# How costly are missed penalties?

The current Premier League season has been partly characterised by a remarkable number of unconverted penalties. Of the 83 taken in 29 rounds of matches, 25 have failed to beat the goalkeeper.

This equates to a conversion rate of 69.9%, below the historical Premier League average of around 77%. We may finish the season back on average, but I thought I’d look at who has paid the price for missed penalties so far.

Liverpool immediately stand out having failed to score four of their five penalties in the league. Using Soccer Statistically’s Outcome Probability Calculator, we can get a sense of how many points Liverpool have squandered through these misses.

The first four columns are fairly self explanatory. The rest is explained:

- Actual points (AP): the points Liverpool took from the match.
- Expected points (EP): the points Liverpool would have expected to have taken
*had the penalty been scored*. This is calculated using the outcome probability calculator. By entering the minute of the penalty, location and resulting margin from a successful penalty, the calculator gives us win and draw probabilities. By multiplying these probabilities by 3 and 1 respectively, we get expected points from the time when the penalty was taken. - EP – AP: the ‘cost’ of the penalty. Had Suarez converted against Sunderland, Liverpool would have taken 2.53 points on average from that position. In the end, they took only 1, meaning the cost of the miss was about one and a half points.
- Result: a missed penalty won’t be costly if a team wins, as was the case at Everton. Thus, only if the previous column is positive is a penalty deemed ‘costly’.
- Pressure: the expected points added (EPA) from a converted penalty. This is calculated through the difference in expected points between scoring and not scoring the penalty. The expected points after Suarez’s miss was 1.68 (not on table); this is subtracted from the EP had he scored (2.53), giving a ‘pressure level’ of 0.85. Late penalties in games with tight margins present opportunities for a large ‘swing’ in expected points and thus exhibit more pressure – more on this later.

**Costly misses**

The sum of Liverpool’s costly misses is therefore just over five points, making them the league ‘leaders’ in this respect. Of course it’s a little simplistic to attribute dropped points to a single penalty miss, but this isn’t an exercise in apportioning blame. Instead, the numbers give a sense of the frustration from missed opportunities.

Two of Blackburn’s three misses came in the same match (see table below), so the less costly of the two has been subtracted from the EP loss. On eleven occasions this season a team has missed a penalty but still won; the remaining fourteen penalties are in the table above.

No missed penalty has perhaps been as painful as Sebastian Larsson’s for Sunderland at Wolves. 1-0 up with 17 minutes left, Larsson should have doubled the visitors’ advantage, a lead that would have given them, on expectation, 2.97 points. His penalty was saved, and Sunderland eventually lost 2-1.

Formica, Hoilett, Kuyt and Watson all had the opportunity to open the scoring, whilst Dunn missed a chance to equalise for Blackburn. Again, it’d be unfair to suggest Larsson himself cost Sunderland nearly three points, but the numbers delve into the realms of ‘what ifs’, a popular place for many football fans!

Since around three quarters of penalties are scored, we could assign points expectations from the mere awarding of a penalty, and quantify points gained/loss from this value after it is taken – thanks to Mark from the Power of Goals blog for pointing this out to me.

**Feeling the pressure**

As noted earlier, points expectations also help us quantify some level of pressure. Take Mario Balotelli’s penalty in the 95^{th} minute against Spurs in January, with the score at 2-2. A miss would have almost certainly guaranteed a draw, a goal a win. Therefore two points – the maximum – were at stake on the penalty.

Similar deductions can be made for all other penalties, using the difference in points expectations from scoring and missing. All of the highest-pressure penalties this season were late second half attempts to give teams the lead, with only Formica missing.

On the whole, Everton have faced the most pressure from the spot, converting all of their four penalties as well. Meanwhile, only two of United’s nine penalties have been to draw level or take the lead, perhaps a reflection of their ability to score freely in open play.

Unconverted penalties tended to have more points at stake than converted penalties, but the difference – 0.83 points vs 0.74 points – is statistically insignificant.

Clearly there are factors missing from the expected points evaluations, and it’s practically impossible to precisely quantify such scenarios. Nevertheless, hopefully the above analysis and examples somewhat illustrate that pain and pleasure that can come from penalties.

The next time you hear a commentator say ‘that could be a costly miss’, ask yourself – how costly?

*Expected points calculated using Soccer Statistically’s **Outcome Probability Calculator**.*

Omar,

Thanks for another piece of original research! Excellent stuff.

One remark though. I’m quite hesitant to accept a method that allows post-hoc events to influence the value attributed to that event.

For example, Luis Suarez misses a sixth minute penalty for Liverpool against Sunderland and the value attributed to that miss is dependant on the events during the 84+ minutes of the remainder of the match.

For me it would make more sense to use what you’ve termed the ‘pressure’ attribute. Should Suarez have scored the penalty, Liverpool would have won on average 2.53 out of a 1-0 home lead against the quality of opposition that Sunderland provided at that moment. Should he have missed, this turns into 1.68 expected points (EP). Hence, the value lost (or not won) by missing the penalty is 0.85 EP.

Even better would be to count the value of winning the penalty in the first place by multiplying the expected conversion rate and the potential EP won. Say the EPL conversion is 0.7, this would indicate an EP increase of 0.7 * 0.85 = 0.6 at the moment the penalty is won.

Suarez fails to convert, hence this minus 0.6 EP won should be accredited to him, and should he have scored, 0.25 EP should have been his. Furthermoe, 0.6 EP should have been accredited to the player winnning the penalty.

Which may, BTW, even be Suarez too, given Liverpool’s lack of offensive quality…

Cheers, Sander

Thanks Sander, and excellent points. It’s definitely something I’ll consider the next time I do a similar analysis. Mark from Power of Goals suggested multiplying by the conversion rate too.