfit_srsoti 11 27225 27313 -13602    27203  3.35      4        0.5

We can double-check this by eyeballing the data, and by explicitly testing the effect of sideout at each position in the serve run (i.e. fitting a new model for each serve run position, and testing whether timeout has a significant effect). In this case we only compare post-timeout serves to serves during general play (i.e. not using data from serves after technical timeouts or first serve of a set). Compare the “Sideout rate (general play)” and “Sideout rate (followed timeout)” columns in the following table:

3.2 Calling timeouts during serve runs

When during serve runs are timeouts called? After how many breakpoints (points won on serve)?

Are multiple timeouts ever called during a single serve run?

Rarely. There were 1436 serve runs in which at least one timeout was called. Two timeouts were called in only 42 of these.