# A Few More Simulations: Losing With More Scoring Shots and Playing a Draw

The last few blogs here on the Statistical Analyses part of the website have used a model of team scoring that I fitted late last year to explore features of game scores and outcomes that we might expect to observe if that model is a reasonable approximation of reality.

In the most recent of those blogs we looked at the impact of goal-kicking accuracy on a Home team's victory chances across a variety of scenarios spanning different, realistic combinations of expected Home and Away team Scoring Shot production. For today's blog I'll be using the same scoring model as I used in that blog and applying it to the same set of Scoring Shot assumptions so, rather than repeat them again here, I'll refer you to that blog if you're curious about the details.

I prefaced the previous blog by revealing noting that eight games in 2015 have been won by the team recording fewer Scoring Shots than their victorious opponents, and that three more have been lost by teams generating the same number of Scoring Shots but converting fewer of them into Goals. That got me to wondering about how prevalent we might reasonably expect such games to be, which is another question that can be addressed via the simulation approach we've been using recently.

The chart below records the simulated likelihood of such games for different assumptions about the pre-game expected excess of Home team over Away team Scoring Shots, and groups games on the basis of their total expected score. (Note that all simulations in the current blog assume that the Home and Away teams convert Scoring Shots to Goals with a 53% probability.)

The chart reveals that:

• Games that are expected to be closer (ie where the expected Scoring Shot excess for the Home team is nearer zero) are more likely to finish with the winning team registering fewer Scoring Shots than the losing team. Roughly speaking, about 14% of games where the expected Scoring Shot excess is zero are likely to finish this way.
• The larger, in absolute terms, the expected Scoring Shot excess, the smaller the probability that the losing team registers the greater number of Scoring Shots
• The higher the expected aggregate score in a game for a given Scoring Shot excess, the larger the probability that the losing team registers the greater number of Scoring Shots

Now the 'typical' game has an expected margin, in absolute terms, of about 22 points, which is about 6 Scoring Shots at a 53% conversion rate so, reading from this chart, we might expect about 12% of games to finish with the loser registering more Scoring Shots and lamenting its inaccuracy in front of goal.

Next, let's include games where the loser registers the same number of Scoring Shots too.

This adds about 3  to 4% points the the probability for games where the expected Scoring Shot excess is near zero, and this figure tapers off to near zero as the excess gets larger in absolute terms. At the 6 Scoring Shot mark, the estimated proportion of games finishing with the loser generating as many or more Scoring Shots as the winner is about 16%, which is approximately the proportion we've seen so far in 2015 (ie 11 of 72, which is 15.3%).

We can obtain an empirical estimate from a larger sample by looking at the figures for 2014, which show that 13% of games ended in that season with the losing team registering more Scoring Shots than the winners, and 16.5% ended with the losing team registering as many or more Scoring Shots as the winning team. So, firstly, the simulations appear to align well with reality and, secondly, the phenomenon isn't as rare as we might have expected it to be.

### PROBABILITY OF A DRAW

Assessing the likelihood of a draw has been another common theme here on MatterOfStats (see, for example, this post from 2013 where we showed that the probability is likely to vary with the strength of pre-game favouritism for either of the teams but nonetheless to never exceed about 1.1% for any game, however closely contested it was expected to be).

This aspect can also be explored with the current team scoring model and for feasible sets of pre-game expected Scoring Shot scenarios. Doing this provides the following, final chart for this blog.

We find that, consistent with the earlier analysis, the probability of a draw is maximised when the teams are evenly matched and reduces as the extent of mismatch increases. We find also that the maximum probability is, as before, around 1.1%, a little higher in games expected to be low-scoring contests, and a little lower in games expected to be high-scoring. It's again sobering to realise that bookmakers generally offer, at most, \$51 for a wager on the draw, and often reduce this to as low as \$41 for games between evenly-matched teams.