Nufflenomics: What is the value of a good coach?

Unfortunately, this isn’t a dissection of getting a good mentor to help you train for Blood Bowl in a Rocky-esque montage, but instead an analysis of the value of hiring a coach for your team.

Like Einstein’s best theory, it is all relative. It really depends on the number of coaches you have compared to your opponent. If they have 2 and you have 2, then the net effect is the same as if you both hadn’t bothered to bring along any coaching staff.

Let’s first consider when coaches come into play during the game. The only time that they directly affect the on-field game is when Brilliant Coaching is rolled on the kick-off table. This is a result of 7 which has a 17% probability of occurring, just below 1 in 5. When this happens, both coaches roll a D6 and add the number of coaches. If one coach scores higher than the other, they gain a re-roll for the drive. If both coaches score the same, then there is no effect.

Below is a table which shows, based on how many coaches you have more than your opponent, the likelihood of you winning the Brilliant Coaching roll on the kick-off table.

No of coaches more	You win re-roll	No-one wins re-roll	Your opponent wins re-roll
0	42%	17%	42%
1	58%	14%	28%
2	72%	11%	17%
3	83%	8%	8%
4	92%	6%	3%
5	97%	3%	0%
6	100%	0%	0%

 

There are two things you want to happen when the Brilliant Coaching result is rolled. In terms of priority these are:
1. You want to deny your opponent a re-roll.
2. You want to gain a re-roll.

On a 17% chance of the result being rolled on the kick-off table, 1 additional coach over your opponent will give you a 58% change of winning a re-roll. Whilst that looks good, we should be comparing the incremental gain of each coach to you, and the incremental loss to your opponent. Looking at the table below, we can see that there are decreasing gains from each additional coach.

No of coaches more	You win re-roll	Incremental gain	Your opponent wins re-roll	Incremental loss
0	42%	-	42%	-
1	58%	17%	28%	14%
2	72%	14%	17%	11%
3	83%	11%	8%	8%
4	92%	8%	3%	6%
5	97%	6%	0%	3%
6	100%	3%	0%	0%

 

If we look at just one coach, the incremental gain is 17%. How can we value this accurately? We can multiply this 17% by the 17% chance of rolling Brilliant Coaching (which comes to 3%), and then multiply it by the value of your re-roll. The below shows the value of the coach at each re-roll price point. We should also factor in the gain of denying your opponent a re-roll at each price point.

 

Re-roll cost	Value of a re-roll gain	Value of re-roll denial
50k	1.4k	1.2k
60k	1.7k	1.4k
70k	2.0k	1.7k

 

This is just for the first coach you have above your opponent. The values are even less for additional coaches. In the biggest scenario (i.e. if both of you have 70k re-rolls), then one additional coach is worth 3.7k per kick-off. Assuming 4 kick offs per game, then the value of a coach can be measured at 14.8k in the scenario that both coaches have 70k re-rolls.  However, we have to remember that if this re-roll isn’t used by the end of the drive, then it is lost. This is difficult to factor into the calculations, so we will just assume for the moment that it is used.

This table shows the total win from the first additional coach with re-rolls at various price points.

		Your opponent’s re-roll cost
		50	60	70
Your re-roll  cost	50	2.6	2.9	3.1
	60	2.9	3.2	3.4
	70	3.2	3.5	3.7

 

The value of the coach at each kick off then varies between 2.6 and 3.7k – across 4 kick-offs that is then a range of 10.4-14.8k.

In a league setting where you buy a coach for 10k, you are getting slightly more value out of it than you are spending. That is of course, if your opponent doesn’t also hire a coach. If they do, then it becomes an arms race. If you are buying three coaches at a total of 30k to get an advantage of one coach, then you are probably not spending your cash effectively.

You also need to consider whether hiring the additional coach(es) will give your opponent a team value (TV) advantage such that they will be able to hire a better inducement than they may otherwise have been able to.

If you have 20k available as an inducement, then the return on this can be calculated by looking at the team’s relative re-roll costs. You will also need to factor in whether your opponent has any rostered coaches already. There isn’t much else you can buy for the cash other than a cheerleader – and I will look into the efficiency of them another time, suffice to say now that as Brilliant Coaching is much more likely to come up on the kick off then it is probably a better investment.

One other thing to think about is if you are playing a team that is likely to foul. As described in the Argue the Call section, if you get sent off as a coach for arguing the call, then you need to apply a -1 modifier every time Brilliant Coaching is rolled. In this instance, you may want a rostered coach to prevent your opponent getting an advantage in this situation.