Ze question

Which stats best explain a defender’s impact on winning or losing a game, and what are their contributions?

I took all the weekly stats by player from TagPro League, which span MLTP seasons 11-17 and mLTP seasons 15-17. I guessed each player’s position each week by looking at whether their prevent per min or hold per minute was higher. I also chucked anyone who played fewer than 10m that week. Ideally, you would want the stats split up into 10m halves, in order to break it down by map, and get more accurate O vs D assignments in case someone switched between positions.

Correlations

As a first cut, here’s a plot of correlations between pm.pm (plus/minus per minute) and different stats. All stats have been standardized to be either per minute or percent of total.

(Read down the first column.)

Not surprisingly, prevent (ppha is prevent per hold against, which is highly correlated to prevent itself, so prevent will be used from here on) exhibits the highest positive correlation to pm.pm, while hold against anchors the other end.

Notice though, that a couple of offensive stats pop up too, like cap % and flaccid %.

Some models

Random forest

I built a random forest, which is a simple decision tree algorithm, to predict win/loss based on these stats. The model achieved an accuracy of just under 2/3. That means, given only a defender’s stats for a single week, I can tell you if that player won or lost, and I’d be right 2/3 of the time. Without a model, I could just flip a coin and be right half the time. Maximizing the accuracy isn’t the end goal though. What I’m after is seeing which stats contributed the most to predicting the outcome.

The feature importance chart below tells us that hold against and prevent are the 2 most important, followed, strangely enough, by cap % and hold per grab. Tags and returns are middle of the pack, and contribute roughly half as much to the final result as the top 2.

Boosted trees

I built another tree model to predict the same, this time using a gradient boosting algorithm. It managed to achieve roughly the same accuracy. But again, I was more interested in the feature importance.

The boosted tree model tells us yet again that hold against is the most important stat. Next 2 are cap % and prevent, and then tags and hold per grab. In this model, returns is further down the list, but tags is further up (the difference, non-return tags, doesn’t even show up). I’m not sure what to make of the gap given that they have a 90% correlation. One conclusion I can draw though, is that tags trump returns consistently across correlations, random forests and boosted trees.

Some charts

Let’s explore some of the top contributors further.

Returns vs Prevent

This one’s my favorite. Prevent has a higher correlation to +/- (40%) than returns (25%), and the 2 have a ~25% correlation to each other. But what does all of that look like?

I apologize to that 1 colorblind person who is reading this and only sees one giant blob… but for everyone else, the wins (in green) are heavily clustered to the right (higher prevent), while the losses (in red) are heavily clustered to the left (lower prevent). The top-bot (higher-lower returns) clustering is much less pronounced, meaning returns don’t factor into +/- as much.

Fun fact: you can mouse over any point and the hover info will give you details on that point. For example, that big green dot on the top right is Iblis for S12 W7, who put up almost 3 returns a minute, >20s of prevent per minute, and contributed to 2 caps every 3m.

(The size of the dots represent the magnitude of the +/- per minute.)

Hold against vs Prevent

Hold against and prevent have a -70% correlation. It’s kind of obvious that a higher prevent would mean a lower hold against, and vice versa. Clearly you want to be in the top (higher prevent) left (lower hold against) quadrant.

Pops and flaccids

Stats relating to dying consistently screened near the top of the importance plots and anchored the negative end of correlations to +/-.

A high flaccid rate probably means you’re playing poor O/D. A high pop rate encompasses that (pops per minute and flaccids per minute have a ~60% correlation), plus possibly a lot of unforced deaths (running into gates and spikes) and/or dying to tagpros, which is a symptom of losing the pup battle or just not knowing how to play around tagpros. Point is, dying too much is not good, and leads to losses.

You want to be in the lower (fewer pops) left (fewer flaccids) quadrant on this chart.

(Each point is jittered a random amount to make the distribution of points more legible.)

Offensive stats

Of all the offensive stats - grabbing, holding, capping - being good at a couple of them matter to defense players. We’ve established that flacciding is bad, so it makes sense that having quality holds (higher hold per grab) and lower flaccid rates (both flaccids per minute and flaccids per grab) contribute to the win condition. Additionally, if a defender has a high conversion rate, capping directly increases +/-, and could also be indicative of the other team having a weaker defense and/or O/D.

You want to be in the top (higher hold per grab) left (lower flaccids per grab) quadrant of this one.

(Each point is jitered a random amount to make the distribution of points more legible.)

What didn’t matter

  • Returns in base %
    • I’m a little surprised this didn’t matter. You would think more returns in base is better, but it could reflect a defender’s weakness in chasing properly and getting resets.
  • Pup %
    • This is probably more predictive at a team level.
  • Non-return tags
    • Alas, I am sad about this one.
    • It’s plausible that non-return tags factor in more on certain maps like Emerald. But I would need the data and map for each half to see this.
  • Grabs/hold/drops per minute
    • If a defender is doing too much of any of these, then they’re not doing their actual job.
    • Contrast these stats with flaccids per minute, flaccids per grab, and hold per grab, which do matter.

Discussion

My answer to the original question would be this - yes, returns matter, but not as much as prevent and hold against, as unsexy as those may be. Most likely, returns only matter if they lead to resets, which increase prevent. To win games as a defender also requires knowing how to convert caps and playing quality O/D.

I don’t know how the current GASP and NISH weight prevent and returns, but it’s worth going back and thinking about adjusting the weights. Based on relative correlations and random forest feature importance, maybe have prevent worth 1.5-2x returns. I don’t think hold against is even part of the formula. But this is all based on judging defenders on their +/- i.e. ability to win games, and not their raw mechanical ability, which I feel like has been the standard historically. Maybe we don’t want to change the current system at all. There’s definitely something fun and shiny to racking up stats even while losing.

Random fun stuff

Please take everything below with a huge grain of salt. I didn’t clean any names, and excluded any player with <100 minutes. Majors and minors are separated, so some players can appear once in each. It’s also a lazy guess for O vs D, and doesn’t account for position switches.