@ Emperor and Dean.
They can also look into the apprentice's history. Question the tutor, their friends, and other templars who didn't go after the mage to get their impressions of the apprentice.
None of which would be an accurate indicator of the apostate in question in the context in question. Apostates on the run while being pursued by Templars are in an extremely high-stress situation- stressed people, especially when they perceive cornered or unable to flee, are frequently known to act in atypical ways that the accounts of people who knew them in less stressful contexts wouldn't know.
Backstory and prior history before an escape attempt does not constitute evidence or suspicion on a claim of death during an escape attempt.
They can also look into the background of the templars who hunted the apprentice, look at their history of how often they are sent to chase run-aways, how often the apprentice is killed or brought back alive, and how often they killed a human vs an elvhen apprentice. Do they have a history of blaming blood magic on frequent deaths, or are they raw recruits who may or may not be prone to panicking?
If they do have a history of reporting blood magic, is there reason to believe they are incorrect or unreasonable in their assumptions or conclusions? What is the 'acceptable' range of a blood magic accusations, and how do you decipher erroneuous/noise reports from valid ones after the fact? What are the persons, Templar squadmates and otherwise, who were involved with the mission? What time of day (or night) was the apostate encountered? Did the apostate have companions with them at the time? Had the apostate eaten in the last eight hours? How many kills are associated with the Templar in question- do they already have a reputation, or is the mage more comfortable with them by familiarity? At what range did the apostate notice the Templars? Is there a maleficar cabal or mage underground resistance center in the area that might affect the decision to resist?
I could go on. The context and reasons for why a mage might fight or not is far more complicated than having a hanging judge of a Templar come after them. Take it from someone who looked at these sort of statistics on a regular basis: pattern analysis has severe limitations, and can't be used as a magic ratio detector.
There's a lot more to help establish the facts beyond simply taking their word.
Sure- but none of what you've provided offers any proof that a Templar kills an apostate in cold blood. What you do offer is terribly vulnerable to being corrupted and rendered unusable by bias and personal interests. If I were a mage, I would have a vested interest in downplaying the possible guilt of any fellow mage, and if I were a Templar I would have pressures and reasons to give my fellow Templars the benefit of the doubt. This isn't just us-vs-them mentality: there's self-interest on the account of those being investigated as well.
Having worked on the analysis end of what you're trying to describe, I could propose about five different factors or ways to break your system's accuracy off the top of my head. Statistical analysis and trend-watching is a useful tool, but it is never, ever a substitute for proof.
Sure, some apprentices may turn to blood magic, summon a demon or whatever and the templars may have to put them down, but if it's discovered that the templar who hunted Aneirin (as an example) also hunted five or seven other apprentices, and every single one of them were killed for the same reason, you can establish a pattern, and also use data gathered by other templars who hunted runaways and see how often mages do turn abomination when they run.
Data patterns only become meaningful and reliable over much greater numbers of incidents in much narrower contexts. Because every mage, every templar, every region, and every chase context is different, there is no uniform standard that can be used. Especially when entirely undefinable but real factors, such as the veil or relative activity or presence, come into play.
In analysis of event patterns, context is everything. Trends that are remarkable in one context can be completely unexceptional in another. Statistical analysis is limited because it's really bad at filtering these various important contexts when used at a broad scale: it can't tell you that abominations are more common in Kirkwall because of a thin veil, that apostates are bolder and better established in Rivain because of the limited influence of the Chantry and complicit Templars, that Ferelden had a healthy working relationship between mages and templars and a relatively leniant capture policy so that even repeat offenders didn't fear being taken back.
And that's without valid but significant changes in policy and vigor of enforcement. In intel analysis, there tend to be two kinds of intel blank zones: areas where there is no intel because there is no enemy to collect on, and areas where there is no intel because the enemy is so strong they keep intel from being collected on. Old patterns can change very quickly in the later just by moving an enforcement presence in.
Consider a valid Meredith policy: she cracked down on internal corruption that allowed people to bribe their mages out of the Templars sight. Statistically, this was almost certainly going to increase the number of apostate incidents in Kirkwall. Two reasons for this: the first is that blind eyes suddenly find what they were previously ignorring, and the second is that Meredith was going to encourage and promote the sort of aggressive, driven people who ignored bribes and hunted down hiding apostates. (People, it should be noted, who would include Kerran.) Meredith's numbers were going to go up... but statistically would this be considered an increase past the norm, or returning to an appropirate level after an artificial low brought on by complacency and corruption?
Take it a bit further, and were the mage rebels in the streets a consequence of Meredith's actions, or did Meredith's actions bring out mages who were already hiding in the populace?
This is the sort of thing statistical analysis doesn't get very well- the why.
Give the templars the authority to put down a mage who is putting them, themselves, and many others at risk through blood magic or by turning into an abomination, but why not make it so much a hassle for the templars when they are sent to retrieve an apprentice that if they are forced to kill the mage, they via paperwork, questions, being taken off duty or reassigned during such times, that it doesn't become an excuse for the more fervent templars.
There's a pretty basic answer for this: because when agencies face more restrictions in doing their job than not doing it, they either stop doing the job or they start actively circumventing the restrictions.
If you think I'm joking, I'm not. It's been an off-and-on issue in Iraq and Afghanistan, trying to teach and convince security forces to be organized. Lazy police just didn't go out. Dirty Harry cops who would take the law into their own hands just wouldn't report killing people.