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- Gorgon the Wonder Cow

Hero Sacrifices

Objective Sacrifices

sacrifices are different than trades: in a trade, there is an immediate swap of similarly valued objectives

while sacrifices are the decision to give objectives because it is better than the alternative; they sow advantage which will be reaped later

A hero sacrifice is when a player puts his hero in harm's way in order to prevent the death of a more important unit or attempt to kill a more important unit,

the five heroes with the most deaths in winning games for 6.83 had above-average performance success

This graph shows us that there is a loose relationship between a hero's average deaths in winning games (X axis) and his average performance (Y axis). The line is a visualization of the trend. This graph shows us that there is a loose relationship between a hero's average deaths in winning games (X axis) and his average performance (Y axis). The line is a visualization of the trend.

As you can see, the trend explains much less when using just winrate to measure success (as expected). The grey lines are 60% and 40% winrate with the middle line representing a 50% winrate. As you can see, the trend explains much less when using just winrate to measure success (as expected). The grey lines are 60% and 40% winrate with the middle line representing a 50% winrate.

Io, Clockwerk, Lion, and Vengeful Spirit

Io wins games.

In essence, heroes with low farm and the ability to exchange positions with allies (or in Lion's case prevent enemies from chasing) have high influence over the win or loss of a game.

whether or not a hero averages more kills is not an indicator of his odds of winning or losing

As with the previous graphs, this only counts average kills for games heroes win. As with the previous graphs, this only counts average kills for games heroes win.

what do teams do in the early game instead of grouping up on towers, and why is this better than just pushing down towers for advantage?

Fig 3.1: for definitions of these measurements, see my postscript at the bottom of the page.

taking towers before you can control territory gives your opponents an advantage

Every time a team kills their opponents who have a tower advantage, they are actually given some of that tower gold back because AOE gold bounties are influenced by team net worth difference

If a team gives up fifteen kills after taking a single tier one, it means their opponents will have earned about 18% more tower gold once towers even out.

this is regardless of how many kills Team A manages to take, how well either team is farming, or what the item worth for either team is.

Comeback mechanics have not hit all forms of income equally: on average, Net Worth advantage has only dropped 4.46% in reliability

there are bad times to take a tower despite popular consensus which says otherwise

Once again, I have to give an enormous thanks to datdota.com for making this series possible.

tweet me any responses or suggestions you have @TheWonderCow.



Postscript



The "average" range indicated in these charts is a positive and negative standard deviation away from the mean. I called it "average" to make it less technical and easier to understand for less stats-minded readers. Here is the equation for the best-fit line describing the loose relationship between hero death and win impact:



win impact = 0.0024windeats2 - 0.0167windeaths + 0.0271



For my ANOVA results, the significance F is .017 for this model to fit the data to the quadratic regression. The P-Value against win square is .004 and the Adjusted R Square is .185.



Definition of terms from figure 3.1:



Deaths : The average number of deaths occuring during that five minute span for either team.

Jungle Farm : The average amount of gold taken from neutral, non-ancient creeps.

Towers Taken : The average number of towers dropped by either team up to that point in the game.

Visibility : The average amount of time players are not hidden from their opponents by fog of war.

DPM : The average damage done by heroes to heroes per minute.

Creep Stats : The average last hits on lane creeps.

Net Worth : The average value of unspent gold summed with the price of all owned items.

Item Worth : The average price of all owned items.



And here are some additional graphs I found interesting but didn't end up using directly. Notice that the difference between kills for a winning performance and for a losing performance seems to have more noise.





Edit:



To those asking for sample size, I did not include that number (but did graph the entire sample). The data included every hero with rankings (see MGF4 for a description of which heroes were qualified to be ranked in game impact) for a total of 36. The k/d information included every game up to last Friday (March 13th). This is the exact same sample size as the kills graph, which had the same criteria.



The winrate graph had a sample size of 65 heroes, which is every hero with over a 3% pickrate on 6.83. The data included every game in 6.83 up to Friday March 13th.



Fig 3.1 included every game from 6.81 and every game from 6.83 up to March 13th. If I see any other reasonable requests, I will continue to update the postscript accordingly!









The "average" range indicated in these charts is a positive and negative standard deviation away from the mean. I called it "average" to make it less technical and easier to understand for less stats-minded readers. Here is the equation for the best-fit line describing the loose relationship between hero death and win impact:For my ANOVA results, the significance F is .017 for this model to fit the data to the quadratic regression. The P-Value against win square is .004 and the Adjusted R Square is .185.Definition of terms from figure 3.1:: The average number of deaths occuring during that five minute span for either team.: The average amount of gold taken from neutral, non-ancient creeps.: The average number of towers dropped by either team up to that point in the game.: The average amount of time players are not hidden from their opponents by fog of war.: The average damage done by heroes to heroes per minute.: The average last hits on lane creeps.: The average value of unspent gold summed with the price of all owned items.: The average price of all owned items.And here are some additional graphs I found interesting but didn't end up using directly. Notice that the difference between kills for a winning performance and for a losing performance seems to have more noise.Edit:To those asking for sample size, I did not include that number (but did graph the entire sample). The data included every hero with rankings (see MGF4 for a description of which heroes were qualified to be ranked in game impact) for a total of 36. The k/d information included every game up to last Friday (March 13th). This is the exact same sample size as the kills graph, which had the same criteria.The winrate graph had a sample size of 65 heroes, which is every hero with over a 3% pickrate on 6.83. The data included every game in 6.83 up to Friday March 13th.Fig 3.1 included every game from 6.81 and every game from 6.83 up to March 13th. If I see any other reasonable requests, I will continue to update the postscript accordingly!

In Judo, there are certain maneuvers called "Sutemi Waza" (sacrifice throws) in which a judoka puts herself into a seemingly disadvantageous position (usually on the ground) in order to take the greater advantage of a successful throw. Later, I'll touch briefly on the concept of Sutemi Waza in Dota... and why the heroes who die the most also do the most.At least for this week I've had to suspend my predictions: performing rigorous data checks on every hero to have an informed opinion regarding growth potential is just taking too much time. I am very satisfied with the performances of the heroes I selected for my first three issues, though, and hope to return the segment once I redesign and streamline my methods.There are two major types of sacrifice plays in Dota:in which a hero gives a kill to the opposition in order to mitigate loss or take a more important kill.in which a team gives their opponents an objective in order to sow an advantage later.I want to emphasize that(such as kills in teamfights, towers, or barracks). If a team decides to give up an undefended tower and use their time to farm instead, they are sacrificing the tower in hopes of sowing a greater advantage eventually. It is, in essence, a delayed reward.A hero can also make a sacrifice for the opportunity to trade, such as Vengeful Spirit swapping out her opponent so that both of them can die.typically a stronger hero but sometimes this happens to defend towers, barracks, or ancients as well. It is the "I'm taking a bullet for you" moment.Hero sacrifices are hugely impactful and a willingness to perform them is often what separates professional support players from legendary ones. But any position and any hero can make a sacrifice play under the right circumstances, but some are better at them than others. How valuable are these plays?You may expect that the more a hero dies, the less successful that hero is. That's not true:(for more information about how I'm defining success, see @NoxvilleZA's win impact calculations as described in Metagame Fortnight #4 ).In fact, when we look at hero deaths in games they won, very low and very high deaths correlate with positive impact, but average deaths trend toward netural or negative impact on the game.There is also a similar trend when you look at all heroes' winrates in 6.83. This is much less reliable and has a lot more noise because winrates don't control for the sorts of factors that win impact does, specifically relative team skills.Why is this? To understand, let's look at some of the heroes who have high win impact and high deaths:(although this is not ALL of the heroes who exemplify this trend). These heroes average the highest deaths in winning games out of any other heroes played often enough to rank and all of them positively impact team performance. All of these heroes are typically played with high mobility and mass obstructionist abilities (stuns and slows). Look at this example of a carry Tiny finding himself out of place and his Io buddy sacrificing himself to save immense gold loss and preserve team advantage.His death is his team's gain. A friend of mine likes to call this, "Feed to succeed." and it's apparently a much bigger deal than people realize.Now, you may be saying that you already knew that, but what you probably didn't know is that. That's right: dying is linked more to success than killing, at least in terms of hero trends. These heroes are also able to secure kills on far more valuable, more farmed, and more crucial opponents by giving their lives in sacrifice for their team's needs.I should stress that a sacrifice play does not require a hero save--it is any hero death which leads to minimized losses or creates an opportunity for advantage later. This could include suicides, stalling tactics where a hero saves a barracks by running into a group of five alone to buy time, or a hero who dies distracting her opponents while her allies ward. It can also be a play securing a kill.The heroes who are doing the killing don't seem to be the heroes who are doing the winning: we have no direct measurements of strong support play, but supports seem to be doing the heavy lifting (once again). When Vengeful Spirit swaps out her ally only to be mowed underneath her furious opponents... that's what really wins games.In 6.81 and before, we saw "deathball" strategies focusing on very early victories which used heroes like Viper, Death Prophet, and Shadow Shaman to force opponent objectives to fall and claim a GG between 20 and 30 minutes.We don't often ask why these strategies receded, nor do we frequently ask what replaced them. Many readers think this is because the answers are obvious, and I can already hear recitations of the hive mind now: “Late-game carries replaced deathball pushes because the 6.82 rubber band machinegun made early-game victories impossible!” Sort of, but that kind of misses the point of my question.Think of it this way:The great elastic hand of Ice Frog puts them at equal risk of losing advantage regardless of how they get their gold.The first question we asked is easy to answer: they're farming, just not in lane: here are the differences in gameplay between 6.81 and 6.83:When we measure all the activities they could be doing, we see the only large changes between 6.81 and 6.83 are towers taken and jungle creeps farmed. Heroes are equivalently visible to their opponents (meaning they aren't team-fighting or waiting for gank opportunities more) and they are dying the same amount. Yet their very early GPM has gone up and their use of the jungle has skyrocketed.So they're jungling more and earning more gold than before, but how is that better than taking towers? The 6.82 area-of-effect gold bounty mechanics do not differentiate between net worth from towers or gold from creeps, hero kills, or any other sources.There are the somewhat obvious reasons:heroes who push well early game don’t typically scale great into the late game, so drafts tend to have less early push because they are instead focused on the mid and late game.When teams group up to push, they take gold advantage from towers but they usually lose experience because they are all sharing experience from one lane while their opponents have heroes spread out, taking experience from multiple sourcesTaking Tier 1’s gives your opponents extra fortifications, meaning pushing rapidly is much harder than it used to be… and more dangerous as your team is susceptible while grouped in an opposition towerBut here’s the most important point that most people just don’t really understand, even six months after the 6.82 reworks:. That’s right: knocking down an enemy tower can hurt your team in the long run.Let's consider towers as piggy banks: each team can crack them and take the money any time they want. In past patches, where teams were never punished for being rich, it benefited them to get as much as they possibly could as fast as they possibly could. These piggy banks were effective ways to take control.But there is a down side to cracking them early: your opponents can still crack theirs if you let them. That means towers give a temporary advantage. This is different to time spent farming, because the time you use is automatically used by your opponents... and they can't get it back. They might be able to farm faster than you later in the game, but towers have an exact equivalent waiting to be taken.Why is this distinction important?The above chart tells us how much of total tower advantage is given back for every death a winning team gives up. All this assumes is that the team remains ahead by at least the amount of gold they earned from towers, which is always the goal when you move in to take them. This effect can be up to three or four times as impactful for carry kills or about half as impactful for support kills. It also diminishes slightly after each kill, but as a benchmark it is pretty accurate.So, for example,Let's take a more realistic example: Team A gives up two kills after taking a single tier one, four after taking their second, and six after taking their third, then they give up four more kills immediately after taking a tier two. Then Team B starts to make a comeback and takes all the equivalent towers from behind. Team B actually earned around 40% more gold from towers because they waited patiently and chose their moment. So long as Team B doesn't take the gold lead,Sacrificing a tower in order to eventually take this gold advantage from them is actually a very effective strategy, especially for teams which are expecting to get many kills and eventually carry harder in the late-game. For teams that are not expecting to carry harder in the late game, the best course of action is to actually wait until they can domino towers down rather than taking them periodically.This is reflected in winrates: if you total the average winrate of all possible tower leads at every five minute mark, you'll find that tower leads average 10% less reliable on 6.83 than on 6.81 (for a whopping total of 943% of changes across all categories).and if you take tower gold of net worth the advantage is even less impacted. There's never a stage in the game where taking a tower lead is on average a losing move, but that's only because by definition winning teams almost have to have a tower lead. When you control for team skill and hero composition,Because items bought later in the game tend to be more expensive than those bought early, this issue is only really notable in cases where a team takes their opponents' tower, then gives deaths and loses their own equivalent tower before they have actually spent the tower gold earned. That's a worse-case scenario, and it's why ideally towers are taken in groups just before a team has enough gold for major items. Of course, most teams push just after their team has purchased major items, meaning that they will hold onto that gold for longer... giving their oppponents extra gold for every kill lost.I've been getting fewer suggestions, which hopefully means I'm doing a better job. Or maybe people have stopped caring enough to send me feedback. Either way, if you have an idea for a topic, change, stat, or any general inquiry,This article was written byGorgon the Wonder Cow, joinDOTA's Elder writer.Gorgon is an analyst and freelance caster for joinDOTA, CEVO, and anywhere needing a fast tongue with top insight. He is jD's resident "new patch" guy, and has a weekly segment on Defense of the Patience podcast.Location: Ann Arbor, MIFollow him on @TheWonderCow.