I’ve been tinkering with a set of small unitwargame rules informed by operational research rather than fashions in wargaming for a couple of years. The crux of these rules is the morale mechanism.  These haven’t quite got as far as I would have liked as I’ve not really had any time to complete or playtest them. However there is enough here as a work in progress to run a session at Chestnut Lodge Wargames Group the next time I manage to make it. Also others that also design wargames might find some of this of interest.
My main sources are two books that I’ve reviewed elsewhere on this blog (although before I split out the wargaming and military history bits from Themself to form Hot Blood & Cold Steel). I’ve also got some bits from various military OR articles in the Journal of the Operational Research Society and things I’ve found using the Open University library.
These rules are intended to cover small unit actions at a platoon plus to company minus in size. The sort of thing that has happened a lot over the last decade or so for most armies.
There are some gaps in these, but it shows the structure. The primary gap is that I’ve not yet properly incorporated the effects of casualties, and there isn’t a proper OR driven basis for this (there’s loads of source material though). There is a morale driven combat model though, that determines whether attacks will be successful or not.
Attacker casualties don’t seem to be determined by the success or failure of the attack. They are more affected by whether the defenders are engaged. Defender casualties are completely different when the defence is overwhelmed (about 80% including killed, wounded and prisoners). If the attack fails and defenders are well sited then they can take no casualties.
Here are the rules, both as open document text ODT and PDF. Also another ODS spreadsheet that shows some of the workings out of probabilities and charts etc.
Prince of Orange Landing at Torbay, engraving by William Miller after J M W Turner, (Photo: Wikipedia)
In November 1688 William of Orange landed at Torbay with a combined force of Dutch and British troops. Early in 1689 the English Parliament declared for William. In Scotland and Ireland things were less clear cut, Scotland was finely balanced and Ireland was more Jacobite than Williamite. The events of 1689 determined who sat on the throne, and Britain becoming a global power.
A 1689 megagame will let players explore this and see if the outcome was a foregone conclusion or not (I don’t believe it was as easy as history makes out, and the Jacobite rebellions of the first half of the 18th Century bear out the continuing support for King James II and his descendants).
Aim
The 1689 megagame will be a political and military game about the events of 1689 that historically lead to the overthrow of King James II and his replacement with William & Mary.
The events in Scotland must be played
Events in Ireland could be played
events in England are unlikely to be played (it was much less contentious)
The 1689 megagame should cover the strategic options of both Kings, and the immediate political issues from the ruling classes of the Kingdoms. Specifically there should be a real dilemma for players on whether to switch sides (and at what point to jump, and whether to jump back). Historically changing sides was common, and some major figures did so more than once.
Underlying this there is a military game. Although all out war was avoided in England (the memory of the Civil Wars was too recent) this was not true in Scotland or Ireland (where the memory was still recent, but there were more scores to settle and force of arms was used more often). Significantly the settlement was rapid in England because William threatened to take his army home.
There are also resource constraints. Money needs to be borrowed, and paid back, to finance the campaigns. William appears to have planned better and has more immediate resources.
Potential Structure for a 1689 Megagame
Two Kings
William’s Government
William III (“William of Orange”) King of England, Scotland and Ireland, Stadtholder of the Netherlands (Photo credit: Wikipedia)
William has a Government in London and the Netherlands. It supplies him with money and troops and he needs to engage politically with both Parliaments. He is also fighting a war with France, of which this becomes a wider part.
Decisions here are about deployment of resources and diplomatic efforts to close down support for James, and ensure that he does not have to get blood on his hands directly. His orders in late 1688 specifically allow James to escape, he was worried that elements of the English aristocracy would push him into a position where a captured James would have to be executed.
Members of the government (not William himself) could potentially be subject to desertion to James, so they need to be kept onside.
Scaling at the lower end this can be a control role, in a high turnout game it could be a small player team to co-ordinate across Scotland and Ireland and do some diplomacy (via control).
James’s Government in exile
Portrait of King James II & VII (Photo credit: Wikipedia)
As with William King James II has some loyal followers with him. Initially he is in France, having fled London in December 1688. After getting help from the French he returns to Ireland to raise an army to fight against William’s troops. Throughout the period his government is in letter communications with a number of officials and sympathisers across the three kingdoms to keep them in play as his loyal subjects.
Within his cabinet there is a high level of political intrigue and this leads to it being dysfunctional. In particular the Drummond brothers are hated by many who are otherwise loyal to James. There are also other enmities, often borne of the same issues that lead to William being invited over.
Defections and desertions from and to James are common.
Scaling this could be a control role in a small game. In a larger turnout it would be useful to play some of the Cabinet roles with James as Control. In a very large game then there could be a Hitler’s Henchmen style sub game going on with this team.
This represents the Nobles, Clergy and Gentry of Scotland. It met in March 1689 and was initially neutral, however when Viscount Dundee left it then it eventually declared for William & Mary. Potentially this could have been different. Orange or Lemon deals with this area and I’d re-use it as a sub-game in a 1689 megagame.
In effect this group of players hold the Government in Scotland in their control. They have agreement of who is the King, and to some extent the office holders of the Scottish Government are drawn from their ranks. Which way the Convention jumps will have a major impact on the course of the game (if they went for King James it could lead to him landing in Scotland rather than Ireland and calling on the Scottish Army to march south (it was disbanded at Reading in December along with the English Army)).
Scaling this needs at least 7 players, of which two are staunch supporters of one of the Kings. If the ‘wrong’ King is chosen by the convention there is a role for these characters elsewhere in military opposition to the decision. The minimal player set are the leaders of the main interest groups, most of whom are undecided. In a medium sized game there are roles for up to 20 members of the Convention, the decided factions get a little larger and more undecided players are added. Each of the undecided will have agendas they want to see to gain their support, and a fear of being on the wrong side. It will take longer to make the Convention choose with more players, but it should become decisive if lobbied correctly.
Highland Clans
These are a disparate bunch, with internal conflict within them. Typically the Chiefs are well educated men (many are university graduates, or have studied). However they have a distrust of central government and obey only in so far as the King is willing to enforce things. They recognise authority in force of arms rather than de jure. An internal power struggle will be seen as a golden opportunity to settle old scores and raid for plunder in the guise of supporting the King.
There are few that can control Highland clans, their Chiefs and people they respect. An example of this is the recent Battle of Maol Ruadh (anglicised as ‘Mulroy’) in June 1688. Though government troops were involved, the fight was essentially a localised, private power struggle between clans (the MacIntosh clan settling a land dispute against the Keppoch MacDonalds). It was the result of deeply-entrenched, on-going clan tensions exacerbated by decades of political upheaval and lack of centralised authority in the Highlands. The battle of Mulroy highlights King James’ tenuous political authority and inability to maintain order in Scotland.
Scaling the major clans need to be played, ideally with at least two players per clan to allow dealing with both political and military issues (or both sides simultaneously if they aren’t active military). This would make for at least eight players (two each of the Grants, Camerons, MacDonalds and Campbells – although the last have at least one in the Convention). With a larger turnout there are 18 major Chiefs that were involved in the 1689 battles that could be played. There is also the possibility of running the clan sub-game in a similar way to the ancient celt game.
Military Forces
James II disbanded the armies, but William brought his own loyal troops from the Netherlands, including a Scots Lowland brigade. There were also some other Lowland troops raised either to fight for William, or re-mobilised by William. There are also some castle garrisons.
Conventional Forces
Conventional forces operating North of the Highland line are hard to keep supplied and operational. Also the terrain makes a lot of the training and doctrine hard to implement. The primary military leader for William was Major General Mackay, a highlander who had spent over 20 years in the service of the Netherlands. He has considerable freedom of action in how he deals with Jacobite forces in Scotland. His primary constraints are money and logistics.
Scaling the conventional forces need 2-3 players as a minimum. They have a standard command structure which means that the subordinate players have less freedom of action. If the game was larger there could be scope to add some liaison officers and logistics officers, but this is unlikely to take the need to more than 5 players. The key determining factor is the number of independent forces that could be created and the level of diplomacy done by military players. In the latter case I would expect this to be done by players from the Convention once it had reached a consensus on the King it was supporting.
Castle Garrisons
There are three significant castles, Edinburgh, Stirling and Dumbarton.
Edinburgh is a player role and casts an important shadow over the convention. The other two could be run by control if necessary. They guard important routes to and from the Highlands and are nominally controlled by the King. Other castles exist but these are private strongholds.
Time Period
The entire revolution took just under two years, but mostly the decisive phase is between March 1689 and August 1689. Ireland takes another year to mop up, there are also some loose ends in Scotland to deal with after the clans return home after the defeat at Dunkeld.
Potentially the Convention decision cycle could be extended from when it actually happened to allow it to go in parallel with the raising of the clans. That would allow the events to take place over 8-10 turns of about 40 minutes each (longer first turn and variable end). This would give a notional turn period of about two weeks.
Thoughts or comments?
Would you play in a 1689 megagame if it was worked up?
is there anything else you think could be included or left out?
would you want to work with me to make it happen?
leave a comment and let me know what you think. If there is enough interest I’ll approach Megagame Makers and see if it can go on the programme.
This is the third post on my Operational Research driven wargame rules (and it’s probably about time that I came up with a catchy name for them, ideas in the comments section most welcome).
One of the most unrealistic things I find in most commercial wargames that I have read or played is that it is very easy for players to change their plans and give new orders to their troops every turn. This is so common that there’s even a name for it, the 200ft General.
What is the Problem?
The concept being that the player is like a General with perfect perception and control of his troops, and he can react to things that they aren’t yet aware of because the player can see the models on the table.
Here are a couple of relevant quotes from the Operational Research that demonstrate why this is a problem.
“a detailed, well-rehearsed plan blocks acceptance of the quick orders rattled out over the radio ten minutes before an attack starts. This mix of friction and mental block can be seen to play a part in nearly half of all mission failures.” Murray in Brains & Bullets
“complicated plans were much more likely to fail.” Murray in Brains & Bullets
So this gives a constraint to the game design. A successful OR driven wargame will ensure that it isn’t easy to change orders and that the more complicated a plan is the more likely it will be to fail.
Potential Solutions
This isn’t a new problem, many wargame designers have grappled with it over the decades that wargaming has been popular. Lots of games have mechanisms of one sort or another to counteract this, ranging from hidden movement and deployment through to complex activation systems. All of these have problems, but at least they’re trying to solve the core problem of limiting player decisions to those that are reasonable for a commander on the ground.
Hidden movement & Deployment. This is a very good solution, and one that lots of games try to implement. It has difficulties in that you either need to trust the other player or have an umpire. Failing that some pre-game organisation to produce maps that can be annotated helps. It tends not to be used for competition wargames.
Written Orders. This is what real armies do, and so far as I’m aware only one commercial game has attempted this (Spearhead). It slows down the game, or increases setup time. Possibly producing a pro-forma might speed things up.
Unit activations. This seems to be common in popular rules. The actual mechanisms vary considerably, but the gist of it is that as a player you cannot be sure whether or not particular units will be activated. About all you can be sure of is that you cannot move your entire army. A good example of this is the DBA PIP system. A general gets 1d6 unit activations each turn.
I think that a good solution would be streamlined and easy to implement by players. Something like this is likely to have a major impact on gameplay speed, and we’re looking for ‘fast’ as a default setting. Each game turn needs to take 5-10 minutes to run through so that a whole game (including setup) can happen in about 2 hours.
Do you have any other potential solutions to this problem?
Further to the previous post Faith in Morale I’ve tried to synthesize the varioius readings on military psychology into a set of morale rules that might give a realistic ebb and flow to an engagement. I’ve not had a chance to test these yet, but here’s what the chart looks like.
v01 of the 2D Morale Chart, (c) 2014 James Kemp
Reading through the various OR type publications it seems to me that morale is affected by proximity to both friends and the enemy. The closer solders get to the enemy the more they seem to do things other than follow orders. This is not really a surprise, but it’s nice to see the research back up the gut feel.
Where I can find hard numbers for things I have used them to construct the 2D morale chart. In some ways this is sort of arbitrary, the numbers aren’t comprehensive enough to complete it. I’ve taken distance from the enemy as one axis and propensity to fight as the other axis. Probability isn’t as straightforwards as counting the squares, as I’ve chosen to use a 2d6 roll on this chart. This tends the answer towards 7 and I have used the probabilty of a given result (or greater) as the method for putting the shading on the boxes. Where certain conditions make something more or less likely the difference from the probability of 7 or more is what I’ve used to decide whether the die modifier would be +/- 1, 2 or 3 (most end up as +/-1).
I’ll post up more of this, along with some ideas on how I expect it to work, in a later post. Broadly though each glob of troops will have a marker on the chart showing their current morale state. Each time morale is tested they will roll 2d6 and modify. Scores of 6-8 (about 45%) will remain unchanged. scores of 9-11 will improve morale and 12 will improve it and move the unit closer to the enemy (except for defenders in prepared positions). Scores of 4 or 5 will decrease morale, a 2 or 3 will decrease morale and cause the soldiers to give ground back to cover.
I’ve been reading operational research on the psychology of combat recently. It got me to thinking about the role of religious faith in morale of soldiers. I’m not personally religious and don’t have an axe to grind on this. What I am trying to do is build a game design model that properly accounts for relevant factors.
The thought that struck me was that combat is very stressful and that soldiers are called on to do unpleasant things to others. This isn’t an every day thing but it does happen. The after effects can be very severe, PTSD isn’t pleasant for anyone and can last for years after the traumatic events have finished. Psychological casualties are as real as the physical ones, they just have a delayed onset and are harder to spot.
Faith in Morale
Looking at rational human reactions in combat and life threatening situations you can see that the belief system of the individual plays a strong part. If you read first hand accounts enough you begin to understand this. Heroes often do what they do because they don’t see other options that they find acceptable. People run into burning buildings or stay at a point of danger to help others. A selfish rational view would get you out of there. This often comes down to helping other members of the in group, not letting others down or not being able to live with themselves if they hadn’t tried to help. It is rare to hear patriotism cited, although often modestly you’ll hear ‘I was just doing my job’. That last is rarely true from a technical perspective but it reveals that the person that said it was driven by their belief system.
You’ll have noticed that I’ve been writing about a belief system here rather than faith. That’s deliberate. Faith is a kind of belief system but isn’t all of it. Everyone has a belief system, even atheists. Not everyone has faith.
They are a product of our upbringing and life experiences. Religious faith has a major part in shaping them, as does the dominant culture in the society that we live in. Even those that consciously reject those are shaped by it in their rejection.
Some examples. Homophobia is driven by belief systems. The dominant culture in the UK has taught us that it is a bad thing. Some religious groups disagree, and there is a high level of support far that point of view from the older members of society and those that have arrived from other cultures that don’t share the same belief as our dominant culture. In the main the driver for homophobia is the classic out group of psychology. Humans form groups of similar outlooks and turn against other groups. It’s animal instinct and manifests in many places and in many ways. Civilised humans learn to control the behaviour it drives and accept that other people (mostly) aren’t a threat. Being indoctrinated from birth into thinking about things makes this much easier.
Back to combat. The fundamental beliefs that go on here are about harming others and self preservation. Religion tends to have a view on both of these. Typically it is don’t harm others and you need to make earthly sacrifices for a heavenly reward.
The combat calculus every combatant goes through is pretty much ‘does the risk to me outweigh the benefits of what I’m doing?’
If you are an atheist with no belief in an afterlife then you aren’t going to be as keen on checking out as someone expecting a massive reward for furthering the cause of their chosen religion (and it is the individual combatant’s interpretation that counts here, not the orthodox view).
Avoids taking risks where possible, but is ready to kill to do the job at hand. Unlikely to operate outside the rules of engagement lest there is an earthly punishment.
Kills only when there iis no alternative. Will stay well within the rules of engagement as it is what their belief system demands. Won’t take unnecessary risks but will do what they can to help others.
Orthodox Christian/Muslim
Killing is wrong, but God accepts that sometimes it is necessary.
I don’t want to die yet, but there will a reward in the afterlife if I do good work.
As with the Humanist avoids harm to others, but if it him or me will kill the enemy. Will self-sacrifice to save/help others but tries where possible to preserve their ability to continue to act.
If I do God’s work I will be rewarded in the after life.
Disregards personal safety to achieve the mission objective (which implictly includes doing what God demands and converting or killing the unbelievers.
Let me know what you think in the comments thread.
Brains and Bullets is an excellent and very readable book which tries to put some hard numbers on a variety of psychological tactics that can be used to persuade your own troops to fight and the enemy to give up.
This is an excellent work on what happens in combat and why. It is very readable, structured into bite sized chunks on the key phenomena and then some joining up when it has all been explained. Each chapter opens with an account from a real soldier who experienced that psychological effect in combat. This is then analysed and explained, pulling in other examples as required to show that it isn’t an isolated incident but a general effect. Those examples range from the Napoleonic Wars right up to operations in Afghanistan, and they’re the products of proper scientific research not just a collection of war stories from unreliable sources.
That said there is no need to be an operational researcher, or scientist to understand the book. The language used is straightforward and direct, each of the concepts is very well explained and it forms an excellent introductory work as well as being well researched. The target audience is ordinary people without a technical or military background (although the author hopes that many military officers and civil servants will read it and think about it). Here’s my favourite line from the end of the book “if you are paid to be a military analyst, don’t forget that you work for the Crown (or the people) and for soldiers. You owe no allegiance to your cost centre manager. Crack on.”
If you do have a serious interest then it is worth saying that this isn’t fluffy pop psychology (I like those as light reading, having read Psychology at uni). All the conclusions are backed up with hard numbers from years of solid operational research. The author is hoping to influence army officers to use tactical psychology to make them more effective, so for example “even the hardest-fought flank attack seized ground with a smaller force, captured more of the enemy and caused fewer fatalities on both sides. flanking attack was six times more effective than a frontal attack.”
I’m not going to summarise this book like I did for the Stress of Battle, it’s way more available and affordable. Go buy it yourself (or borrow from the Library) and enjoy it. I certainly did.
At Chestnut Lodge Wargames Group we design and play a lot of games involving game money. We do this to the extent that we often joke that all you need for a game are CLWG members and some (play) money. Â By definition none of this is real, but in game terms it is always genuine. There is never any question that some of it could be fake. For more modern games involving high value government expenditures this is definitely fine, but in some of the games we play it would make for an interesting dynamic if it turned out we couldn’t rely on the value of the coins.
Game money (Photo credit: James Kemp)
So while my daughter was playing with my stack of play money (see the photo above) I was thinking that I could run a game, probably in a fantasy setting, where the different players had briefings about what they saw as acceptable money. Â I thought it would need to be a trading game, perhaps with merchants from different parts of the world with their own coinage, and supplying things to either each other or to city/principality governments. I could brief them about the relative values they had for each of the types of coins, and I could also suggest to some of them that damaged coins, or those where the paint had come off, weren’t worth as much (or were even totally worthless). This would add an interesting dynamic to the game, especially if the briefing wasn’t too widespread. An additional possibility would be to deliberately add in counterfeit currency and have someone try and pass as much of it as they could into circulation.
Three turns per year, March – June (Spring), July to September (Summer) and October to February (Winter).
Actions
Small offensives can be prepared and launched within one turn. Large offensives take a turn of preparation and then take a whole turn of offensive action. Small offensives can be carried on into large offensives.
Battles are fought in phases.
Preparation: divisions are allocated to the line, first wave, second wave, exploitation, training and reserve tasks
All divisions of a particular kind are the same except for level of experience and training. This can be open to the player as it was generally well known which units were the most effective and had the most offensive spirit.
Special training can be given to units to allow them to be competent at tasks, e.g. building fortifications, pioneer tasks, tank support, amphibious landings etc. The number of turns that they get in this task should be recorded separately from that of infantry training.
Infantry divisions take one turn to raise, cavalry and artillery take two turns. Ideally more training should be given before a unit is used in combat. A minimum of three turns of training is suggested before committing a new Division to the assault.
Experienced 6 time in major offensive (including defending)
Veteran 8 Several major offensives
Both the number of turns training and the combat experience are required for the troops to be considered at the higher training state. Note that the training state is just a label and not a guarantee of performance.
Taxation – can set a proportion of GDP to be spent on government. Level has effect on popularity, standard of living, economic growth, industrial output.
Loans – need to be repaid later but avoids some of the problems with increasing taxation. Can also inject foreign capital into paying for the war which increases overall resources available to any particular nation.
Manpower
Can conscript or get volunteers. Quality issues with conscription but increased numbers may offset that. Volunteers make more aggressive units, conscripts more passive ones. Has impact on economic growth, popularity & industrial output. Also issue of women’s rights if they are mobilised for the war effort.
This is the fifth and final part of my extended review of The Stress of Battle by David Rowland. It is such a strong piece of operational research on WW2 heroism that I thought that it would be useful for wargame designers (and players) to understand what the research evidence is for what went on in WW2 battles. This part is on the effects of heroism and combat degradation.
Combat degradation is a measure of how less effective weapon systems and individual soldiers are in actual combat when compared to training exercises and range work. A score of 1.0 is equivalent to not being degraded at all. Degradation to 0.3 would mean that it was operating at 30% of its peacetime range effectiveness.
the analysis by Rowland’s team broadly matches that done by Wigram in 1943, that there are three classes of effectiveness.
About 20% of those involved could be classed as heroes (26% for guns, 9% for tanks).
Of the rest, one third were ineffective (either they didn’t engage, or what they did do didn’t have any significant impact) (27% of the total);
The remaining two-thirds were about 30% effective (53% of the total);
Weapon systems crewed with at least one hero were about five times more effective than those with no heroes;
Overall effectiveness of a unit = 0.2+([Heroes/gun]*0.8)
Leadership improves combat effectiveness (i.e. more officers/SNCOs present leads to greater effectiveness, which is the reason that tanks are less effective than gun crews).
Rowland and his team compared the effectiveness of the most effective and the partly effective groups in both the historical battles for which there was information and also for the field trials conducted by the British Army in the 1970s & 1980s. What they found was that there was the same variability within the two groups, which was attributed to opportunities to engage. However there was a significant difference between the groups, which was attributed to heroes being more effective.
Heroism seems to be a product of genetics, social conditioning and values. Many recipients of gallantry awards had previously been mentioned in despatches, or were decorated again.
Comments on citations for subsequent decorations indicate that a second award always required a stronger case than the first award did.
Heroes maintain their combat effectiveness in future battles, even if not further awarded.
Heroism is more likely at higher ranks (i.e. officers and senior NCOs (Sergeants and above) are more likely to be in the higher performing groups than other ranks).
NB there is a possibility that the awarding of decorations was unfairly skewed by rank, and that those of lower rank that performed heroically weren’t adequately recognised.
Gurkhas
Gurkha units were noticably different from British unit, and appear to be 60% more effective in inflicting casualties on the enemy and 60% more likely to be decorated. This comes at the price of higher levels of casualties.
The defintion of Surprise is “the achievement of the unexpected in timing, place or direction such that the enemy cannot react properly”. This is distinct from Shock, where soldiers could react, but didn’t.
Again historical analysis was used and battles where surprise and shock were involved were identified. These were then compared with other battles with similar characteristics so that only either Shock or Surprise were different. The two factors being compared individually with a reference set.
Surprise
Attack surprise reduces infantry defence effectiveness by 60% at 3:1 attack ratio.
Attack surprise may vary with force ratio (being more marked at low ratios and less effective at higher ratios)
Surprise for tank vs tank reduces casualties  by a factor of 3 at 1:1 attack ratio for the side achieving surprise.
Attacks below 1:1 ratio were successful 65% of the time when surprise was achieved, where attacks at these ratios were never successful without surprise
At force ratios above 1:1 surprise is less important to success, although there is still higher levels of success with surprise, just not statistically significant.
with surprise force ratio is less important to success (at 1:1 70%, at 3:1 76%)
without surprise the probability of success increases in proportion to the force ratio (at 1:1 40%, at 3:1 54%)
Shock
Infantry attacks caused shock in about 15% of cases, rising to 50% when combined with surprise and some of the factors below. Three factors were found to have influenced the ability of infantry to inflict shock:
Charge distance was usually under 100 metres (limited by weight of kit), where it was longer that was found to be because the enemy had already broken.
Visibility was significant, typically shock occurs at night or in poor visibilityincluding where the terrain offers concealment
Defence morale was affected by Battle cries, cheers and yells seemed to put defenders off balance.
Bayonets played a major role (but not to cause casualties, as a psychological weapon inducing the enemy to surrender or run away).
Tank attacks caused shock in about 10% of battles analysed.
‘Invulnerable’ tanks cause shock which can lead to panic, in about 50% of cases
Surprise alone caused shock in 27% of the time
Surprise + invulnerable tanks gave 70% Shock
Surprise + poor visibility gave 85% shock
Surprise + all of the above gave 95% shock
Air attacks cause shock most often when they are a dive/strafe attack where the aircraft is aimed directly at the target.
Typically shock by ground attack reduces defence effectiveness by 65%.
IWM caption : El Alamein 1942: British tanks move up to the battle to engage the German armour after the infantry had cleared gaps in the enemy minefield. (Photo credit: Wikipedia)
Unlike small arms, the effectiveness of weapons used for anti-tank combat has changed considerably over the course of the mid-20th century. From non-specialist gunfire in WW1, to high velocity armour piercing in WW2 and then to Anti-Tank Guided Weapons in the Cold War period. This makes the operational research on anti-tank combat harder to do because the start point needs to be battles where only one kind of AT weapon is in action. Much of the analysis on anti-tank combat starts with the ‘Snipe’ action during the second battle of El Alamein in North Africa where data on each of the guns individually was available.
‘heroic performance’ plays a large factor in the effectiveness of anti-tank guns
about a quarter of guns (at most) performed heroically (including those where platoon, company or battalion level officers assisted with firing guns)
 rate of fire is proportionate to target availability (i.e. when there are multiple targets crews fire faster)
the median point for heroes was 0.3 tank casualties per gun, where for non-heroes it was 0.03 tank casualties per gun
tanks are less effective in defence than AT guns alone, or tanks supported by AT Guns
AT Guns with tanks apparently kill three times more tanks than the tanks would on their own
AT Gun performance is attributed to having a higher concentration of SNCOs and Officers with deployed ATG compared to tanks (about three times as many)
heroes were disproportionately represented by SNCOs and Officers (at least in terms of who got the medals), in 75% of cases an SNCO or Officer senior to the gun crew commander was involved
Paddy Griffith is quoted on tank casualties that “relatively few appeared to have been caused by enemy tanksâ€
Overall it shows that the biggest single effect in anti-tank combat was down to leadership. Where gun crews are well lead then they are significantly more effective in battle. This is assuming that the guns in question can have some effect on the tanks that they are shooting at, which was the case in all of the battles examined (including a mix where the guns defended successfully with those where the gun lines were overrun by tanks).
 by David Rowland, which is an essential piece of 
